Elon

Go through the enVision Math Common Core Grade 3 Answer Key Topic 14 Solve Time, Capacity, and Mass Problems regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 14 Solve Time, Capacity, and Mass Problems

Essential Question:
How can time, capacity, and mass be measured and found?

Answer:
The time is measured in hours.
the capacity is measured in liters.
the mass is measured in grams.

Explanation:
In the above-given question,
given that,
1 hour = 60 min.
1000 ml = 1 liter.
1000 g = 1 kg.
The time is measured in hours.
the capacity is measured in liters.
the mass is measured in grams.

enVision STEM Project: Forces and Interactions
Do Research Use the Internet or other sources to find information about magnets. How are magnets used? What types of magnets are there? Attach different amounts of paper together using a metal paper clip. How can you lift the paper using the magnet? How much mass can the magnet lift?

Answer:
There are three types of magnets are there.

Explanation:
In the above-given question,
given that,
there are three types of magnets are there.
they are permanent magnets, temporary magnets, and electromagnets.
Magnet is defined as a material that can produce its own magnetic field.
permanent magnets are magnets that are used permanently.
temporary magnets are used as per the situation.
electro magnets are used due to the support of an electric field.

Journal: Write a Report Include what you found. Also in your report:

• Give examples of magnetic and non-magnetic materials.
• Find the masses of the paper clip and of the paper.
• Write an equation to show how much mass you can lift using the magnet.

Review What You Know

Vocabulary

• denominator
• numerator
• number line
• unit fraction

Choose the best term from the box. Write it on the blank.
Question 1.
The _________ tells the number of repetitions of the unit fraction.

Answer:
The numerator tells the number of repetitions of the unit fraction.

Explanation:
In the above-given question,
given that,
the numerator tells the number of repetitions of the unit fraction.
for example:
the numerator is 1.
the denominator tells how many equal parts are there.
examples of the unit fractions are 1/2, 1/3, 1/4, and 1/8.
so the numerator tells the number of repetitions of the unit fraction.

Question 2.
The ________ tells what fractional part is being counted.

Answer:
The denominator tells what fractional part is being counted.

Explanation:
In the above-given question,
given that,
the denominator tells what fractional part is being counted.
for example:
2/8 = 1/4.
so the denominator tells what fractional part is being counted.

Question 3.
One equal part of a whole can be represented using a _________

Answer:
One equal part of a whole can be represented using a number line.

Explanation:
In the above-given question,
given that,
one equal part of a whole can be represented using a number line.
for example:
if the number line is divided into 4 parts.
the fractions can be written as 1/4, 2/4, 3/4, and 4/4.
one equal part of a whole can be represented using a number line.

Solving 2-Step Problems
Question 4.
Mr. Vernon rides a train for 188 miles. Then he rides a subway for 9 stops. Each stop is 2 miles apart. How far does he travel?

Answer:
The number of miles Mr. Vernon rides = 206 miles.

Explanation:
In the above-given question,
given that,
Mr. Vernon rides a train for 188 miles.
then he rides a subway for 9 stops.
each stop is 2 miles apart.
9 x 2 = 18.
188 + 18 = 206.
so the number of miles Mr.Vernon rides = 206 miles.

Question 5.
Ms. Slate has a box of 320 new light bulbs. She replaces the light bulbs in 50 lamps. Each lamp has 5 sockets. How many new light bulbs does Ms. Slate have left?

Answer:
The number of light bulbs does Ms. Slate has left = 70 bulbs.

Explanation:
In the above-given question,
given that,
Ms. Slate has a box of 320 new light bulbs.
She replaces the light bulbs in 50 lams.
each lamp has 5 sockets.
50 x 5 = 250.
320 – 250 = 70.
so the number of light bubls does Ms. Slate has left = 70 bulbs.

Number Lines

Label the missing numbers on the number lines.
Question 6.

Answer:
The missing numbers on the number line are 2/6, 4/6, 5/6, 6/6, 7/6, and 1.

Explanation:
In the above-given question,
given that,
label the missing numbers on the number lines.
the number line is divided into 6 parts.
the missing numbers are 2/6, 4/6, 5/6, 6/6, 7/6, and 1.
so the missing number is 2/6, 4/6, 5/6, 7/6, and 1.

Question 7.

Answer:
The missing numbers are 50, 100, 150, 200, 350, and 400.

Explanation:
In the above-given question,
given that,
label the missing numbers on the number line.
the distance between each point is 50.
so the starting point is 50.
50 + 50 = 100, 100 + 50 = 150, 150 + 50 = 200, 200 + 50 = 250, 250 + 50 = 300.
so the missing numbers are 50, 100, 150, 200, 350, and 400.

Fractions

Question 8.
Rena divides a square into 8 equal parts. What unit fraction should she write as a label for each of the parts?
A. \(\frac{0}{8}\)
B. \(\frac{1}{8}\)
C. \(\frac{8}{8}\)
D. \(\frac{8}{1}\)

Answer:
Option B is the correct answer.

Explanation:
In the above-given question,
given that,
Rena divides a square into 8 equal parts.
1/8 is the correct fraction.
so option B is the correct answer.

Question 9.
Write two fractions that are equal to 1.

Answer:
The two fractions are 5/5 and 1/1.

Explanation:
In the above-given question,
given that,
the two fractions that are equal to 1 are,
5/5 = 1.
1/1 = 1.
so the two fractions are 5/5 and 1/1.

Pick a Project

PROJECT 14A
How do you show elapsed time on a clock?
Project: Write and Tell a Story About Time

Answer:
The time is 11:55.

Explanation:
In the above-given question,
given that,
the minute hand is on the 11.
the hour hand is on the 12.
so the time is 11:55.
5 x 11 = 55.
so the time is 11:55.

PROJECT 14B
What is the best way to plan for a full day?
Project: Create and Play a Matching Game

Answer:
The numbers 12 and 29 comes on Saturday and Tuesday.

Explanation:
In the above-given question,
given that,
the numbers on the calendar are:
1, 2, 3, 4, 5, 6, …..and 31.
the numbers are 12 and 29 comes on Saturday and Tuesday.

PROJECT 14C
How did people tell time before clocks?
Project: Design and Make a Sundial

PROJECT 14D
What is your favorite recipe?
Project: Perform a Song About the Masses of Objects

Lesson 14.1 Time to the Minute

Solve & Share
Xander and his mother are visiting a store. In the store, there are many clocks on the shelves. The clocks show different times. Tell the times shown on each of the clocks below.
I can … show and tell time to the minute using clocks.

Answer:
The times are 1’o clock, 5’30, and 5:55.

Explanation:
In the above-given question,
given that,
in the 1st watch, the minute hand is on the 12 and the hour hand on the 1.
so the time is 1:00.
in the 2nd watch, the minute hand is on the 6 and the hour hand on the 5.
so the time is 5:30.
in the 3rd watch, the minute hand is on the 11 and the hour hand on the 6.
so the time is 5:55.

Look Back! Xander and his mother leave the store at 8:47. How can you use the clock to show this time?

Answer:
The minute hand is on the 9 and the hour hand is on the 8.

Explanation:
In the above-given question,
given that,
Xander and his mother leave the store at 8:47.
the minute hand is on the 9.
the hour hand is on the 8.
so the time is 8:47.

Essential Question
How Do You Tell Time to on the Nearest Minute?

Visual Learning Bridge
The clock shows the time a train from Memphis is scheduled to arrive at Central Station. What time is the train scheduled to arrive? Write the time in digital form and in two other ways.

Convince Me! Model with Math A train arrives from Atlanta one hour after the Memphis train. Write the arrival time of the Atlanta train in digital form and two other ways. Use a clock face to help.

Guided Practice

Do You Understand?
Question 1.
In the Memphis train example, why is 42 minutes after 12 o’clock the same as 18 minutes before 1 o’clock? Explain.

Answer:
The 42 minutes after 12 o’clock is the same as 18 minutes before 1 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 8 after two small points.
5 x 8 = 40.
40 + 2 = 42.
the hour hand is in between 12 and 1.
the time is 12:42.
so the 42 minutes after 12 o’clock is the same as 18 minutes before 1 o’clock.

Question 2.
An airplane landed at 3:55. Does the clock show the time the airplane landed? Explain.

Answer:
Yes, the time is correct.

Explanation:
In the above-given question,
given that,
the minute hand is on the 11.
the hour hand is on the 3.
5 x 11 = 55.
so the time is 3:55.
the time is correct.

Do You Know How?
In 3 and 4, write the time shown on each clock in two ways.
Question 3.

Answer:
The time is 3:12 and 12 minutes after 3 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 2.
the hour hand is on the 3.
the time is 12 minutes after 3 o’clock.
5 x 2 = 10.
10 + 2 = 12.
so the time is 3:12.

Question 4.

Answer:
The time is 5:43 and 43 minutes after 5 o’clock .

Explanation:
In the above-given question,
given that,
the minute hand is on the 5.
the hour hand is on the 8.
5 x 8 = 40.
40 + 3 = 43.
so the time is 5:43.
the time is 43 minutes after 5 o’clock.

Independent Practice

In 5-7, write the time shown on each clock in two ways.
Question 5.

Answer:
The time is 11:20 and 20 minutes after 11 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 4.
the hour hand is on the 11.
the time is 20 minutes after 11 o’clock.
5 x 4 = 20.
so the time is 11:20.

Question 6.

Answer:
The time is 7:39 and 21 minutes before 8 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 7.
the hour hand is on the 7.
the time is 21 minutes before 8 o’clock.
5 x 7 = 35.
35 + 2 = 37.
so the time is 7:39.

Question 7.

Answer:
The time is 8:44.

Explanation:
In the above-given question,
given that,
the minute hand is on the 2.
the hour hand is on the 3.
5 x 2 = 10.
10 + 2 = 12.
so the time is 3:12.

Problem Solving

In 8 and 9, use the table.

Question 8.
Roy says that the scarf and the hat together cost about the same amount as a blanket and a hat. Is this a reasonable estimate? Explain.

Answer:
No, it is not reasonable.

Explanation:
In the above-given question,
given that,
Roy says that the scarf and the hat together cost about the same amount as a blanket and a hat.
the scarf cost $18.
the hat cost $12.
blanket cost $19.
18 + 12 = 30.
19 + 12 = 31.
so both are not same.

Question 9.
What did Jorge buy at the sale if $19 + $19+ $19+ $18 stands for the total cost of his purchase?

Answer:
The total cost is $75.

Explanation:
In the above-given question,
given that,
Jorge buy at the sale $19 + $19 + $19 + $18.
19 + 19 = 38.
19 + 18 = 37.
37 + 38 = 75.
so the total cost is $75.

Question 10.
Be Precise Mia left her house at 25 minutes before 3 o’clock. Draw hands on the clock to show when she left.

Answer:
The time is 2:35.

Explanation:
In the above-given question,
given that,
Mia left her house 25 minutes before 3 o’clock.
the minute hand is on the 7.
the hour hand is on the 2.
5 x 7 = 35.
so the time is 2:35.

Question 11.
Higher Order Thinking Sandra’s party started at 7:00. Her friends Theo and Lily arrive at 10 minutes after 7 o’clock. Her friend Marcus arrives 35 minutes after Theo and Lily. What time did Marcus arrive? Write this time in two other ways.

Answer:
The time did Marcus arrive = 7:45.

Explanation:
In the above-given question,
given that,
Sandra’s party started at 7:00.
Theo and Lily arrive 10 minutes after 7 o’clock.
Her friend Marcus arrives 35 minutes after Theo and Lily.
7:10 + 35 = 7:45.
so the time Marcus arrive = 7:45.

Assessment Practice

Question 12.
Clay and his family sit down to eat dinner at the time shown on the clock. Which of the following are other ways to write that time? Select all that apply.

☐ 3 : 25
☐ 5 : 16
☐ 16 minutes after 5 o’clock
☐ 44 minutes before 5 o’clock
☐ 16 minutes before 5 o’clock

Answer:
The time is 5:16 and 16 minutes after 5 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 3 after 1 point.
the hour hand is on the 5.
5 x 3 = 15.
15 + 1 = 16.
so the time is 5:16 and 16 minutes after 5 o’clock.

Question 13.
Mary Ann called her grandmother. She ended the call at the time shown on the clock. Which of the following are NOT other ways to write this time? Select all that apply.

☐ 14 minutes before 9 o’clock
☐ 3 : 46
☐ 46 minutes after 3 o’clock
☐ 9 : 19
☐ 14 minutes before 4 o’clock

Answer:
The wrong options are 3:46 and 14 minutes before 9 o’clock.

Explanation:
In the above-given question,
given that,
Mary Ann called her grandmother.
She ended the call at the time shown on the clock.
so the minute hand is on the 9.
the hour hand is in between 3 and 4.
5 x 9 = 45.
45 + 1 = 46.
so the time is 3:46.

Lesson 14.2 Units of Time: Measure Elapsed Time

Solve & Share
Denise went to see a movie. The movie started at 1:05 P.M. It ended at 2:35 P.M. How long did the movie last? Explain your reasoning.
I can… measure intervals of time in hours and minutes.

Look Back! Without counting hours and minutes, how do you know the movie Denise went to see was less than 2 hours long?

Answer:
The number of minutes the movie lasts = 1 hour 30 minutes.

Explanation:
In the above-given question,
given that,
Denise went to see a movie. The movie started at 1:05 P.M.
It ended at 2:35 P.M.
2:35 – 1:05 = 1:30.
so the number of minutes the movie lasts = 1 hour 30 minutes.

Essential Question
How Can You Find Elapsed Time?

Visual Learning Bridge
Janey took part in a charity walk. The walk started at 7:10 A.M. It ended at 11:20 A.M. How long did the walk last?

Convince Me! Make Sense and Persevere After the charity walk, Janey talked with friends from 11:25 A.M. to 11:40 A.M. Then lunch was served from 11:45 A.M. until 2:10 P.M. How long did lunch last?

Another Example!
You can also use a number line to measure elapsed time.
Janey’s charity walk lasted 4 hours, 10 minutes.
The number line shows the number of hours and minutes that elapsed during the walk.

Guided Practice

Do You Understand?
Question 1.
If a start time is 7:15 A.M. and an end time is 7:45 A.M., why do you not have to count hours to find the elapsed time?

Answer:
The elapsed time is 7:30 A.M.

Explanation:
In the above-given question,
given that,
If a start time is 7:15 A.M. and an end time is 7:45 A.M.
7:45 – 7:15 = 7:30.
so the elapsed time is 7 hours 30 minutes.

Question 2.
A movie started at 2:30 P.M. and ran for 2 hours, 15 minutes. What time did the movie end?

Answer:
The time did the movie end = 4:45 P.M.

Explanation:
In the above-given question,
given that,
The movie started at 2:30 P.M and ran for 2 hours, 15 minutes.
30 + 15 = 45.
2 + 2 = 4.
so the time did movie end = 4:45 P.M.

Do You Know How?
Question 3.
Draw a number line to count the hours from 11:00 A.M. to 5:00 P.M. What is the elapsed time?

Answer:
The elapsed time = 6 hours.

Explanation:
In the above-given question,
given that,
hours from 11 to 5 is 6 hours.
the time is 11:A.M to 5:00 P.M.
11 + 1 = 12.
1 + 5 = 6.
so the elapsed time is 6 hours.

Independent Practice

Leveled Practice In 4-7, use clocks or number lines to find the elapsed or end time.

Question 4.
Hours from 6:30 P.M. to 9:30 P.M. ___________
Minutes from 9:30 P.M. to 9:50 P.M. ___________
The elapsed time is ___________ hours, ___________ minutes.

Answer:
3 hours.
20 minutes.
the elapsed time is 3 hours and 20 minutes.

Explanation:
In the above-given question,
given that,
the hours from 6:30 P.M to 9:30 P.M is 6 + 3 = 9.
the minutes from 9:30 P.M to 9:50 P.M is 30 + 20 = 50.
9 – 6 = 3.
50 – 20 = 30.
so the elapsed time is 3 hours and 20 minutes.

Question 5.
Start Time: 10:00 A.M.
End Time: 3:00 P.M.
Elapsed Time: ___________

Answer:
The elapsed time = 5 hours.

Explanation:
In the above-given question,
given that,
Start Time: 10:00 A.M.
End Time: 3:00 P.M.
10 A.M + 1 = 11 + 1 = 12.
12 + 1 = 1.
1 + 2 = 3.
3  + 2 = 5 hours.

Question 6.
Start Time: 9:15 A.M.
End Time: 10:45 A.M.
Elapsed Time: ___________

Answer:
The elapsed time = 1 hour 30 minutes.

Explanation:
In the above-given question,
given that,
Start Time: 9:15 A.M.
End Time: 10:45 A.M.
45 – 15 = 30.
10 – 1 = 9.
so the elapsed time is 1 hour 30 minutes.

Question 7.
Start Time: 11:30 A.M.
Elapsed Time: 5 hours, 25 minutes
End Time: ___________

Answer:
The End time = 4:55 P.M.

Explanation:
In the above-given question,
given that,
Start Time: 11:30 A.M.
Elapsed Time: 5 hours, 25 minutes
11:30 + 5 = 4:30.
30 + 25 = 55.
so the End Time = 4:55 P.M.

Problem Solving

In 8 and 9, use the list at the right.

Question 8.
Reasoning Mr. Flores made a list of the times it takes for different items to bake. Which items will take less than \(\frac{1}{2}\) hour to bake?

Answer:
The items that take half an hour to bake are bread, granola bars, vegetables.

Explanation:
In the above-given question,
given that,
Mr. Flores made a list of the times it takes for different items to bake.
1/2 hour = 30 minutes.
bread will bake in 27 minutes.
granola bars bake in 21 minutes.
vegetables bake in 24 minutes.
The pasta dish bakes in 48 minutes.
so the items that take half an hour to bake are bread, granola bars, vegetables.

Question 9.
Which two items, when you add their baking time together, take less time to bake than the pasta dish?

Answer:
The two items that take less time to bake are granola bars and vegetables.

Explanation:
In the above-given question,
given that,
Mr. Flores made a list of the times it takes for different items to bake.
1/2 hour = 30 minutes.
bread will bake in 27 minutes.
granola bars bake in 21 minutes.
vegetables bake in 24 minutes.
The pasta dish bakes in 48 minutes.
21 + 24 = 45.
so the two items that take less time to bake are granola bars and vegetables.

Question 10.
Sally finds elapsed time using these clock faces. She counts the hours by 1s, but counts the minutes by 5s. Why does she count the minutes by 5s instead of by 1s?

Answer:
The elapsed time = 5 hours 15 minutes.

Explanation:
In the above-given question,
given that,
Sally finds elapsed time using these clock faces.
She counts the hours by 1s but counts the minutes by 5s.
minutes hand is between 5 seconds.
hours hand is between 5 minutes.
the start time = 3 :30.
the end time = 8:45.
45 – 30 = 15.
8 – 3 = 5.
so the elapsed time = 5 hours 15 minutes.

Question 11.
Higher Order Thinking A basketball tournament started at 12:15 P.M. and ended at 4:00 P.M. Did the tournament last more than 4 hours? Explain.

Answer:
No, the tournament did not last more than 4 hours.

Explanation:
In the above-given question,
given that,
A basketball tournament started at 12:15 P.M. and ended at 4:00 P.M.
12:15 + 1 hour = 1:15.
1 :15 + 2 hours = 3:15.
3 :15 + 1 hour = 4:15.
so the tournament last for 3 hours 15 minutes.

Question 12.
Algebra A farmer is selling 744 pieces of produce. He has 162 watermelons, 345 ears of sweet corn, and some avocados. Write and solve an equation to find how many avocados the farmer is selling. Let x stand for the unknown quantity of avocados.

Answer:
The number of avocados = 237.

Explanation:
In the above-given question,
given that,
A farmer is selling 744 pieces of produce.
He has 162 watermelons, 345 ears of sweet corn, and some avocados.
345 + 162 = 507.
744 – 507 = 237.
so the number of avocados = 237.

Assessment Practice

Question 13.
Geo is taking a train from Carlton to Elgin. The train leaves Carlton at 9:25 A.M. and reaches Elgin 9:25 A.M. at 10:55 A.M. How long does the ride last? Use the leave number line to help.

A. 30 minutes
B. 1 hour
C. 1 hour, 30 minutes
D. 2 hours

Answer:
Option C is the correct answer.
The long does the ride last = 1 hour 30 minutes.

Explanation:
In the above-given question,
given that,
Geo is taking a train from Carlton to Elgin.
The train leaves Carlton at 9:25 A.M. and reaches Elgin at 9:25 A.M. at 10:55 A.M.
9 + 1 = 10.
25 + 30 = 55.
so the time is 10:55.
option c is the correct answer.

Lesson 14.3 Units of Time: Solve Word Problems

Solve & Share
Madison wants to exercise 30 minutes every day. Before school, she only has enough time to exercise for 10 minutes or less. One day, she exercised for 8 minutes before school and 22 minutes after school. This is one way she can exercise for 30 minutes. Find two other ways she can exercise before school and after school to reach her goal of exercising for 30 minutes each day.
I can … use representations to solve word problems about time.

Look Back! Do you think there are more than two ways to solve the problem above? Explain.

Answer:
She exercised for 4 minutes before school and 26 minutes after school.
the other way is 5 minutes before school and 25 minutes after school.

Explanation:
In the above-given question,
given that,
Madison wants to exercise 30 minutes every day.
4 + 26 = 30.
5 + 25 = 30.
so she exercised for 4 minutes before school and 26 minutes after school.
the other way is 5 minutes before school and 25 minutes after school.

Essential Question
How Can You Add or Subtract on Time Intervals?

Visual Learning Bridge
Joaquin made a list of the time he should spend on different activities. Joaquin has practiced playing the piano 35 minutes so far. How much longer does he need to practice?

One Way
You can use a bar diagram to represent the problem and show time intervals.

Another Way
You can use a number line to represent the problem and show time intervals.

Convince Me! Model with Math How much longer will it take Joaquin to finish all of his after-school activities? Show one way to represent and solve.

Answer:
The longer will it take Joaquin to finish all of his after-school activities = 155 minutes.

Explanation:
In the above-given question,
given that,
play with Ron for 50 minutes.
practice piano for 45 minutes.
homework 60 minutes.
50 + 45 + 60 = 155.
so the longer will it take Joaquin to finish all of his after-sccool activities = 155 minutes.

Guided Practice

Do You Understand?
In 1 and 2, complete the bar diagram or number line to solve.
Question 1.
Rhody plans to ride his bicycle for 55 minutes. So far, he has ridden for 29 minutes. How many more minutes does he have to ride?

Answer:
The more minutes he wants to ride = 26 minutes.

Explanation:
In the above-given question,
given that,
Rhody plans to ride his bicycle for 55 minutes.
So far, he has ridden for 29 minutes.
55 – 29 = 26.
so the more minutes he wants to ride = 26 minutes.

Do You Know How?
Question 2.
Ms. Darren spends the reading period working with two different reading groups. She meets with the first group for 23 minutes and meets with the second group for 17 minutes. How long is the reading period?

Answer:
The long is the reading period = 40 minutes.

Explanation:
In the above-given question,
given that,
Ms. Darren spends the reading period working with two different reading groups.
She meets with the first group for 23 minutes and meets with the second group for 17 minutes.
23 + 17 = 40.
so the long is the reading period = 40 minutes.

Independent Practice

Leveled Practice In 3-6, complete or draw a bar diagram or number line to solve.
Question 3.
Claire and Owen played video games. The first game lasted 24 minutes. After the first game, Claire and Owen had lunch for 30 minutes. The second game lasted 36 minutes. How many minutes did they play the games?

Answer:
The number of minutes did they play the games = 60.

Explanation:
In the above-given question,
given that,
Claire and Owen played video games.
The first game lasted 24 minutes.
After the first game, Claire and Owen had lunch for 30 minutes.
The second game lasted 36 minutes.
24 + 36 = 60.
so the number of minutes did they play the games = 60.

Question 4.
Yan jogged for 60 minutes on Friday. Dino jogged 12 fewer minutes than Yan. Both friends swim for 40 minutes each week. How many minutes did Dino jog on Friday?

Answer:
The number of minutes did Dino jog on Friday = 48 minutes.

Explanation:
In the above-given question,
given that,
Yan jogged for 60 minutes on Friday.
Dino jogged 12 fewer minutes than Yan.
Both friends swim for 40 minutes each week.
60 -12 = 48.
so the number of minutes did Dino jog on Friday = 48 minutes.

Question 5.
Mr. Hart’s class is putting on a play. The play is divided into two acts. Each act lasts 27 minutes. How many minutes long is the play?

Answer:
The number of minutes that long the play = 54 minutes.

Explanation:
In the above-given question,
given that,
Mr. Hart’s class is putting on a play.
The play is divided into two acts.
Each act lasts 27 minutes.
27 + 27 = 54.
so the number of minutes that long the play = 54 minutes.

Question 6.
A chef wants to bake a dish for 30 minutes. So far, the dish has been baking for 12 minutes. How many more minutes does the dish need to bake?

Answer:
The more minutes the dish needs to bake = 18 minutes.

Explanation:
In the above-given question,
given that,
A chef wants to bake a dish for 30 minutes.
So far, the dish has been baking for 12 minutes.
30 – 12 = 18.
so the more minutes the dish needs to bake = 18 minutes.

Problem Solving

Question 7.
Reasoning Ms. Merrill spends 55 minutes washing all the windows in her two-story house. How much time could she have spent on each floor? Complete the chart to show three different ways.

Answer:
25 + 30 = 55.
30 + 25 = 55.
20 + 35 = 55.

Explanation:
In the above-given question,
given that,
Ms. Merrill spends 55 minutes washing all the windows in her two-story house.
On the 1st floor, he spends 25 minutes, and 2nd floor he spends 30 minutes.
30 + 25 = 55.
20 + 35 = 55.
so that are the three ways to wash all the windows.

Question 8.
Number Sense Harry measures a sticker that is \(\frac{4}{2}\) inches. Rhea’s sticker is \(\frac{6}{2}\) inches. Whose sticker is longer? Explain.

Answer:
Rhea’s sticker was long.

Explanation:
In the above-given question,
given that,
Harry measures a sticker that is \(\frac{4}{2}\) inches.
Rhea’s sticker is \(\frac{6}{2}\) inches.
4/2 = 2.
6/2 = 3.
so Rhea’s sticker was long.

Question 9.
Higher Order Thinking Mr. Collins is learning to drive a truck. He drives 22 minutes on Monday and 14 minutes on Tuesday. Finally, he drives 6 more minutes on Wednesday than he did on Tuesday. How many total minutes does he practice driving a truck?

Answer:
The total number of minutes does he practice driving a truck = 56 minutes.

Explanation:
In the above-given question,
given that,
Mr. Collins is learning to drive a truck.
He drives 22 minutes on Monday and 14 minutes on Tuesday.
he drives 6 more minutes on Wednesday than he did on Tuesday.
22 + 14 + 20 = 56.
so the total number of minutes does he practice driving a truck = 56 minutes.

Assessment Practice

Question 10.
Sonya hikes up a mountain. It takes her 25 minutes to hike to a cliff that is partway up the mountain. After that, she hikes for 17 more minutes to the summit. Use the number line and complete the table to show how many total minutes Sonya spends hiking.

Answer:
The total number of minutes Sonya spends hiking = 42.

Explanation:
In the above-given question,
given that,
Sonya hikes up a mountain.
It takes her 25 minutes to hike to a cliff that is partway up the mountain.
After that, she hikes for 17 more minutes to the summit.
25 + 17 = 42.
so the total number of minutes Sonya spends hiking = 42.

Question 11.
Meg walks a dog named Shep for 12 minutes. Then she walks Sparky. Finally, she walks Brownie for 18 minutes. Meg spends 52 minutes walking all three dogs. Use the number line and complete the table to show how many minutes Meg spends walking each dog.

Answer:
The number of minutes Meg spends walking each dog = 22 minutes.

Explanation:
In the above-given question,
given that,
Meg walks a dog named Shep for 12 minutes.
Then she walks Sparky.
Finally, she walks Brownie for 18 minutes.
Meg spends 52 minutes walking all three dogs.
18 + 12 = 30.
52 – 30 = 22.
so the number of minutes Meg spends walking each dog = 22 minutes.

Lesson 14.4 Estimate Liquid Volume

Solve & Share
The water bottle below has a capacity of 1 liter. Estimate the capacity of a small bowl, a large bowl, and a pitcher to the nearest half liter. Use an actual 1-liter water bottle, small and large bowls, and a pitcher to solve this problem.
I can … use a standard unit to estimate liquid volume.

Look Back! After you estimate the capacity of the containers, how can you use a 1-liter water bottle to check that your estimate for each container is reasonable? Check your estimates.

Essential Question
Do You Estimate Capacity?

Visual Learning Bridge
What is the capacity of the pail?

Compare the capacity of the water bottle to the capacity of the pail.

The pail appears to be large enough to hold several liters.
Count how many times you can fill a liter container and empty it into the pail.
This pail holds about 8 liters.

Convince Me! Be Precise Suppose you want to estimate the capacity of the pail to the nearest half liter. How can you check that your estimate is reasonable?

Guided Practice

Do You Understand?
Question 1.
Susie estimates the capacity of a water glass as 3 liters. Hakim estimates the capacity as á liter. Is Susie’s or Hakim’s estimate more reasonable? Explain.

Answer:
Hakim estimates the capacity as a liter was more reasonable.

Explanation:
In the above-given question,
given that,
Susie estimates the capacity of a water glass as 3 liters.
Hakim estimates the capacity as a liter.
so Hakim’s estimation was correct.

Question 2.
Find a container that you predict will hold more than a liter and another that you predict will hold less than a liter. Use a liter container to check your predictions by finding the actual capacity of each container.

Answer:
The containers are a small bowl and a large bowl.

Explanation:
In the above-given question,
given that,
container that you predict will hold more than a liter and another that you predict will hold less than a liter.
container hold exactly 1 liter.
a small bowl holds less than a liter.
A large bowl holds more than a liter.
so the containers are a small bowl and a large bowl.

Do You Know How?
In 3-6, circle the better estimate for each.
Question 3.

\(\frac{1}{4}\) L or 2 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 2 liters.
the glass holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 4.

100 L or 1 L

Answer:
The better estimate is 100 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 100 liters.
the bucket holds 100 liters.
so the better estimate is 100 liters.

Question 5.
Bottle of juice
3 L or 1L

Answer:
The better estimate is 1 liter.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 3 liters.
the bottle holds 1 liter.
so the better estimate is 1 liter.

Question 6.
Cereal bowl
\(\frac{1}{4}\) L or 3 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 3 liters.
the cereal bowl holds 1/4 liter.
so the better estimate is 1/4 liters.

Independent Practice

In 7-14, circle the better estimate for each.
Question 7.

\(\frac{1}{4}\) L or 40 L

Answer:
The better estimate is 40 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 40 liters.
the glass aquarium holds 40 liters.
so the better estimate is 40 liters.

Question 8.

\(\frac{1}{8}\) L or 1 L

Answer:
The better estimate is 1/8 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/8 liter and 1 liter.
the spoon holds 1/8 liter.
so the better estimate is 1/8 liters.

Question 9.

\(\frac{1}{2}\) L or 14 L

Answer:
The better estimate is 1/2 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/2 liter and 14 liters.
the glass holds 1/2 liter.
so the better estimate is 1/2 liters.

Question 10

\(\frac{1}{4}\) L or 250 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 250 liters.
the juice holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 11.
Teacup
\(\frac{1}{4}\) L or 15 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 15 liters.
the teacup holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 12.
Bathtub
15 L or 115 L

Answer:
The better estimate is 115 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
15 liter and 115 liters.
the bathtub holds 115 liters.
so the better estimate is 115 liters.

Question 13.
Soup bowl
\(\frac{1}{2}\) L or 3 L

Answer:
The better estimate is 1/2 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/2 liter and 3 liters.
the soup bowl holds 1/2 liter.
so the better estimate is 1/2 liters.

Question 14.
Teapot
1 L or 10 L

Answer:
The better estimate is 1 liter.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 10 liters.
the teapot holds 1/4 liter.
so the better estimate is 1 liters.

Question 15.
Write an estimate for the capacity of a dog bowl. _________

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 2 liters.
the dogbowl holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 16.
Write an estimate for the capacity of a flower vase. __________

Answer:
The better estimate is 1 liter.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 2 liters.
the flower vase holds 1 liter.
so the better estimate is 1 liter.

Problem Solving

Question 17.
Generalize Which cooler has the greater capacity? Explain your thinking

Answer:
Cooler B has the greatest capacity.

Explanation:
In the above-given question,
given that,
the two coolers with different capacities.
cooler A has a small capacity.
cooler B has a larger capacity.

Question 18.
List these containers in order from least capacity to greatest capacity.
Washing machine
Large pot
Soup spoon
Travel mug

Answer:
The containers from least to greatest = soup spoon, travel mug, large pot, and washing machine.

Explanation:
In the above-given question,
given that,
there are 4 containers.
they are a washing machine, large pot, soup spoon, travel mug.
soup spoon, travel mug, large pot, and washing machine.
so the containers from least to greatest = soup spoon, travel mug, large pot, and washing machine.

Question 19.
A basketball team scores 27 points in its first game and 41 points in its second game. After three games, it scores 100 points in all. How many points does the team score in its third game?

Answer:
The number of points does the team score in its third game = 32 points.

Explanation:
In the above-given question,
given that,
A basketball team scores 27 points in its first game and 41 points in its second game.
After three games, it scores 100 points in all.
27 + 41 = 68.
100 – 68 = 32.
so the number of points does the team score in its third game = 32 points.

Question 20.
Higher Order Thinking Becky wants to measure the capacity of her brother’s baby pool. She has a 1-liter container and a 10-liter container. Which should she use? Explain your reasoning.

Answer:
The capacity of her brother’s baby pool is a 10-liter container.

Explanation:
In the above-given question,
given that,
Becky wants to measure the capacity of her brother’s baby pool.
She has a 1-liter container and a 10-liter container.
so a 10-liter container is the capacity of her brother’s pool.

Question 21.
A sandgrouse can soak up water in its fluffy feathers. It can carry the water a long way to its chicks. Does a sandgrouse carry \(\frac{1}{10}\) liter of water or 2 liters of water?

Answer:
Sandgrouse carries 1/10 liter of water.

Explanation:
In the above-given question,
given that,
A sandgrouse can soak up water in its fluffy feathers.
It can carry the water a long way to its chicks.
sandgrouse can carry 1/10 liter of water.

Assessment Practice

Question 22.
Gary is painting a small storage shed. He estimates that he can do the job with one can of paint. Which of the following is the best estimate of the total liquid volume of a can of paint?

A. \(\frac{1}{4}\) liter
B. 4 liter
C. 40 liters
D. 400 liters

Answer:
The best estimate of the total liquid volume of a can of paint = 4 liters.

Explanation:
In the above-given question,
given that,
Gary is painting a small storage shed.
He estimates that he can do the job with one can of paint.
the best estimate of the total liquid volume of a can of paint = 4 liters.

Lesson 14.5 Measure Liquid Volume

Solve & Share
Select six different containers. Estimate the capacity of each container. Record your estimates in the table, and arrange the containers in order from least to greatest liquid volume. Then use a marked liter beaker to measure the capacity of each container. Record your measurements in the table. Compare your estimates to your measures. Using your measures, rearrange the containers in order from least to greatest liquid volume.
I can … use a standard unit to measure liquid volume.

Answer:
The containers in order from least to greatest are teacup, glass, mug, bottle, tea jar, kettle, and bucket.

Explanation:
In the above-given question,
given that,
they have given 7 containers.
they are teacup, glass, mug, bottle, tea jar, kettle, and bucket.
teacup = 1/4 liter.
glass = 1/3 liter.
mug = 1/8 liter.
bottle = 1 liter.
tea jar = 1/2 liter.
kettle = 3/4 liter.
bucket = 10 liters.

Look Back! How did you measure the capacity of containers that are less than 1 liter? Is there another way to measure?

Essential Question
How Do You Measure Capacity?

Visual Learning Bridge
Eric is cleaning his fishbowl and wants to know how much water he needs to refill the fishbowl. How can he find the capacity of the fishbowl?

Pour from the filled fishbowl into the 1-liter container. Empty the container and repeat until the fishbowl is empty.

It is helpful to keep a record of measurements made.
The 1-liter container was filled 5 times.
So, the capacity of the fishbowl is 5 liters.

Convince Me! Critique Reasoning Jason says, “I think it is better to find the measurement of the fishbowl by filling the fishbowl with liters of water instead of emptying the fishbowl into liter beakers.” Is Jason correct?

Another Example!
When only part of the 1-liter container is filled, use fractions of liters.

The capacity of the pot is 2\(\frac{1}{2}\) liters.

Guided Practice

Do You Understand?
Question 1.
What is the capacity of 2 pots like the one shown in the Another Example! above?

Answer:
The capacity of the 2 pots like the one shown is 5 liters.

Explanation:
In the above-given question,
given that,
the capacity of one pot is 2 and 1/2 liters.
2 + 2 + 1 = 5.
so the capacity of the 2 pots like the one shown is 5 liters.

Question 2.
Find a container that you think holds less than a liter. Estimate, and then check your estimate for the capacity of the container.

Answer:
The container that holds less than a liter = teacup.

Explanation:
In the above-given question,
given that,
the container is a teacup.
teacup holds 1/8 of a liter.
so the container that holds less than a liter = teacup.

Do You Know How?
In 3 and 4, find the total capacity represented in each picture.
Question 3.

Answer:
The total capacity represented in each picture = 2 liters.

Explanation:
In the above-given question,
given that,
there are 4 containers.
the containers each weight is 1/2 liter.
1/2 + 1/2 + 1/2 + 1/2 = 2 liters.
so the total capacity represented in each picture = 2 liters.

Question 4.

Answer:
The total capacity represented is 1 and 1/2 liter.

Explanation:
In the above-given question,
given that,
there are 2 containers.
they are 1 is totally filled and the other one is half-filled.
1 + 1/2 = 1.5 liters.
so the total capacity represented is 1 and 1/2 liter.

Independent Practice

In 5-7, find the total capacity represented in each picture.
Question 5.

Answer:
The total capacity represented is 18 liters.

Explanation:
In the above-given question,
given that,
there are 2 containers.
they are 1 is totally filled and the other one is 8 liters filled.
10 + 8 = 18 liters.
so the total capacity represented is 18 liters.

Question 6.

Answer:
The total capacity represented is 20 liter.

Explanation:
In the above-given question,
given that,
there are 2 containers.
they are totally filled.
10 + 10 + 10 + 10 = 20 liters.
so the total capacity represented is 20 liters.

Question 7.

Answer:
The total capacity represented is 24 liters.

Explanation:
In the above-given question,
given that,
there are 3 containers.
they are 2 is totally filled and the other one is half-filled.
10 + 10 + 4 = 24 liters.
so the total capacity represented is 24 liters.

Problem Solving

Question 8.
Lawrence manufactures jam. He makes 200 liters of grape jam and 350 liters of strawberry jam. He then sells 135 liters of the grape jam. How much jam does Lawrence have left?

Answer:
The quantity of jam does Lawrence has left = 415 liters.

Explanation:
In the above-given question,
given that,
Lawrence manufactures jam.
He makes 200 liters of grape jam and 350 liters of strawberry jam.
He then sells 135 liters of grape jam.
200 – 135 = 65.
350 + 65 = 415.
so the quantity of jam does Lawrence have left = 415 liters.

Question 9.
Use Appropriate Tools Find a container that you think holds more than a liter. Estimate, and then check your estimate for the capacity of the container.

Answer:
The capacity of the container is more than 2 liters and it is a kettle.

Explanation:
In the above-given question,
given that,
the container is a kettle.
the kettle holds 2 liters.

Question 10.
How many 2-liter cartons can be filled with 18 liters of juice?

Answer:
The number of 2-liter cartons can be filled with 18 liters of juice = 9 liters.

Explanation:
In the above-given question,
given that,
2 x 9 = 18.
so the number of 2-liter cartons can be filled = 9.

Question 11.
Which of the following measurements is NOT reasonable for the capacity of a full bathroom sink: 15 liters, \(\frac{1}{2}\) liter, 10 liters, 9 liters, or 12 liters? Explain.

Answer:
The 1/2 liter is not reasonable for the capacity of a full bathroom sink.

Explanation:
In the above-given question,
given that,
the capacity of a full bathroom sink is 15 liters, 1/2 liter, 10 liters, 9 liters, 12 liters.
so I am thinking that the capacity of a full bathroom sink is 12 liters.
so half-liter is not reasonable.

Question 12.
Higher Order Thinking Emma prepares 72 liters of punch for an event. She pours all of the punch equally into the pitchers on 9 different tables. If there are 4 pitchers on each table, how many liters of punch are in each pitcher?

Answer:
The number of liters of punch is in each pitcher = 32.

Explanation:
In the above-given question,
given that,
Emma prepares 72 liters of punch for an event.
She pours all of the punch equally into the pitchers on 9 different tables.
9 x 8 = 72.
8 x 4 = 32.
so the number of liters of punch are in each pitcher = 32.

Assessment Practice

Question 13.
Use the picture of the water jugs to find the amount of water the team drank during soccer practice.

A. 6 liters
B. 7 liters
C. 8 liters
D. 23 liters

Answer:
Option B is the correct answer.

Explanation:
In the above-given question,
given that,
the amount of water before soccer practice is 15 liters.
15 – 8 = 7liters.
so the amount of water before soccer is 15 liters.
option B is the correct answer.

Lesson 14.6 Estimate Mass

Solve & Share
Look at the measurements for the mass of the book and the mass of the olive. List 4 items that should be measured using kilograms and 4 items that should be measured using grams. Explain your reasoning.
I can … use standard units to estimate the masses of solid objects.

Look Back! How could you use tools to check that the items in part of your list are reasonable choices for measuring mass with grams? Explain.

Answer:
The weight of the cup = 250 grams.

Explanation:
In the above-given question,
given that,
1kilo gram = 1000 grams.
so the weight of the cup = 250 grams.
the weight of the bottle is 1000 grams.

Essential Question
How Can You Use Reasoning to Estimate Mass?

Visual Learning Bridge
Stephen and Marissa estimated the mass of an apple. Stephen’s estimate is 250 grams. Marissa’s estimate is 2 kilograms. Which is the better estimate of the mass of an apple?

Step 1
Use known masses and the table to compare grams to kilograms. Select the unit that will give a better estimate.

The apple is smaller than the cantaloupe. A kilogram is too large of a unit to estimate the mass of the apple.
The grape is smaller than the apple. Grams are smaller units that can be used to estimate the mass of the apple.

Step 2
Use a pan balance to find the mass of the apple. Then evaluate Stephen’s estimate.

The apple has a mass of 262 grams.
250 grams is close to 262 grams. Stephen’s estimate is reasonable.
250 grams is a better estimate than 2 kilograms.

Convince Me! Critique Reasoning Zoe says two apples would have a mass greater than a kilogram. Do you agree? Explain.

Answer:
No, i do not agree with it.

Explanation:
In the above-given question,
given that,
Zoe says two apples would have a mass greater than a kilogram.
one apple = 250 grams.
250 x 2 = 500.
250 + 250 = 500 grams.
so zeo says wrong.

Guided Practice

Do You Understand?
Question 1.
In Step 2 on the previous page, why do you need to find the actual mass of the apple?

Answer:
The actual mass of the object is 262 grams.

Explanation:
In the above-given question,
given that,
the actual mass of the object is 262 grams.
262 grams is approximately equal to 250 grams.
262 + 262 = 524.
so the actual mass of the object is 262 grams.

Question 2.
Find an object that you think has a mass more than a kilogram and another that has a mass less than a kilogram. Then determine what tools to use to check your estimate.

Answer:
The tools are apple and jaggery.

Explanation:
In the above-given question,
given that,
the object that you think has a mass more than a kilogram and has a mass less than a kilogram.
the weight of the apple is 250 grams.
the weight of the jaggery is 1200 grams.
so the tools are apple and jaggery.

Do You Know How?
In 3-6, circle the better estimate for each
Question 3.

5 g or 5 kg

Answer:
The better estimation of the coin is 5 g.

Explanation:
In the above-given question,
given that,
the measurements are 5 g and 5 kg.
the weight of the coin is 5 g.
so the better estimation of the coin is 5 g.

Question 4.

40 g or 4 kg

Answer:
The better estimation of the dog is  4 kg.

Explanation:
In the above-given question,
given that,
the measurements are 40 g and 4 kg.
the weight of the dog is 4 kg.
so the better estimation of the dog is 4 kg.

Question 5.
Sunglasses
16 g or 1 kg

Answer:
The better estimation of the sunglasses is 16 g.

Explanation:
In the above-given question,
given that,
the measurements are 16 g and 1 kg.
the weight of the sunglasses is 16 g.
so the better estimation of the sunglasses is 16 g.

Question 6.
Envelope
1 g or 70 g

Answer:
The better estimation of the Envelope is 1 g.

Explanation:
In the above-given question,
given that,
the measurements are 1 g and 70 g.
the weight of the Envelope is 1 g.
so the better estimation of the Envelope is 1 g.

Independent Practice

Leveled Practice In 7-18, circle the better estimate for each.
Question 7.

100 g or 10 kg

Answer:
The better estimation of the blanket is 10 kg.

Explanation:
In the above-given question,
given that,
the measurements are 100 g and 10 kg.
the weight of the blanket is 10 kg.
so the better estimation of the coin is 10 kg.

Question 8.

15 g or 15 kg

Answer:
The better estimation of the monitor is 15 kg.

Explanation:
In the above-given question,
given that,
the measurements are 15 g and 15 kg.
the weight of the monitor is 15 kg.
so the better estimation of the monitor is 15 kg.

Question 9.

4g or 400 g

Answer:
The better estimation of the spectacles box is 400 g.

Explanation:
In the above-given question,
given that,
the measurements are 4 g and 400 g.
the weight of the spectacles box is 400 g.
so the better estimation of the spectacles box is 400 g.

Question 10.

200 g or 2 kg

Answer:
The better estimation of the net bag is 2 kg.

Explanation:
In the above-given question,
given that,
the measurements are 200 g and 2 kg.
the weight of the bag is 2 kg.
so the better estimation of the net bag is 2 kg.

Question 11.
Bicycles
2 kg or 12 kg

Answer:
The better estimation of the bicycles is 12 kg.

Explanation:
In the above-given question,
given that,
the measurements are 2 kg and 12 kg.
the weight of the bicycles is 12 kg.
so the better estimation of the bicycles is 12 kg.

Question 12.
Feather
1 g or 1 kg

Answer:
The better estimation of the feather is 1 g.

Explanation:
In the above-given question,
given that,
the measurements are 1 g and 1 kg.
the weight of the feather is 1 g.
so the better estimation of the feather is 1 g.

Question 13.
Horse
5 kg or 550 kg

Answer:
The better estimation of the horse is 550 kg.

Explanation:
In the above-given question,
given that,
the measurements are 5 kg and 550 kg.
the weight of the horse is 550 kg.
so the better estimation of the horse is 550 kg.

Question 14.
Penny
3 g or 300 g

Answer:
The better estimation of the penny is 3 g.

Explanation:
In the above-given question,
given that,
the measurements are 3 g and 300 g.
the weight of the penny is 3 g.
so the better estimation of the penny is 3 g.

Question 15.
Dining table
350 g or 35 kg

Answer:
The better estimation of the dining table is 35 kg.

Explanation:
In the above-given question,
given that,
the measurements are 350 g and 35 kg.
the weight of the dining table is 35 kg.
so the better estimation of the dining is 35 kg.

Question 16.
Microwave oven
1,500 g or 15 kg

Answer:
The better estimation of the microwave oven is 15 kg.

Explanation:
In the above-given question,
given that,
the measurements are 1500 g and 15 kg.
the weight of the microwave oven is 15 kg.
so the better estimation of the microwave oven is 15 kg.

Question 17.
Kitten
2 kg or 20 kg

Answer:
The better estimation of the kitten is 2 kg.

Explanation:
In the above-given question,
given that,
the measurements are 2 kg and 20 kg.
the weight of the kitten is 2 kg.
so the better estimation of the kitten is 2 kg.

Question 18.
Crayon
20 g or 200 g

Answer:
The better estimation of the crayon is 20 g.

Explanation:
In the above-given question,
given that,
the measurements are 20 g and 200 g.
the weight of the crayon is 20 g.
so the better estimation of the crayon is 20 g.

Problem Solving

Question 19.
Use Appropriate Tools Choose the best tool to measure each item described. Write the correct letter of the tool on the blank.

The capacity of a mug _______
The temperature of water _______
The length of a box _______
The mass of a pear _______
The time you finish lunch _______

Answer:
The capacity of a mug is 1 liter.
the temperature of the water is 1000 degrees celsius.
the length of a box is 1 cm.
the mass of a pear is 100 g.
the time you finish lunch is 12:15.

Explanation:
In the above-given question,
given that,
the items are mug, pear, temperature, and box.
The capacity of a mug is 1 liter.
the temperature of the water is 1000 degrees celsius.
the length of a box is 1 cm.
the mass of a pear is 100 g.
the time you finish lunch is 12:15.

Question 20.
Number Sense Ethan will subtract a 3-digit number from 920. He says the difference could be a 1-digit number, a 2-digit number, or a 3-digit number. Write three subtraction equations that show each difference. Be sure you start with 920 and subtract a 3-digit number each time.
You can use place value and mental math to solve this problem.

Answer:
The three subtraction equations are 917, 10, and 3.

Explanation:
In the above-given question,
given that,
Ethan will subtract a 3-digit number from 920.
He says the difference could be a 1-digit number, a 2-digit number, or a 3-digit number.
920 – 3 = 917.
920 – 10 = 920.
920 – 917 = 3.
so the three subtraction equations are 917, 10, and 3.

Question 21.
en Vision® STEM Clay learned that solids have a definite shape. Now he wants to measure some solids, so he measures the mass of a bead. The bead has a mass of 10 grams. He estimates that 10 beads will have a mass of 1 kilogram. Is he correct? Explain.

Answer:
No, he was not correct.

Explanation:
In the above-given question,
given that,
Clay learned that solids have a definite shape.
the bead has a mass of 10 grams.
10 beads will have a mass of 1 kilogram.
1000 grams = 1 kilogram.
so he was not correct.

Question 22.
Higher Order Thinking Correct the mistakes in the shopping list below.
Shopping List
2 L of apples
3 kg of milk
5 cm of flour

Answer:
The shopping list contains 2 liters of milk, 3 kg of apples, and 5 cm of flour.

Explanation:
In the above-given question,
given that,
2 l of apples, 3 kg of milk, 5 cm of flour.
the mistakes in the shopping list are apples, milk, and flour.
so the shopping list contains 2 liters of milk, 3 kg of apples, and 5 cm of flour.

Assessment Practice

Question 23.
Todd is thinking of an animal with a mass greater than 1 kilogram, but less than 20 kilograms. Which animal could Todd be thinking of?
A. Horse
B. Cat
C. Elephant
D. Rhinoceros

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
the animal with a mass greater than 1 kilogram, but less than 20 kilograms.
the animals are horse, cat, elephant, and rhinoceros.
the weight of the horse is more than 1 kilogram and less than 20 kilograms.
so option A is correct.

Question 24.
Anna has a bar of soap. She estimates its mass before measuring to find the actual mass. Which units should Anna use for her measure?
A. Grams
B. Kilograms
C. Liters
D. Inches

Answer:
The actual mass of the soap is grams.

Explanation:
In the above-given question,
given that,
the measurements are grams, kilograms, liters, and inches.
so the mass of the soap will be in grams.

Lesson 14.7 Measure Mass

Solve & Share
Work with a group to choose 6 objects whose masses can be measured using a pan balance. Estimate the mass of each object. Then use metric weights to find the actual mass for each in grams (g) or kilograms (kg). Use the table and explain your reasoning.
I can … use grams and kilograms to measure the mass of objects.

Look Back! How did you decide which metric unit(s) to use when making your estimates? Explain.

Essential Question
How Do You Measure Mass?

Visual Learning Bridge
A pan balance with gram and kilogram weights can be used to find the mass of an object. What is the mass of a box of chalk?

Place the box on one pan. Place enough gram and kilogram weights on the other pan so the pans balance.

The box balances with one 1-kilogram weight, two 100-gram weights, and four 10-gram weights.
So, the mass of the box is 1 kilogram 240 grams or 1,240 grams.
Write the larger unit before the smaller unit when recording measurements.

Convince Me! Be Precise What metric units would you use to estimate the mass of half of a box of chalk? Explain.

Answer:
The mass of the half of the box of chalk = 620 grams.

Explanation:
In the above-given question,
given that,
the mass of the box is 1 kilogram 240 grams or 1,240 grams.
1kg = 1000 g.
1240 / 2 = 620.
so the mass of the half of box of chalk = 620 grams.

Guided Practice

Do You Understand?
Question 1.
Find an object that you think has a mass greater than a kilogram. Find another object that has a mass less than a kilogram. Use a pan balance with gram and kilogram weights to measure the mass of each object.

Answer:
The weight of Malachi is 1 g and the mass of the cat is 1200 g.

Explanation:
In the above-given question,
given that,
the object that has a mass greater than a kilogram and has a mass less than a kilogram.
the mass of Malachi is 1 g.
the mass of the cat is 1200g.
the mass of Malachi is less than a kilogram.
the mass of the cat is greater than a kilogram.
so the weight of Malachi is 1 g and the mass of the cat is 1200 g.

Question 2.
If you use a pan balance to measure the mass of a pen, would you use any kilogram weights? Explain.

Answer:
We will use one gram weight.

Explanation:
In the above-given question,
given that,
the mass of a pen is 2 grams.
so we will use the gram weights.

Do You Know How?
In 3 and 4, write the total mass represented in each picture.
Question 3.

Answer:
The total mass is 3500 g.

Explanation:
In the above-given question,
given that,
there are 3 1 kg and 1 500 g.
1 kg = 1000 g.
1000 + 1000 + 1000 + 500 = 3500 g.
so the total mass is 3500 g.

Question 4.

Answer:
The total mass is 245 g.

Explanation:
In the above-given question,
given that,
there are 2 100 g objects, 4 10 g, and 5 1 g objects.
100 + 100 = 200.
10 + 10 + 10 + 10 = 40.
1 + 1 + 1 + 1 + 1 = 5.
200 + 40 + 5 = 245g.
so the total mass is 245 g.

Independent Practice

In 5-7, write the total mass represented in each picture.
Question 5.

Answer:
The total mass is 931 g.

Explanation:
In the above-given question,
given that,
there are 1 500 g.
4 100 g and 3 10 g and 1 g.
500 + 100 + 100 + 100 + 100 = 900.
3 x 10 = 30.
30 + 1 = 31.
900 + 30 + 1 = 931.
so the total mass is 931 g.

Question 6.

Answer:
The total mass is 6 kg.

Explanation:
In the above-given question,
given that,
there are 6 1 kg objects.
1 + 1 + 1 + 1 + 1 + 1 = 6.
so the total mass is 6 kg.

Question 7.

Answer:
The total mass is 2106 g.

Explanation:
In the above-given question,
given that,
there are 2-1 kg objects.
2 x 1000 = 2000.
1 x 100 = 100.
6 x 1 = 6.
2000 + 100 + 6 = 2016 g.

Problem Solving

Question 8.
Algebra Olivia put 220 grams of nuts in a bag. Then she added more nuts to the bag. The total mass of Olivia’s bag of nuts was 850 grams. Use the equation 220 + a = 850 to find the mass in grams of the nuts Olivia added to her bag.

Answer:
The mass of the grams she added = 630 g.

Explanation:
In the above-given question,
given that,
Algebra Olivia put 220 grams of nuts in a bag.
Then she added more nuts to the bag.
The total mass of Olivia’s bag of nuts was 850 grams.
220 + a = 850.
a = 850 – 220.
a = 630.
so she added the 630 grams into the bag.

Question 9.
An adult manatee has a mass of about 450 kilograms. What is the mass of 2 adult manatees?

Answer:
The mass of 2 adult manatees = 900 kg.

Explanation:
In the above-given question,
given that,
An adult manatee has a mass of about 450 kilograms.
450 + 450 = 900.
so the mass of 2 adult manatees = 900 kg.

Question 10.
Reasoning Sophie used a pan balance to measure the mass of a pineapple. The pans balanced when she used one 500-gram weight and three 100-gram weights. Zach measured the same pineapple but used eight 100-gram weights. Did someone make a mistake? Explain.

Answer:
No one makes a mistake.

Explanation:
In the above-given question,
given that,
The pans balanced when she used one 500-gram weight and three 100-gram weights.
Zach measured the same pineapple but used eight 100-gram weights.
500 + 100 + 100 + 100 = 800 gram.
100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 = 800 gram.
so no one makes a mistake.

Question 11.
Higher Order Thinking Lawrence bought some red potatoes with a mass of 410 grams. He also bought white potatoes with a mass of 655 grams. Did he buy more or less than 1 kilogram of potatoes? Explain how you know.

Answer:
He buys more than 1 kilogram of potatoes.

Explanation:
In the above-given question,
given that,
Lawrence bought some red potatoes with a mass of 410 grams.
He also bought white potatoes with a mass of 655 grams.
410 + 655 = 1065.
so he buys more than 1 kilogram of potatoes.

Question 12.
Meg uses 16 kilograms of butter to make 8 large batches of cookies. She uses an equal amount of butter for each batch. How many kilograms of butter are used for each batch?

Answer:
The number of kilograms of butter is used for each batch = 2 kg.

Explanation:
In the above-given question,
given that,
Meg uses 16 kilograms of butter to make 8 large batches of cookies.
She uses an equal amount of butter for each batch.
16 / 8 = 2.
he uses 2 kilograms of butter for each batch.
so the number of kilograms of butter is used for each batch = 2 kg.

Question 13.
Kalista has 154 grams of glitter. She uses 97 grams to sprinkle the tops of the tables. How many grams of glitter remain?

Answer:
The number of grams of glitter remains = 57.

Explanation:
In the above-given question,
given that,
Kalista has 154 grams of glitter.
She uses 97 grams to sprinkle the tops of the tables.
154 – 97 = 57.
so the number of grams of glitter remains = 57.

Assessment Practice

Question 14.
Evan used a pan balance and metric weights to measure the total mass of 3 bricks. What is the mass of the 3 bricks?

A. 6 kilograms
B. 5 kilograms
C. 4 kilograms
D. 3 kilograms

Answer:
The mass of the 3 bricks = 3 kg.

Explanation:
In the above-given question,
given that,
Evan used a pan balance and metric weights to measure the total mass of 3 bricks.
3 x 1000 = 3000.
so the mass of the 3 bricks = 3 kg.

Lesson 14.8 Solve Word Problems Involving Mass and Liquid Volume

Solve & Share
The animals at a pet store eat 80 kilograms of vegetables each day. How many kilograms of vegetables do they eat in one week?
I can … solve problems about mass and liquid volume.

Look Back! Describe the plan you used to solve the problem.

Answer:
The number of vegetables does they eat in 1 week = 560 kg.

Explanation:
In the above-given question,
given that,
The animals at a pet store eat 80 kilograms of vegetables each day.
1 week = 7 days.
80 x 7 = 560.
so the number of vegetables do they eat in 1 week = 560 kg.

Essential Question
How Can You Solve Problems Involving Mass and Liquid Volume?

Visual Learning Bridge
In a juice factory, one 50-liter container had 28 liters of juice in it. An hour later, it had 45 liters of juice. How many liters of juice were added?

Convince Me! Make Sense and Persevere In the example above, another beaker had 33 liters of juice. How many total liters of juice were there in all? How can you solve this problem?

Answer:
The liters of juice that were added = 5 liters.

Explanation:
In the above-given question,
given that,
another beaker had 33 liters of juice.
one 50-liter container had 28 liters of juice.
33 – 28 = 5.
so the number of liters that were added = 5 liters.

Guided Practice

Do You Understand?
Question 1.
Suppose 42 liters of juice were evenly divided into 6 batches. How many liters of juice are in each batch? Write and solve an equation.

Answer:
The number of liters is in each batch = liters.

Explanation:
In the above-given question,
given that,
Suppose 42 liters of juice were evenly divided into 6 batches.
42 /6 = 7.
6 x 7 = 42.
so the number of liters are in each batch = 7 liters.

Do You Know How?
Question 2.
Alex buys a box of pudding mix and a box of cocoa. The mass of the box of pudding mix is 100 grams. The total mass of the 2 boxes is 550 grams. What is the mass of the box of cocoa?

Answer:
The mass of the box of cocoa is 450 g.

Explanation:
In the above-given question,
given that,
Alex buys a box of pudding mix and a box of cocoa.
The mass of the box of pudding mix is 100 grams.
The total mass of the 2 boxes is 550 grams.
550 – 100 = 450.
so the mass of the box of cocoa is 450 g.

Independent Practice

Leveled Practice In 3-6, use bar diagrams or equations to help solve.
Question 3.
Peter divided 120 liters of water equally into 3 containers. How many liters did Peter pour into each container?

Answer:
The number of liters did peter pour into each container = 40 liters.

Explanation:
In the above-given question,
given that,
peter divided 120 liters of water equally into 3 containers.
c + c + c = 120.
3c = 120.
c = 120/3.
c = 40.
so the number of liters did peter pour into each container = 40 liters.

Question 4.
Adeela pours 235 liters of milk into a blue vat and 497 liters of milk into a red vat. How many liters of milk does she pour in all? Write and solve an equation.

Answer:
The quantity of milk she pours in all = liters.

Explanation:
In the above-given question,
Adeela pours 235 liters of milk into a blue vat and 497 liters of milk into a red vet.
235 + 497 = 732.
so the quantity of milk she pours in all = 732 liters.

Question 5.
Samantha bought 523 grams of grapes. After eating some grapes, she had 458 grams. How many grams did she eat?

Answer:
The number of grams did she eat = 65 g.

Explanation:
In the above-given question,
given that,
Samantha bought 523 grams of grapes.
After eating some grapes, she had 458 grams.
523 – 458 = 65.
so the number of grams did she eat = 65 g.

Question 6.
Omar is shipping 3 boxes. Each has a mass of 8 kilograms. What is the total mass of all of the boxes?

Answer:
The total mass of all the boxes = 24.

Explanation:
In the above-given question,
given that,
Omar is shipping 3 boxes.
each has a mass of 8 kilograms.
8 x 3 = 24.
so the total mass of all the boxes = 24.

Problem Solving

In 7 and 8, use the table. In 8, use the bar diagram.

Question 7.
Professor Newman has collected a soil sample from the forest preserve in her town. What is the total mass of the 3 minerals in the soil sample?

Answer:
The total mass of the 3 minerals in the soil sample is 279 g.

Explanation:
In the above-given question,
given that,
Professor Newman has collected a soil sample from the forest preserve in her town.
the sample of quartz is 141 g.
calcite is 96 g.
feldspar is 42 g.
141 + 96 + 42 = 279.
so the total mass of the 3 minerals in the soil sample is 279 g.

Question 8.
Higher Order Thinking The professor finds that there is the same amount of feldspar in each of the soil samples that she takes. If there are 210 grams of feldspar in all, how many soil samples does she collect?

Answer:
The number of soil samples does she collect = 447 g.

Explanation:
In the above-given question,
given that,
If there are 210 grams of feldspar in all.
141 + 96 + 210 = 447 g.
so the number of soil samples does she collect = 447 g.

Question 9.
Elijah has 2 hours before dinner. He spends the first 37 minutes practicing his guitar and the next 48 minutes doing his homework. How much time is left until dinner?

Answer:
The number of times is left until dinner is 35.

Explanation:
In the above-given question,
given that,
Elijah has 2 hours before dinner.
He spends the first 37 minutes practicing his guitar and the next 48 minutes doing his homework.
37 + 48 = 85.
1 hour = 60 minutes.
60 + 60 = 120.
120 – 85 = 35.
so the number of time is left unit dinner is 35.

Question 10.
Make Sense and Persevere Write and solve a word problem about the bar diagram.

Answer:
The mass of the a is 339 g.

Explanation:
In the above-given question,
given that,
the total mass of the object is 678 g.
678 – 239 = 339.
so the mass of the a is 339 g.

Assessment Practice

Question 11.
Eric filled a container to the 18-liter mark with juice an hour ago. The juice is now at the 15-liter mark. Mark the amount of juice Eric had on the beakers. Then find how many liters of juice have been poured out.

A. 3 liters
B. 4 liters
C. 5 liters
D. 6 liters

Answer:
The number of liters of juice that has been poured out = 3 liters.

Explanation:
In the above-given question,
given that,
Eric filled a container to the 18-liter mark with juice an hour ago.
The juice is now at the 15-liter mark.
18 – 15 = 3.
so the number of liters of juice has been poured out = 3 liters.

Lesson 14.9 Problem Solving

Reasoning
Solve & Share
Nina wants to arrive at the community center at 9:30 A.M. for an art class. It takes her 15 minutes to walk to the center, 30 minutes to make and eat breakfast, and 15 minutes to get ready after eating. What time should Nina start making breakfast? Use reasoning to decide.
I can … make sense of quantities and relationships in problem situations.

Thinking Habits
Be a good thinker! These questions can help you.

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Does it make sense to use “minutes” as the unit for the answer to this problem? Explain.

Essential Question
How Can You Use Reasoning to Solve Problems?

Visual Learning Bridge
Eric’s family wants to arrive at a movie theater at 2:30 P.M. It takes them 30 minutes to eat lunch, 15 minutes to get ready after eating, and 30 minutes to travel to the theater.

What do I need to do to solve this problem?
I need to start with the end time. Then I need to use the time lengths given and work backward to find the starting time.

Answer:
The starting time is 1:15 P.M.

Explanation:
In the above-given question,
given that,
Eric’s family wants to arrive at a movie theater at 2:30 P.M.
It takes them 30 minutes to eat lunch.
15 minutes to get ready after eating, and 30 minutes to travel to the theater.
30 + 30 + 15 = 1 hour 15 minutes.
so the starting time is 1:15 P.M.

How can I use reasoning to solve this problem?
I can

• identify the quantities I know.
• draw a number line to show relationships.
• give the answer using the correct unit.

Here’s my thinking..
I used a number line to show the quantities and my reasoning.

30 minutes before 2:30 P.M. is 2:00 P.M.
15 minutes before 2:00 P.M. is 1:45 P.M.
30 minutes before 1:45 P.M. is 1:15 P.M.
Eric’s family should start eating lunch at 1:15 P.M.

Convince Me! Reasoning How can you check that the solution given above makes sense?

Guided Practice

Reasoning Kevin’s doctor appointment is at 10:30 A.M. It takes Kevin 30 minutes to clean his room, 20 minutes to get ready after he cleans, and 20 minutes to walk to the doctor’s office. What time should Kevin start cleaning his room? Use reasoning to decide.

Question 1.
Describe the quantities you know.

Answer:
The starting time is 9:20 A.M.

Explanation:
In the above-given question,
given that,
Kevin’s doctor appointment is at 10:30 A.M.
It takes Kevin 30 minutes to clean his room,
20 minutes to get ready after he cleans, and 20 minutes to walk to the doctor’s office.
10 : 30 – 30 = 10.
10 – 20 = 9:40.
9: 40 – 20 = 9:20.
so the starting time is 9:20 A.M.

Question 2.
Solve the problem and explain your reasoning. You can use a picture to help.

Answer:
The starting time is 9:20 A.M.

Explanation:
In the above-given question,
given that,
Kevin’s doctor appointment is at 10:30 A.M.
It takes Kevin 30 minutes to clean his room,
20 minutes to get ready after he cleans, and 20 minutes to walk to the doctor’s office.
10 : 30 – 30 = 10.
10 – 20 = 9:40.
9: 40 – 20 = 9:20.
so the starting time is 9:20 A.M.

Independent Practice

Reasoning Doreen’s favorite television show begins at 5:30 P.M. She will get her hair cut before the show. It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home. Her haircut takes 25 minutes. What time should Doreen leave home so that she will get back in time for her show? Use reasoning to decide.
Question 3.
Describe the quantities you know.

Answer:
The time should Doreen leave home so that she will get back in time for her show = 4: 45 P.M.

Explanation:
In the above-given question,
given that,
Doreen’s favorite television show begins at 5:30 P.M.
She will get her hair cut before the show.
It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home.
Her haircut takes 25 minutes.
10 + 10 + 25 = 45.
4 : 45 P.M + 45 = 5:30.
so the time should Doreen leave home so that she will get back in time for her show = 4:45 P.M.

Question 4.
Solve the problem and explain your reasoning. You can use a picture to help.

Answer:
The time should Doreen leave home so that she will get back in time for her show = 4 : 45 P.M.

Explanation:
In the above-given question,
given that,
Doreen’s favorite television show begins at 5:30 P.M.
She will get her hair cut before the show.
It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home.
Her haircut takes 25 minutes.
10 + 10 + 25 = 45.
4 : 45 P.M + 45 = 5:30.
so the time should Doreen leave home so that she will get back in time for her show = 4:45 P.M.

Question 5.
How did you know whether to use A.M. or P.M. in your answer to Exercise 4 above?

Answer:
We have to use P.M.

Explanation:
In the above-given question,
given that,
Doreen’s favorite television show begins at 5:30 P.M.
She will get her hair cut before the show.
It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home.
Her haircut takes 25 minutes.
10 + 10 + 25 = 45.
4 : 45 P.M + 45 = 5:30.
so the time should Doreen leave home so that she will get back in time for her show = 4:45.

Problem Solving

Performance Task
School Talent Show Karina is planning a talent show for 28 students. The table below tells how long each act lasts. Karina needs 5 minutes to introduce each act. She also needs to allow a 20-minute break. The break does not need to be introduced. The show must end at 9:00 P.M.

Question 6.
Be Precise What is the total time needed for all the acts before the break? Explain your thinking.

Answer:
The total time needed for all the acts before the break = 45 minutes.

Explanation:
In the above-given question,
given that,
the 3rd-grade dancers = 10 minutes.
the 3rd-grade singers = 10 minutes.
the 4th-grade singers = 10 minutes.
the 4th-grade magic act = 15 minutes.
10 + 10 + 10 + 15 = 45.
so the total time needed for all the acts before the break = 45 minutes.

Question 7.
Critique Reasoning Sachi says that the 5th grade singers should begin at 7:40 P.M. Phil says that the 5th grade singers should begin at 8:00 P.M. Who is correct?

Answer:
Phil says was correct.

Explanation:
In the above-given question,
given that,
Sachi says that the 5th-grade singers should begin at 7:40 P.M.
Phil says that the 5th-grade singers should begin at 8:00 P.M.
fifth-grade singers will sing in 10 minutes.
10 + 10 + 10 + 30 = 60.
so fifth grade singers will start at 8:00 P.M.
so Phil was correct.

Question 8.
Reasoning What time should the talent show begin? Explain your reasoning. You can draw a picture to help.

Answer:
The talent show begins at 7:15 P.M.

Explanation:
In the above-given question,
given that,
the 3rd-grade dancers = 10 min.
3rd-grade singers = 10 min.
4th-grade singers = 10 min.
4th-grade magic act = 15 min.
5th-grade singers = 10 min.
5th-grade magic act = 10 min.
5th grade dancers = 10 min.
finale = 30 min.
10 + 10 + 10 + 15 + 10 + 10 + 10 + 30 = 7:45 P.M.

Topic 14 Fluency Practice Activity

Point & Tally
Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue.
Partner 1 and Partner 2 each point to a black number at the same time. Both partners subtract the lesser number from the greater number.
If the answer is on your color, you get a tally mark. Work until one partner has seven tally marks.
While playing the game, partners can use addition to check their subtraction.

I can… add and subtract within 1,000.

Topic 14 Vocabulary Review

Understand Vocabulary
Question 1.
Cross out any units below that are NOT measurement units of capacity.
gram
inch
kilogram
hour
liter

Answer:
The not measured units of capacity are gram and kilogram.

Explanation:
In the above-given question,
given that,
the units are gram, inch, kilogram, hour, and liter.
so the not measured units of capacity are gram and kilogram.

Question 2.
Cross out any units below that are NOT measurement units of mass.
kilogram
minute
hour
gram
liter

Answer:
The units that are not measured units of mass = gram and kilogram.

Explanation:
In the above-given question,
given that,
the units are kilogram, hour, gram, and liter.
mass is measured in weight.
so the units that are not measured units of mass = gram, and kilogram.

Question 3.
Cross out any amounts below that are shown in grams or kilograms.
5 kg
2L
80 in.
250 g
12 kg

Answer:
The amounts that are shown in grams or kilograms = 5 kg, 250 g, and 12 kg.

Explanation:
In the above-given question,
given that,
the units are 5 kg, 2 l, 80 in, 250 g, and 12 kg.
so the amounts that are shown in grams or kilograms = 5 kg, 250 g, and 12 kg.

Choose the right term from the box. Write it in the blank.
Word List

• A.M.
• capacity
• elapsed time
• gram
• hour
• kilogram
• liter
• mass
• minute
• P.M.
• time interval

Question 4.
The hours between midnight and noon are ________ hours.

Answer:
The hours between midnight and noon are A.M hours.

Explanation:
In the above-given question,
given that,
the words are P.M and A.M.
so the hours between midnight and noon are:
for example,
if it is the morning we will say it is 10:30 A.M.
if it is the evening we will say it is 4:00 P.M.

Question 5.
An amount of time is a __________.

Answer:
An amount of time is a time interval.

Explanation:
In the above-given question,
given that,
if we want to know the start time and end time we will use the time interval.
so an amount of time is a time interval.

Question 6.
The hours between noon and midnight are ________ hours.

Answer:
The hours between noon and midnight are P.M hours.

Explanation:
In the above-given question,
given that,
the words are P.M and A.M.
so the hours between midnight and noon are:
for example,
if it is the morning we will say it is 10:30 A.M.
if it is an evening we will say it is 4:00 P.M.

Question 7.
1 _________ equals 1,000 grams.

Answer:
1 kilogram equals 1000 grams.

Explanation:
In the above-given question,
given that,
the words are grams and kilograms.
1 kg = 1000 grams.

Question 8.
The total amount of time that passes from the beginning time to the ending time is called the _________.

Answer:
The time that passes from beginning to ending time is elapsed time.

Explanation:
In the above-given question,
given that,
the words are beginning time and elapsed time.
for example:
beginning time is 10:00 A.M.
ending time is 1: 00 P.M.
so the elapsed time is 3 hours.

Use Vocabulary in Writing
Question 9.
Maggie wants to measure this container. Use at least 3 terms from the Word List to explain how Maggie can measure the container in different ways.

Answer:
The container is 500 grams and half kg.

Explanation:
In the above-given question,
given that,
the container is a paint bucket.
so the container weight is 500 grams and half kg.

Topic 14 Reteaching

Set A pages 533-536

What is the time to the nearest minute?

The digital time is 10:27.
It is 27 minutes after 10 o’clock or 33 minutes before 11 o’clock.

Remember that, for minutes, count numbers on the clock by 5s, then count marks by 1.

Write the time shown on each clock in two ways.
Question 1.

Answer:
The time is 12:17.

Explanation:
In the above-given question,
given that,
the hour hand is between 12 and 1.
count by 5’s from 12 to 5.
that is 5, 10, 15.
count by 1’s from 15, 16, and 17.
so the time is 12:17.

Question 2.

Answer:
The time is 6:44.

Explanation:
In the above-given question,
given that,
the hour hand is between 6 and 7.
count by 5’s from 12 to 5.
that is 5, 10, 15, 20, 25, 30, 35, 40.
count by 1’s from 40, 41,42, 43, and 44.
so the time is 6:44.

Set B pages 537-540

Tomaz starts practicing his viola at 4:25 P.M. He practices until 5:05 P.M. How much time does he practice?

The amount of time is under 1 hour, so count the minutes from the start time to the end time, by 5s.

There are 40 minutes between 4:25 P.M. and 5:05 P.M. So, Tomaz practices for 40 minutes.

Remember that you can use a clock face to find elapsed time.

In 1-3, find the elapsed time.
Question 1.
Basketball practice begins at 6:30 P.M. and lasts until 8:15 P.M. How much time does practice last?

Answer:
The time does practice last = 1:45 min.

Explanation:
In the above-given question,
given that,
Basketball practice begins at 6:30 P.M.
lasts until 8:15 P.M.
6:30 + 1 hour = 7:30.
1 hour = 60 minutes.
7:30 + 45 min = 8:15.
so the time is 1:45 min.

Question 2.
Mr. Walters starts preparing breakfast at 6:45 A.M. He finishes at 7:50 A.M. How long does it take for him to prepare breakfast?

Answer:
The time it takes for him to prepare breakfast = 1 hour 5 min.

Explanation:
In the above-given question,
given that,
Mr. Wallets starts preparing breakfast at 6:45 A.M.
He finishes at 7:50 A.M.
7:50 – 6:45 = 1:05.
so the time it takes for him to prepare breakfast = 1 hour 5 min.

Question 3.
Jean goes for a horseback ride. She leaves the barn on her horse at 2:10 P.M., and comes back at 2:50 P.M. How long was her ride?

Answer:
The long was her ride = 40 min.

Explanation:
In the above-given question,
given that,
Jean goes for a horseback ride.
She leaves the barn on her horse at 2:10 P.M.
and comes back at 2:50 P.M.
2:50 – 2:10 = 40.
so the long was her ride = 40 min.

Set C pages 541-544

You can show addition and subtraction of time intervals on a number line.
In the morning, Xavier runs for 19 minutes. In the evening, he runs for 27 minutes. How much time does he spend running in all?

19 + 27 = ?
19 + 27 = 46
So, Xavier runs for 46 minutes.

Remember to decide whether you need to add or subtract.

In 1, solve by drawing a number line or a bar diagram.
Question 1.
It takes Don 52 minutes to drive to work. He has already driven for 16 minutes. How many more minutes will it take Don to drive to work?

Answer:
The more minutes will it take Don to drive to work = 36 minutes.

Explanation:
In the above-given question,
given that,
It takes Don 52 minutes to drive to work.
He has already driven for 16 minutes.
52 – 16 = 36.
so the more minutes will it take Don to drive to work = 36 minutes.

Set D pages 545-548

Estimate the capacity of a pitcher.

Think about what you already know. A liter is about the same size as a large water bottle. A pitcher usually holds more liquid than a water bottle. So, 2 liters seems like a good estimate.

Remember that capacity can be measured using liters.

In 1-4, circle the better estimate.

Question 1.

1 L or 10 L

Answer:
The better estimation of a bottle is 1 l.

Explanation:
In the above-given question,
given that,
the given measurements are 1 L or 10 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a bottle is 1 liter.

Question 2.

\(\frac{1}{4}\) L or 8 L

Answer:
The better estimation of a bucket is 8 l.

Explanation:
In the above-given question,
given that,
the given measurements are 1/4 L or 8 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a bucket is 8 liter.

Question 3.
Drinking glass
5 L or \(\frac{1}{2}\) L

Answer:
The better estimation of drinking glass is 1/2 l.

Explanation:
In the above-given question,
given that,
the given measurements are 5 L or 1/2 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a drinking bottle is 1/2 liter.

Question 4.
Washing machine
40 L or 4L

Answer:
The better estimation of a washing machine is 40 l.

Explanation:
In the above-given question,
given that,
the given measurements are 40 L or 4 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a washing machine is 40 liter.

Set E pages 549-552

How much water is in this beaker?
Use the scale to determine how full the beaker is. Think of the scale as a number line. Each mark represents 1 liter. The water is 3 marks : – 10 liters above 5 liters.

There are 8 liters in the beaker.

Remember to use the correct units when measuring capacity.

In 1 and 2, find the total capacity.
Question 1.

Answer:
The total capacity of two beakers = 3 liters.

Explanation:
In the above-given question,
given that,
the 1st beaker contains 1 n 1/2 liter.
the 2nd beaker contains 1 n 1/2 liter.
1.5 + 1.5 = 3 liters.
so the total capacity of two beakers = 3 liters.

Question 2.

Answer:
The total capacity of the beaker = 6 liters.

Explanation:
In the above-given question,
given that,
the 1st beaker contains 6 liters.
5 + 1 = 6 liters.
so the total capacity of beakers = 6 liters.

Set F pages 553-556

Estimate the mass of a battery.

A kilogram is too heavy, so estimate using grams.

Think about what you already know. A gram is about the same weight as a grape. A battery weighs about as much as a bunch of grapes. So 30 grams seems like a good estimate.

Remember that mass can be measured using grams and kilograms.

In 1-6, circle the better estimate for the mass.
Question 1.

15 g or 15 kg

Answer:
The better estimation of the pen is 15 g.

Explanation:
In the above-given question,
given that,
the given measurements are 15 g or 15 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a washing machine is 15 g.

Question 2.

500 g or 500 kg

Answer:
The better estimation of the pen is 500 g.

Explanation:
In the above-given question,
given that,
the given measurements are 500 g or 500 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a washing machine is 500 g.

Question 3.
One sheep
800 g or 80 kg

Answer:
The better estimation of sheep is 80 kg.

Explanation:
In the above-given question,
given that,
the given measurements are 800 g or 80 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a sheep is 80 kg.

Question 4.
Bag of flour
2 g or 2 kg

Answer:
The better estimation of the bag of flour is 2 kg.

Explanation:
In the above-given question,
given that,
the given measurements are 2 g or 2 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a bag of flour is 2 kg.

Question 5.
Notebook computer
3 g or 3 kg

Answer:
The better estimation of the Notebook computer is 3 kg.

Explanation:
In the above-given question,
given that,
the given measurements are 3 g or 3 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a washing machine is 3 kg.

Question 6.
Quarter
5 g or 500 g

Answer:
The better estimation of the Quarter is 500 g.

Explanation:
In the above-given question,
given that,
the given measurements are 5 g or 5 00 g.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a quarter is 500 g.

Set G pages 557-560

What is the mass of this bar of soap?

When a pan balance is even, the mass on the left side equals the mass on the right side.
Find the total of the weights on the left side. Use mental math and place value to help add.
100 + 10 + 5 + 1 + 1 + 1 = 118
The bar of soap has a mass of 118 grams.

Remember to use the correct units when measuring mass.

In 1 and 2, find the total mass.
Question 1.

Answer:
The total mass is 701g.

Explanation:
In the above-given question,
given that,
they have given 1 500 g.
2 100 g.
1 hundred g.
500 + 200 + 1 = 701.
so the total mass is 701 g.

Question 2.

Answer:
The total mass is 2210 g.

Explanation:
In the above-given question,
given that,
they have given 1 100 kg.
2 100 g.
2 5 g.
1000 + 1000 + 200 +10 = 2210.
so the total mass is 2210 g.

Set H pages 561-564

There are 7 people bowling together. Each owns their own bowling ball. The mass of each bowling ball is 5 kilograms. What is the total mass of the team’s bowling balls?

Remember that you can use bar diagrams or equations to represent problems.

In 1 and 2, use bar diagrams or equations to help solve.
Question 1.
The water tank in Mary’s yard holds 60 liters of water. She used 13 liters to water her plants. How many liters of water remain in the water tank?

Answer:
The quantity of water that remains in the water tank = 47 liters.

Explanation:
In the above-given question,
given that,
the water tank in mary’s yard holds 60 liters of water.
she used 13 liters to water her plants.
60 – 13 = 47.
so the quantity of water remains in the water tank = 47 liters.

Question 2.
Eric has 3 dogs that each have a mass of 8 kilograms. What is the total mass of all of Eric’s dogs?

Answer:
The total mass of all of Eric’s dogs = 24 kg.

Explanation:
In the above-given question,
given that,
Eric has 3 dogs that each have a mass of 8 kilograms.
8 x 3 = 24.
24 /8 = 3.
so the total mass of all of Eric’s dogs = 24 kg.

Set I pages 565-568

Think about these questions to help you reason abstractly and quantitatively.
Thinking Habits

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?
  

Remember to consider the units in the information you are given.

At 1:00 P.M., Ted will meet a friend in the park.. Ted needs 30 minutes to walk to the park. Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch. When must Ted start to prepare lunch?
Question 1.
Describe the quantities you know.

Answer:
Ted start to prepare lunch = 12:05 P.M.

Explanation:
In the above-given question,
given that,
Ted will meet a friend in the park.
Ted needs 30 minutes to walk to the park.
Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch.
30 + 15 + 10 = 55 minutes.
so ted start to prepare lunch = 12:05 P.M.

Question 2.
How can you show the relationships in this problem?

Answer:
Ted start to prepare lunch = 12:05 P.M.

Explanation:
In the above-given question,
given that,
Ted will meet a friend in the park.
Ted needs 30 minutes to walk to the park.
Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch.
30 + 15 + 10 = 55 minutes.
so ted start to prepare lunch = 12:05 P.M.

Question 3.
When must Ted start to prepare lunch?

Answer:
Ted start to prepare lunch = 12:05 P.M.

Explanation:
In the above-given question,
given that,
Ted will meet a friend in the park.
Ted needs 30 minutes to walk to the park.
Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch.
30 + 15 + 10 = 55 minutes.
so ted start to prepare lunch = 12:05 P.M.

Topic 14 Assessment Practice

Question 1.
Draw hands on the clock to show 8:36. What time will it be in 2 hours and 6 minutes?

Answer:
The time is 6:42.

Explanation:
In the above-given question,
given that,
the hour hand is on the 8.
the minute hand is on the 8.
the second’s hand is on the 42.
so the time is 6:42.

Question 2.
Jessica and Cody ran a long-distance race during an afternoon. The start times were different so that all the runners did not start at the same time. Who finished faster, and by how many minutes?

A. Jessica; 5 minutes faster than Cody
B. Cody; 5 minutes faster than Jessica
C. Jessica; 10 minutes faster than Cody
D. They finished in the same amount of time.

Answer:
Option D is the correct answer.

Explanation:
In the above-given question,
given that,
Jessica and Cody ran a long-distance race during the afternoon.
The start times were different so that all the runners did not start at the same time.
Jessica starts at 3:55 and ends at 4:40.
Cody starts at 4:15 and ends at 5:05.
5:05 – 4:15 = 90 min.
4:40 – 3:55 = 85 min.
so option D is the correct answer.

Question 3.
Two stores in a small town sell bags of apples. At Store A, each bag weighs 2 kilograms. At Store B, each bag weighs 4 kilograms. If you buy 6 bags at each store, how many more kilograms of apples will you buy from Store B?

Answer:
The kilograms of apples will you buy from store B = 24 kg.

Explanation:
In the above-given question,
given that,
Two stories in a small town sell bags of apples.
At Store A, each bag weighs 2 kilograms.
At Store B, each bag weighs 4 kilograms.
6 x 2 = 12 kg.
4 x 6 = 24 kg.
so the number of kilograms of apples will you buy from store B = 24 kg.

Question 4.
Name the metric unit that could be used to measure the capacity of a kitchen sink. Then, using that unit, write a reasonable estimate for the capacity of a kitchen sink.

Answer:
The reasonable estimate for the capacity of a kitchen sink = 30 kg.

Explanation:
In the above-given question,
given that,
the unit is kg.
the weight of the kitchen sink is 30 kg.
so the reasonable estimate for the capacity of a kitchen sink = 30 kg.

Question 5.
A. Mason is looking for a tool to measure the mass of an apple. Which tool should he use?
A. Pan balance
B. Ruler
C. 1-cup container
D. Clock

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
the units are panned balance, ruler, 1-cup container, and clock.
pan balance is used to measure the mass of an apple.
so option A is correct.

B. Using the tool identified in Part A, what unit will Mason use to measure the mass of the apple?
A. Grams
B. Minutes
C. Cups
D. Inches

Answer:
Grams are the unit that measures the mass of the apple.

Explanation:
In the above-given question,
given that,
the units are grams, minutes, cups, and inches.
mass of the apple is measured in grams.
so grams is the unit that measures the mass of the apple.

Question 6.
Dale’s school bus picks him up at 7:45 A.M. To get ready for school, Dale needs 15 minutes to eat breakfast, 10 minutes to make lunch, and 10 minutes to get dressed. What time does Dale need to begin getting ready for school?
A. Describe the quantities you know.

Answer:
Dale needs to get ready for school = 7:10.

Explanation:
In the above-given question,
given that,
Dale’s school bus picks him up at 7:45 A.M.
To get ready for school, Dale needs 15 minutes to eat breakfast, 10 minutes to make lunch, and 10 minutes to get dressed.
15 + 10 + 10 = 35 min.
7:45 – 35 = 7:10.
so Dale needs to getting ready for school = 7:10

B. Solve the problem. Explain your reasoning. You can use a picture to help.

Answer:
Dale needs to get ready for school = 7:10.

Explanation:
In the above-given question,
given that,
Dale’s school bus picks him up at 7:45 A.M.
To get ready for school, Dale needs 15 minutes to eat breakfast, 10 minutes to make lunch, and 10 minutes to get dressed.
15 + 10 + 10 = 35 min.
7:45 – 35 = 7:10.
so Dale needs to getting ready for school = 7:10

Question 7.
Mary has a total of 18 liters of water in 6 bottles. Jess has a total of 15 liters in 3 bottles. If the bottles are equally filled, how much more water is in each of Jess’s bottles than in Mary’s bottles?

Answer:
One more bottle of water is filled in Jess.

Explanation:
In the above-given question,
given that,
Mary has a total of 18 liters of water in 6 bottles.
Jess has a total of 15 liters in 3 bottles.
18/6 = 3.
15/3 = 5.
15 + 3 = 18.
so one more bottle of water is filled in Jess.

Question 8.
Eric played the guitar for 33 minutes on Monday and 19 minutes on Tuesday. Write and solve an equation to find how many more minutes Eric played the guitar on Monday.

Answer:
The more minutes Eric played the guitar on Monday = 14 min.

Explanation:
In the above-given question,
given that,
Eric played the guitar for 33 minutes on Monday and 19 minutes on Tuesday.
33 – 19 = 14.
so the more minutes eric played the guitar on Monday = 14 min.

Question 9.
Mrs. Griggs writes a shopping list saying she needs to buy 1 gram of apples. Is this reasonable? Explain.

Answer:
No, it is not reasonable.

Explanation:
In the above-given question,
given that,
Mrs. Griggs writes a shopping list saying she needs to buy 1 gram of apples.
1000 grams = 1 kg.
the mass of the apple is 100 g.
so it is not reasonable.

Question 10.
Irene measured the mass of a bag of apples using kilograms. Forest measured the same bag using grams. How did the measurements compare? Select all the sentences that are true.
☐ There were more grams than kilograms.
☐ There were more kilograms than grams.
☐ There was an equal number of grams and kilograms.
☐ There were fewer grams than kilograms.
☐ There were fewer kilograms than grams.

Answer:
Options A, C, and E are correct.

Explanation:
In the above-given question,
given that,
Irene measured the mass of a bag of apples using kilograms.
Forest measured the same bag using grams.
there were more grams than kilograms.
there was an equal number of grams and kilograms.
there were fewer kilograms than grams.
so options A, C, and E are correct.

Question 11.
Jason said the mass of his book is about 1 kilogram. Julie said it is 1 liter. Who is correct? Select the best answer.
A. Jason is correct because kilograms are units of mass, and liters are units of capacity.
B. Julie is correct because liters are metric units.
C. They are both correct because kilograms and liters are units of mass.
D. Neither is correct because their estimates are not reasonable.

Answer:
The best answer is option A.

Explanation:
In the above-given question,
given that,
Jason said the mass of his book is about 1 kilogram.
Julie said it is 1 liter.
Jason is correct because kilograms are units of mass and liters are units of capacity.
so Option A is correct.

Question 12.
Explain why it would be better to use grams rather than kilograms to measure the mass of a crayon.

Answer:
It is better to use grams.

Explanation:
In the above-given question,
given that,
crayon is a very small object.
it is measured in grams.
so it is better to use grams for crayons.

Question 13.
It took Wallace 45 minutes to read part of a chapter of his science book. He finished reading the rest of the chapter in 17 minutes. Write and solve an equation to find how much time Wallace spent reading the chapter.

Answer:
The time he spent reading the chapter is 62 minutes.

Explanation:
In the above-given question,
given that,
It took Wallace 45 minutes to read part of a chapter of his science book.
He finished reading the rest of the chapter in 17 minutes.
45 + 17 = 62.
so the time he spent reading the chapter is 62 minutes.

Question 14.
Four brothers, Raphael, Don, Leo, and Mike, went to the gym to exercise. Don and Mike both started at 2:21 P.M. and exercised for 33 minutes. Raphael and Leo both started when Don and Mike finished and exercised until 3:36 P.M. For how many minutes did the brothers exercise in total?

Answer:
The number of minutes the brothers exercise in total = 75 minutes

Explanation:
In the above-given question,
given that,
Four brothers, Raphael, Don, Leo, and Mike, went to the gym to exercise.
Don and Mike both started at 2:21 P.M. and exercised for 33 minutes.
Raphael and Leo both started when Don and Mike finished and exercised until 3:36 P.M.
33 + 2:21 = 2:54.
3:36 – 2:54 = 82.
42 + 33 = 75.
so the number of minutes the brothers exercise in total = 75 minutes.

Question 15.
Mark used a pan balance to find the mass of his basketball. He said it was 580 kilograms. Is his answer reasonable? Explain.

Answer:
No, his answer was not reasonable.

Explanation:
In the above-given question,
given that,
Mark used a pan balance to find the mass of his basketball.
He said it was 580 kilograms.
the mass of the basketball is 5 kgs.
so the answer not reasonable.

Question 16.
Look at the time on the clock below.

A. Select all of the ways to write this time.
☐ 3 : 46
☐ 14 minutes before 4 o’clock
☐ 46 minutes after 3 o’clock
☐ 9 minutes before 4 o’clock
☐ 4 : 14

Answer:
Option A is the correct answer.

Explanation:
In the above-given question,
given that,
the hour hand is in between 3 and 4.
the minute’s hand is in between 9 and 10.
5 x 9 = 45.
45 + 1 = 46.
so Option A is the correct answer.

B. What time was it 2 hours, 45 minutes ago?

Answer:
The time was 1 hour 1 minute.

Explanation:
In the above-given question,
given that,
the time is 3:46.
3:46 – 2:45 = 1:01.
so the time is 1 hour 1 minute.

Question 17.
Maryann went to the grocery store at 3:10 P.M. She arrived home 1 hour, 15 minutes later.
A. What time did she arrive home?

Answer:
The time did she arrive = 4:25.

Explanation:
In the above-given question,
given that,
Maryann went to the grocery store at 3:10 P.M.
she arrived home 1 hour 15 minutes later.
3:10 + 1:15 = 4:25.
so the time did she arrive = 4:25.

B. Her neighbor Betty Sue got to the grocery store at the same time as Maryann and got home at 4:02 P.M. How much less time did Betty Sue spend shopping?

Answer:
The less time did Betty Sue spend shopping is 23 minutes.

Explanation:
In the above-given question,
given that,
Her neighbor Betty Sue got to the grocery store at the same time as Maryann and got home at 4:02 P.M.
4:25 – 4:02 = 23.
so the less time did Betty Sue spend shopping is 23 minutes.

Question 18.
Ricardo used 337 grams of flour to bake in the afternoon. He had already used 284 grams of flour to bake in the morning. Write and solve an equation to find how many grams of flour Ricardo used in all.

Answer:
The number of grams of flour Ricardo used in all = 53 g.

Explanation:
In the above-given question,
given that,
Ricardo used 337 grams of flour to bake in the afternoon.
He had already used 284 grams of flour to bake in the morning.
337 + a = 284.
a = 337 – 284.
a = 53.
so the number of grams of flour Ricardo used in all = 53 g.

Question 19.
A tank contained 750 liters of water. After some water drained out, the tank had 250 liters of water. Write and solve an equation to find how many liters of water drained out.

Answer:
The number of liters of water drained out = 500 liters.

Explanation:
In the above-given question,
given that,
A tank contained 750 liters of water.
After some water drained out, the tank had 250 liters of water.
750 + w = 250.
w = 750 – 250.
w = 500.
so the number of liters of water drained out = 500 liters.

Topic 14 Performance Task

Family Reunion
Anita and her brother Logan make plans for a family reunion.

Question 1.
Use the Fruit Bought table to answer the question. Logan estimated the mass of the fruit. He forgot to include the unit of mass. For each item, explain if he used a gram or kilogram.

Answer:
The missing values of mass are 4 kg, 90 g, and 3 kgs.

Explanation:
In the above-given question,
given that,
the estimated unit of the mass is grape is 4 kg.
one lemon has an estimated mass of 90 g.
the mass of the watermelon is 3 kgs.
so the missing values of mass are 4kg, 90 g, and 3 kgs.

Question 2.
Use the Mass of One Lime picture to answer the questions.

Part A
Each lime has the mass shown at the right. What is the mass of one lime?

Answer:
The mass of one lime is 30 g.

Explanation:
In the above-given question,
given that,
there is 3 mass of lime.
10 + 10 + 10 = 30.
3 x 10 = 30.
so the mass of one lime is 30 g.

Part B
Logan needs to buy at least 200 grams of limes. He plans to buy 7 limes. Will he buy enough? Use your response to Part A to explain.

Answer:
Yes, he will buy enough limes.

Explanation:
In the above-given question,
given that,
Logan needs to buy at least 200 grams of limes.
He plans to buy 7 limes.
7 x 30 = 210.
so he will buy enough limes.

Question 3.
Use the Liquids Needed table to answer the question.
Logan measures the liquids they need. Complete the table to show if the capacity of each container will likely be less than or greater than 1 liter.

Answer:
The container contains a spoon of vinegar, milk, and water.

Explanation:
In the above-given question,
given that,
the ingredients are vinegar, milk, and water.
the spoon of vinegar is measured in grams.
the measuring cup of milk is liters.
the large pot is measured in kilograms.

The Broth Used picture shows the amount of broth that Anita started with and the amount she had left after she poured some into two different soups.

Question 4.
Use the Broth Used picture to answer the questions.
Part A
How much broth did Anita use?

Answer:
The amount Anita used is 22 liters.

Explanation:
In the above-given question,
given that,
The Broth Used picture shows the amount of broth that Anita started with and the amount she had left.
20 + 2 = 22.
so the amount Anita used is 22 liters.

Part B
Anita poured an equal amount of broth into 2 pots. How much did she pour into 1 pot?

Answer:
The water she poured into 1 pot = 20 liters.

Explanation:
In the above-given question,
given that,
Anita poured an equal amount of broth into 2 pots.
Anita poured 20 liters in 1 both.
she poured 2 liters in 2nd both.
20 + 2 = 22.
so the water she poured into 1 pot = 20 liters.

Question 5.
Logan’s recipe says it takes 50 minutes to cook chicken. After 22 minutes pass, Logan flips the chicken. How many more minutes does the chicken have to bake after Logan flips it? Show your work on a number line.

Answer:
The many more minutes does the chicken have to bake after logan flips it = 28 minutes.

Explanation:
In the above-given question,
given that,
Logan’s recipe says it takes 50 minutes to cook chicken.
After 22 minutes pass, Logan flips the chicken.
50 – 22 = 28.
so the more minutes does the chicken have to bake after logan flips it = 28 minutes.

Question 6.
Use the Before Reunion table to answer the question.

Anita and Logan want to be at the reunion at 1:45 P.M. They need to clean, pack, and drive to the reunion. What time should they start? Explain.

Answer:
The time should they start = 12:15 P.M.

Explanation:
In the above-given question,
given that,
Anita and Logan want to be at the reunion at 1:45 P.M.
they have to clean for 20 min.
they have to pack for 15 min.
they have to drive for 55 min.
20 + 15 + 55 = 90.
1 hour = 60 min.
90 min = 1 and half hours.
1:45 – 12:15 = 1:30.
so the time should they start = 12:15 P.M.

Go through the enVision Math Common Core Grade 2 Answer Key Topic 10 Add Within 1,000 Using Models and Strategies regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 10 Add Within 1,000 Using Models and Strategies

enVision STEM Project: Building Up to 1,000

Find Out Use drinking straws and pieces of tape. The total number of straws and pieces of tape cannot be more than 1,000. First, decide how many of each to use. Then share. Build the tallest buildings you can.
Journal: Make a Book Describe your building in a book. In your book, also:

• Tell how many drinking straws and pieces of tape you used.
• Tell how you would make a better building if you did it again.

Review What You Know

Vocabulary

Question 1.
Circle all of the hundreds digits in the numbers below.

Answer:

Explanation:
The digit place
Thousands   Hundreds   Tens  Ones
5                0       2
5       8
1              0                0       0
5 and 0 are in the hundreds place and these values are circled.

Question 2.
Write the expanded form of the number.
846
____
Answer:
800 + 40 + 6 is the expanded form of 846.
Explanation:
Given number is a three digit number
8 in Hundreds place
4 in Tens place
6 in Ones place

Question 3.
Write the word form of the number.
265
_____
Answer:
265 = Two hundred and sixty five.
Explanation:
Given number is a three digit number
2 in Hundreds place
6 in Tens place
5 in Ones place

Open Number Lines

Question 4.
Use the open number line to find the sum.

54 + 13 = ___
Answer:
54 + 13 = 67

Mental Math

Question 5.
Use mental math to find each sum.
40 + 37 = ____
6 + 77 + 4 = ___
Answer:
40 + 37 = 40 + (30 + 7) = (40 + 30) + 7 = 70 + 7 = 77.
6 + 77 + 4 = (6 + 4) + 77 = 10 + 77 = 87.
Explanation:
Mental math we break the number of one addend and then giving park of one addend to the other addend.
Here in 40 + 37
we break 37 as 30 + 7
now we add 40 + 30 =70 + 7 = 77.
This simplify the adding of numbers.
In 2nd Sum
6 + 77 + 4
we add 6 + 4 =10 and then 10 + 77 = 87.

Partial Sums

Question 6.
Use partial sums to add.

Answer:

Explanation:
Using partial sum
we add the place values of the numbers separately.
Hundreds place value + Hundreds place value
Tens place value + Tens place value
Ones place value + Ones place value
Here
46 + 53 = (40+50) + (6 + 3) = 90 + 9 = 99
29 + 61 = (20 + 60) + (9 + 1) = 80 + 10 = 90.

pick a Project

PROJECT 10A

What are the run times of two of your favorite movies?
Project: Write Movie Reviews

PROJECT 10B

How many shots do basketball teams block?
Project: Make a Basketball Poster

PROJECT 10C
How many miles are between a State Capital and other cities?
Project: Draw a State Map

PROJECT 10D
How far can people hike in the Sierra Nevada Mountains?
Project: Create a Hiking Guide

Lesson 10.1 Add 10 and 100

Solve & Share

Activity

Forest Park Nursery sells trees.
Sal buys a maple tree for $125. A spruce free costs $10 more than a maple tree. An elm tree costs $100 more than a maple tree. What is the cost of a spruce tree? An elm tree?
Use dollar bills, place-value blocks, or mental math to solve. Be ready to explain how you solved the problem.

Visual Learning Bridge

Convince Me!
Use mental math to find 567 + 10 and 567 + 100. Explain your reasoning.

Guided Practice
Add. Use place-value blocks or mental math.

Question 1.

Answer:

Question 2.

Answer:

Explanation:
The square cube represents 100 square and hundreds place
cube stick represents 10 cubes and tens place
single cube represents 1 cube and ones place.
In the above image
(4 square cube + 1 cube stick + 2 cubes) + 1 cube stick
(400 + 10 + 2) + 10
Adding tens place
10 +10 = 20
the value of the  image = 400+20+2=422.

Question 3.

Answer:

Explanation:
The square cube represents 100 square and hundreds place
cube stick represents 10 cubes and tens place
single cube represents 1 cube and ones place.
In the above image
(3 square cube + 2 square cube) + 1 square cube
(300 + 200) + 100
Adding hundreds place
500 + 100 = 600
the value of the  image = 500 + 100 = 600.

Question 4.

Answer:

Explanation:
The square cube represents 100 square and hundreds place
cube stick represents 10 cubes and tens place
single cube represents 1 cube and ones place.
In the above image
(2 square cube + 5 cube stick + 3 cubes) + 1 Square cube
(200 + 50 + 3) + 100
Adding Hundreds place values
200 + 100 = 300
the value of the  image = 400+20+2=422.

Independent Practice
Add. Use place-value blocks or mental math.

Question 5.
164 + 100 =
Answer:
Using mental math
164 + 100
Dividing 164 into smaller parts
= (100 + 64 ) + 100
Now adding hundreds place values
100 + 100 = 200
200 + 64 = 264.
Sum = 264.

Question 6.
$837 + $10 = ___
Answer:
Using mental math
837 + 10
Dividing 837 into smaller parts
(800 + 30 + 7 ) + 10
Adding tens places
30 + 10 = 40
800+40+7 = 847.
Sum = $847.

Question 7.
329 + 100 = ___
Answer:
Using mental math
329 + 100
Dividing 329 into smaller parts
(300+ 20 + 9) + 100
Adding hundreds place
300+ 100 = 400
400+20+9 = 429
Sum = 429.

Question 8.
610 + 10 = ___
Answer:
Dividing 610 into its smaller values
(600 + 10 ) + 10
Adding tens places
10+10 = 20
= 600 + 20 =  620.
Sum = 620.

Question 9.
295 + 10 = ___
Answer:

Question 10.
$497 + $100 = ___
Answer:

Question 11.
790 + 10 = ___
Answer:
Dividing 790 into its smaller values
(700 + 90 ) + 10
Adding tens places
90+10 = 100
= 700 + 100 =  800.
Sum = 800.

Question 12.
693 + 100 = ___
Answer:
Dividing 693 into its smaller values
(600 + 90 + 3 ) + 100
Adding hundreds places
6 + 1 = 7
= 600 + 100 =  700.
= 700 + 90 + 3
= 793
Sum = 793.

Question 13.
900 + 100 = ___
Answer:

Question 14.
460 + 10 = ___
Answer:
Dividing 460 into its smaller values
(400 + 60 ) + 10
Adding tens places
6 + 1 = 7
= 60 + 10 =  70.
=400 + 70
= 470
Sum = 470.

Question 15.
185 + 10 = ___
Answer:
Dividing 185 into its smaller values
(100 + 80 + 5 ) + 10
Adding Tens places
8 + 1 = 9
= 80 + 10 =  90.
=100 + 90 + 5
= 195
Sum = 195.

Question 16.
723 + 100 = ___
Answer:
Dividing 723 into its smaller values
(700 + 20 + 3 ) + 100
Adding hundreds places
7 + 1 = 8
= 700 + 100 =  800.
= 800 + 20 + 3
= 823
Sum = 823.

Algebra Find the missing numbers. Use mental math to solve.

Question 17.
572 + = 672
Answer:
Given
One addend 572 and
Sum 672
Both are 3-digit number
Hundred  Tens  Ones
5              7        2
6              7        2
The values in the tens place and ones place are same but the values in the hundreds place are different
Subtract the hundreds place values
6 – 5 = 1
600 – 500 = 100.
The missing addend is 100.
572 + 100 = 672.

Question 18.
285 + = 385
Answer:
Given
One addend 285 and
Sum 385
Both are 3-digit number
Hundred  Tens  Ones
2              8        5
3              8        5
The values in the tens place and ones place are same but the values in the hundreds place are different
Subtract the hundreds place values
3 – 2 = 1
300 – 200 = 100.
The missing addend is 100.
285 + 100 = 385.

Question 19.
709 = 699 +
Answer:
Given
One addend 699 and
Sum 709
Both are 3-digit number
Hundred  Tens  Ones
6              9       9
7              0       9
The values in the  ones place are same but the values in the tens and hundreds place are different
Adding 1 to  the tens place values
9 + 1 = 10
Now the value in the tens place is 0 and 1 is carried to the hundreds place
1 is added to hundreds place vale
6 + 1 = 7
10 is the missing number.
699 + 10 = 709.

Question 20.
422 = 322 +
Answer:
Given
One addend 422 and
Sum 322
Both are 3-digit number
Hundred  Tens  Ones
3             2        2           -Addend
4              2        2           – Sum
The values in the tens place and ones place are same but the values in the hundreds place are different
Subtract the hundreds place values
4 – 3 = 1
400 – 300 = 100.
The missing addend is 100.
322 + 100 = 422.

Question 21.
615 + = 625
Answer:
Given
One addend 699 and
Sum 709
Both are 3-digit number
Hundred  Tens  Ones
6              1       5       –   Addend
6              2       5       – Sum
The values in the  ones place and hundreds place are same but the values in the tens are different
subtracting   the tens place values
2 – 1 = 1
Now adding 1 to the addends tens place
1 + 1 = 2
10 is the missing number.
615 + 10 = 625.

Question 22.
600 = + 590
Answer:
Given
One addend 590 and
Sum 600
Both are 3-digit number
Hundred  Tens  Ones
5              9       0
6              0        0
The values in the  ones place are same but the values in the tens and hundreds place are different
Adding 1 to  the tens place values of addend
9 + 1 = 10
Now the value in the tens place is 0 and 1 is carried to the hundreds place
1 is added to hundreds place vale
5 + 1 = 6
10 is the missing number.
590 + 10 = 600.

Problem Solving

Solve each problem. Show your work.

Question 23.
enVision® STEM The Science Club asked 178 people about recycling. The club wants to ask a total of 188 people about recycling. How many more people will the Science Club need to ask?
___ more people
Answer:
Number of people The Science Club asked about recycling = 178 people
Total number of people The Science Club wants to ask about recycling = 188 people.
Number of more people  The Science Club need to ask = 188 – 178 = 10.
10 more people.
Th given number is 3 digit number
Hundred place   Tens place   Once place
1                      8                   8
1                      7                   8
The Hundreds place value and ones place values are same. but the tens place value is different
8 – 7 = 1
80 – 70 = 10.
10 more people.

Question 24.
Use Structure Jordan has four $100 bills, three $20 bills, one $10 bill, and seven $1 bills. What will Jordan’s total be if Jayla gives him one more $10 bill? What will his total be if she gives him one more $100 bill?

Answer:
Number of $100 bills Jordan has = 4
Number of $20 bills Jordan has = 3
Number of $10 bills Jordan has = 1
Number of $1 Jordan has = 7
Number of $10 bills Jayla gave to Jordan = 1
Total money Jordan have after adding Jayla’s $10 bill = $400 + $60 + $10 + $10 + $7 = $487
Jayla gave more $100 bill to Jordan
Total money Jordan have after adding 1 more $100 bill = $487 + $100 = $587.
The value of the hundreds place  = 4
adding 1
4 + 1 = 5.
The value of the hundreds place is 5. The remaining values remain same.
Total money Jordan has = $587.

Question 25.
Higher Order Thinking Think of a 3-digit number. Write a story about adding 100 to your number. Then write an equation to show your solution.

Answer:
A hotel has 250 rooms. Their is an event organized at the hotel the hotel is booked completely. Before the day of event there are 150 rooms filled. How many rooms need to be filled?
Number of room filled = 150
Total number of rooms in the hotel = 250
Number of more rooms to be filled = 250 – 150 = 100 rooms.
100 more rooms need to be filled.
Here the tens and ones place values are same but the Hundreds place value is different.
2 – 1 = 1
The difference in the hundreds place value is 1.
The difference is 100.

Question 26.
Assessment Practice Which equations are true? Choose all that apply.
$251 + $10 = $351
528 + 100 = 628
528 + 10 = 538
$251 + $100 = $351
Answer:
The Equations that are true are
2. 528 + 100 = 628
Adding the hundreds place values
5 + 1 = 6
Sum = 528 + 100 =  628
3. 528 + 10 = 538
Adding the tens places
2 + 1 = 3
Sum = 528 + 10 = 538.
4. $251 + $100 = $ 351
Adding the hundreds place values
2 + 1 = 3
Sum = $251 + $100 =  $351

Lesson 10.2 Add on an Open Number Line

Activity

Solve & Share

Use the open number line to find 598 + 123. Explain your work.

Visual Learning Bridge

Convince Me!
Explain how you can use an open number line to find 599 + 205.

Guided Practice
Use an open number line to find each sum.

Question 1.
375 + 118 = ___

Answer:

Explanation:
Here we are breaking the addend into hundreds , tens, ones which does not change its value.
The equation is 375 + 118
118 is the addend
Breaking the addend 118
118 = 100+ 10+5+3
So, adding these to 375
375+100=475
475+10 = 485
485+  5 =   490
490 + 3=  493
375 +118 = 493.

Question 2.
670 + 232 = ___

Answer:

Explanation:
Here we are breaking the addend into hundreds , tens, ones which does not change its value.
The equation is 670 + 232
232 is the addend
Breaking the addend 232
232 = 100+ 100 + 20 + 10 + 2
So, adding these to 670
670 +100 = 770
770 +100 = 870
870 + 20 = 890
890 + 10 = 900
900 + 2 =  902
670 + 232 = 902.

Independent Practice
Use an open number line to find each sum.

Question 3.
269 + 156 = ___

Answer:

Explanation:
Here we are breaking the addend into hundreds , tens, ones which does not change its value.
The equation is 269 + 156
156 is the addend
Breaking the addend 156
156 = 100 + 20 + 20 + 10 + 5 + 1
So, adding these to 269
269 + 100 = 369
369 + 20 = 389
389 + 20 = 409
409 + 10 =  419
419 + 5 = 424
424 + 1 = 425

Question 4.
637 + 242 = ___

Answer:

Explanation:
Here we are breaking the addend into hundreds , tens, ones which does not change its value.
The equation is 637 + 242
242 is the addend
Breaking the addend 242
242 = 100+ 100 + 20 + 20 + 2
So, adding these to 637
637 +100 = 737
737 +100 = 837
837 + 20 = 857
857 + 20 = 877
877 + 2 = 879
637 + 242 = 879.

Question 5.
886 + 114 = ___

Answer:

Explanation:
Here we are breaking the addend into hundreds , tens, ones which does not change its value.
The equation is 886 + 114
114 is the addend
Breaking the addend 114
114 = 100+ 10 + 4
So, adding these to 886
886 +100 = 986
986 +10 = 996
996 + 4 = 1000
886 + 114 = 1000.

Question 6.
208 + 598 =

Answer:

Explanation:
Here we are breaking the addend into hundreds , tens, ones which does not change its value.
The equation is 208 + 598
598 is the addend
Breaking the addend 598
598 = 100+ 100 + 100 + 100 + 100 + 50 + 40 + 5 + 3
598 = 500 + 50+ 40 + 5 + 3
So, adding these to 208
208 + 100 = 308
308 + 100 = 408
408 + 100 = 508
508 + 100 = 608
608 + 100 = 708
708 + 50 = 758
758 + 40 = 798
798 + 5 = 803
803 + 3 = 806

Question 7.
Higher Order Thinking Lisa finds 550 + 298 using the open number line below. Is her work correct? Explain.


Answer:
No, Lisa work is not correct as of addition expression.
The correct way is as below
550 + 298
breaking the addend 298 into hundreds , tens, ones
298 = 100 + 100 + 50 + 40 + 5 + 3 or
298 = 200 + 90 + 8.

Problem Solving
Use an open number line to find each sum.

Question 8.
Reasoning José has 181 cards. He collects 132 more cards. How many cards does he have now?

Answer:

Question 9.
Vocabulary Complete the sentence using two of these terms.
>
Answer:

Question 10.
Higher Order Thinking Use open number lines to find 446 +215 in two different ways.
446 + 215 = ___

Answer:

Question 11.
Assessment Practice Mary uses an open number line to find 286 + 137. All of the jumps she draws are greater than 1. Draw what Mary could have done. Write the sum.
286 + 137 = ___

Answer:

Lesson 10.3 Add Using Models

Solve & Share

Activity

Use place-value blocks to find 243 + 354. Tell which place value you added first and why. Then draw a picture to show your work.

Visual Learning Bridge

Convince Me!
Are the tens regrouped in the example above? How do you know?

Guided Practice

Use place-value blocks to find each sum. Regroup if needed.

Question 1.
223 + 106 = ___

Answer:

Question 2.
149 + 362 = ___

Answer:

Independent Practice
Use and draw blocks to find each sum. Regroup if needed.

Question 3.
151 + 324 = ___

Answer:

Question 4.
250 + 298 = ___

Answer:

Question 5.
258 + 109 = ___

Answer:

Question 6.
187 + 246 = ___

Answer:

Question 7.
236 + 318 = ___

Answer:

Question 8.
432 + 365 = ___

Answer:

Question 9.
Number Sense Jamal says that the sum of 183 + 198 is less than 300. Is Jamal’s answer reasonable? Why or why not?

Answer:

Problem Solving

Solve the problems below. Show your work.

Question 10.
Reasoning 156 children in a school are girls. 148 children in that school are boys. How many children go to that school?

___ children
Answer:

Question 11.
Higher Order Thinking Write an addition problem about stickers. Use 3-digit numbers. Then solve the problem.

Answer:

Question 12.
Assessment Practice which is the sum of 129 +268?

A. 292
B. 294
C. 389
D. 397

Answer:

Lesson 10.4 Continue to Add Using Models and Place Value

Activity

Solve & Share

Oak School has 256 students. Pine School has 371 students. How many students do the schools have in all?
Use place-value blocks to help. Draw your blocks below and solve.

Visual Learning Bridge

Convince Me!
Look at the example above. Why don’t the Il tens need to be regrouped to get the final sum?

Guided Practice
Draw blocks to find the partial sums.
Record the partial sums to find the sum.

Question 1.
236 + 252 = ___

Answer:

Question 2.
328 + 124 = ___

Answer:

Independent Practice

Question 3.
372 + 281 = ___

Answer:

Question 4.
429 + 163 = ___

Answer:

Question 5.
174 + 245 =

Answer:

Question 6.
Higher Order Thinking Ben said that the sum of 157 and 137 is 284. Nikki said that Ben made a mistake. Who is correct? Explain.

Answer:

Problem Solving

Solve each problem below. You can use models to help.

Question 7.
Model On Friday, 354 people went to the fair. On Saturday, 551 people went to the fair.
How many people went to the fair in all?
___ people

Answer:

Question 8.
Higher Order Thinking Write an addition problem in which the partial sum for tens is greater than 10 tens. Draw blocks and show partial sums to solve.
___ + ___ = ___

Answer:

Question 9.
Assessment Practice Find 448 + 323. Draw place-value blocks and show partial sums to solve.
448 + 323 = ___

Answer:

Lesson 10.5 Add Using Place Value and Partial Sums

Activity

Solve & Share
On Monday, 248 people visit the museum. On Tuesday, 325 people visit the museum. How many people visit the museum on Monday and Tuesday? Solve any way you choose. Be prepared to explain your thinking.

Visual Learning Bridge

Convince Me!
Can the problem above be solved by adding the ones first, then the tens, and then the hundreds ? Explain.

Guided Practice
Add. Use partial sums. Show your work. Use place-value blocks if needed.

Question 1.
425 + 148 = ___

Answer:

Question 2.
394 + 276 = ___

Answer:

Independent Practice

Add. Use partial sums. Show your work.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.
Higher Order Thinking Mark found the sum of 127 and 345. Explain his mistake. What is the correct sum?

Answer:

Question 9.
Reasoning Rhea has a $100 bill, four $20 bills, one $10 bill, and three $5 bills. Is this amount greater or less than $210? Explain.
Answer:

Problem Solving
Solve each problem. Show your work.

Question 10.
Look for Patterns 349 people are on a boat. 255 people are on another boat. How many people are on both boats?

___ people
Answer:

Question 11.
163 students are in first grade. 217 students are in second grade. How many students are in both grades?
___ students
Answer:

Question 12.
Higher Order Thinking Choose a number between 100 and 400. Add 384 to your number. What is the sum? Show your work. Explain the steps you took to find the sum.
Answer:

Question 13.
Assessment Practice which is the same amount as 238 + 164? Choose all that apply.
200 + 190 + 12
300 + 90 + 12
402
400 + 10 + 2
Answer:

Lesson 10.6 Explain Addition Strategies

Activity

Solve & Share

Find 375 + 235. Explain your strategy. Then explain why your strategy works.

Visual Learning Bridge

Convince Me!
Choose a strategy shown above. Explain why it works.

Guided Practice

Use the strategy to solve the problem. Show your work. Then explain your work.

Question 1.
624 + 248 = 872

Answer:

Independent Practice

Choose any strategy to solve each addition problem. Show your work. Then explain why the strategy works.

Question 2.
212 + 487 = ___
Answer:

Question 3.
874 + 109 = ___
Answer:

Question 4.
419 + 532 = ___
Answer:

Question 5.
650 + 270 = ___

Answer:

Problem Solving

Solve each problem any way you choose. Show your work.

Question 6.
Reasoning Lee School needs 407 folders for its students. Jefferson School needs 321 folders for its students. How many folders do both schools need?
___ folders
Answer:

Question 7.
Reasoning There are 229 people at the football game. 108 more people arrive at the game. How many people are at the football game now?
___ people
Answer:

Question 8.
Higher Order Thinking Tommy found 125 + 598. Since 598 is close to 600, he added 125 + 600 = 725. Then he subtracted 2 to get 723. Why did Tommy subtract 2? Explain.
Answer:

Question 9.
Assessment Practice There are 192 ants on an ant farm. 397 more ants join the ant farm. How many ants are on the ant farm now? Use the number line to solve. Explain.

Answer:

Lesson 10.7 Repeated Reasoning

Problem Solving

Activity

Solve & Share

Solve these problems any way you choose. Explain patterns you see.
63 + 28 = ?
263 + 128 = ?

Thinking Habits
What can I use from one problem to help with another problem? Are there things that repeat?

Visual Learning Bridge

Convince Me!
If you start with 36 and add on 24, in the example above, will you get the same sum? Explain.

Guided Practice
Use repeated reasoning to solve the two problems. Circle the digits that are the same in the sums. Explain why the sums are different.

Question 1.

Answer:

Independent Practice

Solve each problem.

Question 2.
Write a problem where you need to regroup to make a ten or a hundred. Each addend must be three digits. Draw place-value blocks to solve your problem. Then explain why you needed to regroup.
___ + ___ = ____

Answer:

Question 3.
Write a problem where you do not need to regroup to make a ten or a hundred. Each addend must be three digits. Draw place value blocks to solve your problem. Then explain why you did not need to regroup.
___ + ___ = ____

Answer:

Problem Solving

Performance Task

Tickets Sold
The table shows how many tickets were sold at a theater. How many tickets were sold on Thursday and Saturday in all?

Question 4.
Make Sense Which numbers and operation can you use to solve the problem?
Answer:

Question 5.
Model Write an equation that shows the problem you need to solve.

Answer:

Question 6.
Generalize Use what you know about adding 3-digit numbers to solve the problem. Explain what you did.
Answer:

Topic 10 Fluency Practice

Point&Tally

Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue.
Partner I and Partner 2 each point to a black number at the same time. Both partners subtract Partner 2’s number from Partner l’s number.
If the answer is on your color, you get a tally mark. Work until one partner gets seven tally marks.

Topic 10 Vocabulary Review

Understand Vocabulary

Choose a term from the Word List to complete each sentence.

Word List
• addend
• break apart
• digits
• hundreds
• mental math
• open number line
• partial sum
• sum

Question 1.
When adding 193 + 564, the sum of 90 + 60 is called a ___
Answer:

Question 2.
In 709 + 187, 709 is an ___
Answer:

Question 3.
You can use an ___ to count on.
Answer:

Question 4.
In 841, there are ___ hundreds
Answer:

Question 5.
Give the value of each digit in 610.
Answer:

Question 6.
Use mental math to find 198 + 362.
Answer:

Use Vocabulary in Writing

Question 7.
Use words to tell how to find 249 + 201. Use terms from the Word List.
Answer:

Topic 10 Reteaching

Set A
You can use mental math to add 10 or 100 to 362.

Add using place-value blocks or mental math.

Question 1.
600 + 10 = ___
Answer:

Question 2.
345 + 100 = ___
Answer:

Question 3.
543 + 100 = ___
Answer:

Question 4.
800 + 100 = ___
Answer:

Question 5.
799 + 10 = ___
Answer:

Question 6.
119 + 10 = ___
Answer:

Set B
You can use an open number line to add. Find 327 + 126.
First, place 327 on the line and then count on by 100s, 10s, and 1s.

Use an open number line to find each sum.

Question 7.
594 + 132 = ___

Answer:

Question 8.
157 + 245 = ___

Answer:

Set C
You can use or draw place-value blocks and use partial sums to add. Find 276 + 137.

Add. Use partial sums. Show your work. Use drawings of blocks if needed.

Question 9.
408 + 326 = ___

Answer:

Set D

Thinking Habits
Repeated Reasoning
What can I use from one problem to help with another problem? Are there things that repeat?

Solve each problem. Use partial sums and repeated reasoning. Use drawings of blocks if needed.

Question 10.

Circle the digits that are alike in each sum.
Answer:

Topic 10 Assessment Practice

Question 1.
Emily has 100 sun stickers. She has 382 star stickers and 10 moon stickers. How many sun and star stickers does Emily have?
Answer:

Question 2.
Tyrone collects baseball cards. He gives 138 cards to his friend. Now he has 428 cards. How many cards did Tyrone have before he gave some away?
___ cards
Answer:

Question 3.
Use the open number line to solve the problem. Write the missing numbers in the boxes.
421 + 250 = ?

Answer:

Question 4.
Which is the same amount as 528 + 167? Choose all that apply.
500 + 80 + 15
500 + 180 + 15
600 + 90 + 5
600 + 80 + 15
Answer:

Question 5.
Choose all the equations in which the sum is 488.
478 + 10 = ?
388 + 100 = ?
248 + 240 = ?
200 + 265 = ?
Answer:

Question 6.
Rich has 335 pennies. Beth has 58 more pennies than Rich. How many pennies do they have in all?
Hundreds

A. 277
B. 393
C. 628
D. 728
Answer:

Question 7.
Use place value and partial sums to find 472 + 256. Show your work.

472 + 256 = ___
Answer:

Question 8.
Molly reads 184 pages. Pat reads 294 pages. What is the total number of pages they read in all?
Use any strategy. Show your work and explain.

Answer:

Question 9.
On Saturday, 449 people visit the zoo. On Sunday, 423 people visit the zoo. How many people visit the zoo in all? Use the open number line to solve. Explain your work.

Answer:

Topic 10 Performance Task

Recycling Race
Westbrook School is having a recycling contest. The table shows the number of cans each grade collected in February.

Answer:

Question 1.
How many cans did the first-grade students and the second-grade students collect in all?
Use the open number line to solve.

__ cans
Answer:

Question 2.
Bruce used partial sums to find how many cans the third-grade students and fourth-grade students collected in all.

Do you agree with his answer?
Circle yes or no.
Explain your answer.

Answer:

Question 3.
Which two grades collected a total of 689 cans? Choose any strategy to solve the problem. Show your work. Explain which strategy you used.

The ___ grade and the ___ grade collected a total of 689 cans.

Answer:

Question 4.
The second-grade collected 432 cans in March. They collected 198 cans in April. Tom and Bill find how many cans the class collected in March and April.

Who added correctly? Explain.

Who answered incorrectly? What did he do?

Answer:

Go through the enVision Math Common Core Grade 5 Answer Key Topic 6 Use Models and Strategies to Divide Decimals regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 6 Use Model Strategies to Divide Decimals

enVision STEM Project: States of Water
Do Research
Use the Internet or other sources to learn about the states of water. Find at least 5 examples of water in nature as a solid, as a liquid, and as a gas. At what temperature does liquid water change to ice? At what temperature does liquid water change to water vapor?

Journal: Write a Report Include what you found. Also in your report:
• Explain how liquid water changes to ice and to water vapor.
• At 23°F, 1 inch of rain equals 10 inches of snow. Convert 2 inches of rainfall to snowfall.
• Make up and solve division problems that involve decimals.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.
• decimal
• dividend
• divisor
• quotient

Question 1.
_____ is the name for the answer to a division problem.
Answer:
Quotient is the name for the answer to a division problem.

Question 2.
A number that is being divided by another number is called the _____
Answer:
A number that is being divided by another number is called the dividend.

Whole Number Operations

Find each value.

Question 3.
9,007 – 3,128
Answer:
9,007 – 3,128 = 5,879
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Subtraction of two whole numbers may not result in whole numbers. It can be an integer too. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Subtract 3,128 from 9,007 then the difference is 5,879.
Question 4.
725,864 + 39,798
Answer:
725,864 + 39,798 = 765,662
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform addition operation on these two numbers 725,864 and 39,798 then the sum is 765,662.

Question 5.
35 × 17
Answer:
35 × 17 = 595
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform multiplication operation on these two numbers 35 and 17 then the result is 595.

Question 6.
181 × 42
Answer:
181 × 42 = 7,602
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself.  Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform multiplication operation on these two numbers 181 and 42 then the result is 7,602.

Question 7.
768 ÷ 6
Answer:
768 ÷ 6 = 128
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 768 and 6. Here 768 is dividend and 6 is divisor then the quotient is 128.

Question 8.
506 ÷ 22
Answer:
506 ÷ 22 = 23
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 506 and 22. Here 506 is dividend and 22 is divisor then the quotient is 23.

Question 9.
6,357 ÷ 60
Answer:
6,357 ÷ 60 = 105.95
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 6357 and 60. Here 6,357 is dividend and 60 is divisor then the quotient is 105.95.

Question 10.
3,320 ÷ 89
Answer:
3,320 ÷ 89 = 37.30
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 3,320 and 89. Here 3,320 is dividend and 89 is divisor then the quotient is 37.30.

Question 11.
88,888 ÷ 20
Answer:
88,888 ÷ 20 = 4,444.4
Explanation:
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. The inverse operation of multiplication is division. Whole numbers are positive integers along with zero. They are all the natural numbers including zero. Perform division operation on these two numbers 88,888 and 20. Here 88,888 is dividend and 20 is divisor then the quotient is 4,444.4.

Rounding Decimals
Round each number to the place of the underlined digit.

Question 12.
0.34
Answer:
0.3
Explanation:
Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 0.34 is rounded to 0.3.

Question 13.
96.5
Answer:
97
Explanation:
Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 96.5 is rounded to 97.

Question 14.
81.27
Answer:
81.3
Explanation:
Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 81.27 is rounded to 81.3.

Question 15.
205.3
Answer:
205
Explanation:
Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. The number 205.3 is rounded to 205.

Decimals

Question 16.
An insect measured 1.25 cm long. Which number is less than 1.25?
A. 1.35
B. 1.3
C. 1.26
D. 1.2
Answer:
Option D is correct.
Explanation:
An insect measured 1.25 cm long. We have to find out the number less than 1.25.
A. 1.35 is greater than 1.25. So option A is not correct.
B. 1.3 is greater than 1.25. So option B is not correct.
C. 1.26 is greater than 1.25 . So option C is not correct.
D. 1.2 is less than 1.25. So option D is correct.

Question 17.
Explain The grid in this model represents 1. What decimal does the shaded part represent? Explain.

Answer:
0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.04 = 0.64
The shaded part represents the decimal 0.64.
Explanation:
The above grid represents 1. In that grid 1 column is shaded. The shaded part decimal value is 0.1. The second column shaded part decimal value is 0.1. The third column shaded part decimal value is 0.1. The fourth column shaded part decimal value is 0.1. The fifth column shaded part decimal value is 0.1. The sixth column shaded part decimal value is 0.1. The seventh column shaded part decimal value is 0.04. By adding these columns decimal values the sum is 0.64.

Decimal Operations

Find each value.

Question 18.
23.7 – 11.82
Answer:

23.7 – 11.82 = 11.88
Explanation:
Four basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
Step 1: Write numbers under each other and line up vertically the decimal points.
Perform subtraction operation on these two numbers 23.7 and 11.82. Subtract 11.82 from 23.7 then the difference is 11.88.

Question 19.
66.8 + 3.64
Answer:

66.8 + 3.64 = 70.44
Explanation:
Four basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
Step 1: Write numbers under each other and line up vertically the decimal points.
Perform addition operation on these two numbers 66.8 and 3.64. Add 66.8 with 3.64 then the sum is 70.44.

Question 20.
9 × 1.4
Answer:

9 x 1. 4 = 12. 6
Explanation:
Four basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
Step 1: Write numbers under each other and line up vertically the decimal points.
Perform multiplication operation on these two numbers 9 and 1.4. Multiply 9 with 1.4 then the result is 12.6.

Question 21.
3.2 × 7.6
Answer:

3.2 x 7.6 = 24.32
Explanation:
Four basic operations on decimals are addition, subtraction, multiplication and division. To add decimals numbers we follow this step.
Step 1: Write numbers under each other and line up vertically the decimal points.
Perform multiplication operation on these two numbers 3.2 and 7.6. Multiply 3.2 with 7.6 then the result is 24.32.

Pick a Project

PROJECT 6A
Can you throw a dinner party?
Project: Plan a Party

PROJECT 6B
How much does it cost to run a company?
Project: Build a Company

PROJECT 6C
How do you organize food?
Project: Open Your Own Fruit Stand

PROJECT 6D
Would you like to build a house?
Project: Draw Plans for a Doll House

Lesson 6.1 Patterns for Dividing with Decimals

Activity

Solve & Share

An object is 279.4 centimeters wide. If you divide the object into 10 equal parts, how wide will each part be? Solve this problem any way you choose.

How can you use structure and the relationship between multiplication and division to help you?

Look Back! What do you notice about the width of the object and the width of each part?
Answer:
The width of the object is 279.4
279.4/10 = 27.94
The width of each part is 27.94
Explanation:
An object is 279.4 centimeters wide. If we divide the object into 10 equal parts. The wide of the each part is 27.94.
Multiplication and division are the reverse or opposite of each other in that when we divide, we break apart, and when we multiply, we put together.

Visual Learning Bridge
Essential Question How Can You Divide Question Decimals by Powers of 10?

A.
Shondra wants to cut a cloth into 10 strips. All the strips should be exactly the same size. You can use place value and what you know about whole numbers to divide decimals by powers of 10. How long will each strip be?

You can divide to find equal parts of a whole.

Remember that
10 = 10!

B.
Find 89.5 ÷ 10.
Place value is based on 10. The value of each place is \(\frac{1}{10}\) the value of the place to the left. Dividing by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left.

89.5 ÷ 10¹ = 8.95
Each cloth strip will be 8.95 cm long.

Convince Me! Use Structure Celinda thought of 89.5 in parts, 80 + 9 + 0.5, and divided each part: 80 ÷ 10 = 8; 9 ÷ 10 = \(\frac{9}{10}\) or 0.9; 0.5 ÷ 10 = 0.05. Then she added the parts to get 8.95. What do you notice?
Answer:
Celinda divided 89.5 into parts as 80 + 9 + 0.5, and divided each part 80 ÷ 10 = 8; 9 ÷ 10 = 0.9; 0.5 ÷ 10 = 0.05. Then she added the parts to get 8.95. I notice when we divide the number 89.5 with 10 then the result is 8.95 and dividing 89.5 into parts also we get same result as 8.95.

Guided Practice999

Do You Understand?

Question 1.
Suppose Shondra wanted to cut the cloth into 10² strips. How long would each strip be?
Answer:
89.5 ÷ 10²
89.5 ÷ 100 = 0.895
Each cloth strip will be 0.895 cm long.
Explanation:
Shondra wanted to cut the cloth into 10² strips. Place value is based on 10². The value of each place is 1/100 the value of the place to the left. Dividing by 10² results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. Each cloth strip will be 0.895 cm long.

Question 2.
Krista divides a number by 10. Then she divides the same number by 50. Which quotient is greater? How can you tell?
Answer:

The quotient 10 is greater.
Explanation:
In the above image we can observe the quotient 10 and 2. Krista divides the number 100 by 10 then the quotient is 10. Then she divides the same number 100 by 50 then the quotient is 2. The quotient 10 is greater.

Do You Know How?

In 3-10, use mental math to find each quotient.

Question 3.
370.2 ÷ 10²
Answer:
370.2 ÷ 10²
370.2 ÷ 100 = 3.702
Explanation:
In the above division method the place value is based on 10². The value of each place is 1/100 the value of the place to the left. Dividing the number 370.2 by 10² results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 370.2 ÷ 100 = 3.702.

Question 4.
126.4 ÷ 10¹
Answer:
126.4 ÷ 10¹
126.4 ÷ 10 = 12.64
Explanation:
In the above division method the place value is based on 10¹. The value of each place is 1/10 the value of the place to the left. Dividing the number 126.4 by 10¹ results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 126.4 ÷ 10 = 12.64.

Question 5.
7.25 ÷ 10
Answer:
7.25 ÷ 10 = 0.725
Explanation:
In the above division method the place value is based on 10. The value of each place is 1/10 the value of the place to the left. Dividing the number 7.25 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 7.25 ÷ 10 = 0.725.

Question 6.
72.5 ÷ 10³
Answer:
72.5 ÷ 10³
72.5 ÷ 1000 = 0.0725
Explanation:
In the above division method the place value is based on 10³. The value of each place is 1/1000 the value of the place to the left. Dividing the number 72.5 by 10³ results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 72.5 ÷ 1000 = 0.0725.

Question 7.
281.4 ÷ 10⁰
Answer:
281.4 ÷ 10⁰
281.4 ÷ 1 = 281.4
Explanation:
In the above division method the place value is based on 10⁰. The value of each place is 1 the value of the place to the left. Dividing the number 281.4 by 1 results in moving each digit zero places to the right. This looks the same as moving the decimal point zero places to the left. The quotient for 281.4 ÷ 1 = 281.4.

Question 8.
2,810 ÷ 10⁴
Answer:
2,810 ÷ 10⁴
2,810 ÷ 10000 = 0.2810
Explanation:
In the above division method the place value is based on 10⁴. The value of each place is 1/10000 the value of the place to the left. Dividing the number 2,810 by 10⁴ results in moving each digit four places to the right. This looks the same as moving the decimal point four places to the left. The quotient for 2,810 ÷ 10000 = 0.2810.

Question 9.
3,642.4 ÷ 10²
Answer:
3,642.4 ÷ 10²
3,642.4 ÷ 100 = 36.424
Explanation:
In the above division method the place value is based on 10². The value of each place is 1/100 the value of the place to the left. Dividing the number 3,642.4 by 10² results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 3,642.4 ÷ 100 = 36.424.

Question 10.
364.24 ÷ 10¹
Answer:
364.24 ÷ 10¹
364.24 ÷ 10 = 36.424
Explanation:
In the above division method the place value is based on 10¹. The value of each place is 1/10 the value of the place to the left. Dividing the number 364.24 by 10¹ results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 364.24 ÷ 10 = 36.424.

Independent Practice

Leveled Practice in 11-25, find each quotient. Use mental math.

Question 11.
4,600 ÷ 10
460 ÷ 10
46 ÷ 10
4.6 ÷ 10
Answer:
4,600 ÷ 10 = 460
460 ÷ 10 = 46
46 ÷ 10 = 4.6
4.6 ÷ 10 = 0.46
Explanation:
In the above division method the place value is based on 10. The value of each place is 1/10 the value of the place to the left.
Dividing the number 4,600 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 4,600 ÷ 10 = 460.
Dividing the number 460 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 460 ÷ 10 = 46.
Dividing the number 46 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 46 ÷ 10 = 4.6.
Dividing the number 4.6 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 4.6 ÷ 10 = 0.46.

Question 12.
134.4 ÷ 10³
134.4 ÷ 10²
134.4 ÷ 10¹
134.4 ÷ 10⁰
Answer:
134.4 ÷ 10³ 
134.4 ÷ 1000 = 0.1344
134.4 ÷ 10²
134.4 ÷ 100 = 1.344
134.4 ÷ 10¹
134.4 ÷ 10 = 13.44
134.4 ÷ 10⁰
134.4 ÷ 1 = 134.4 

Explanation:
Dividing the number 134.4 by 10³ results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 134.4 ÷ 1000 = 0.1344.
Dividing the number 134.4 by 10² results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 134.4 ÷ 100 = 1.344.
Dividing the number 134.4 by 10¹ results in moving each digit one two place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 134.4 ÷ 10 = 13.44.
Dividing the number 134.4 by 10⁰ results in moving each digit zero places to the right. This looks the same as moving the decimal point zero places to the left. The quotient for 134.4 ÷ 1 = 134.4.
Question 13.
98.6 ÷ 1
98.6 ÷ 100
98.6 ÷ 10
98.6 ÷ 1,000
Answer:
98.6 ÷ 1
98.6 ÷ 1 = 98.6
98.6 ÷ 100
98.6 ÷ 100 = 0.986
98.6 ÷ 10
98.6 ÷ 10 = 9.86
98.6 ÷ 1,000
98.6 ÷ 1,000 = 0.0986
Explanation:
Dividing the number 98.6 by 1 results the quotient for 98.6 ÷ 1 = 98.6.
Dividing the number 98.6 by 100 results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 98.6 ÷ 100 = 0.986.
Dividing the number 98.6 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 98.6 ÷ 10 = 9.86.
Dividing the number 98.6 by 1000 results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 98.6 ÷ 1,000 = 0.0986.

Question 14.
136.5 ÷ 10
Answer:
136.5 ÷ 10 = 13.65
Explanation:
In the above division method the place value is based on 10. The value of each place is 1/10 the value of the place to the left. Dividing the number 136.5 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 136.5 ÷ 10 = 13.65.

Question 15.
753 ÷ 100
Answer:
753 ÷ 100 = 7.53
Explanation:
In the above division method the place value is based on 100. The value of each place is 1/100 the value of the place to the left. Dividing the number 753 by 100 results in moving each digit two place to the right. This looks the same as moving the decimal point two places to the left. The quotient for 753 ÷ 100 = 7.53.

Question 16.
890.1 ÷ 10⁰
Answer:
890.1 ÷ 1 = 890.1
Explanation:
In the above division method the place value is based on 10⁰. Dividing the number 890.1 by 1 results in moving each digit zero places to the right. This looks the same as moving the decimal point zero places to the left. The quotient for 890.1 ÷ 1 = 890.1.

Question 17.
3.71 ÷ 10²
Answer:
3.71 ÷ 100 = 0.0371
Explanation:
In the above division method the place value is based on 10². The value of each place is 1/100 the value of the place to the left. Dividing the number 3.71 by 10²results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 3.71 ÷ 100 = 0.0371.

Question 18.
8,100 ÷ 10⁴
Answer:
8,100 ÷ 10000 = 0.81
Explanation:
In the above division method the place value is based on 10⁴. The value of each place is 1/10000 the value of the place to the left. Dividing the number 8100 by 10⁴ results in moving each digit four places to the right. This looks the same as moving the decimal point four places to the left. The quotient for 8,100 ÷ 10000 = 0.81.

Question 19.
864 ÷ 10³
Answer:
864 ÷ 1000 = 0.864
Explanation:
In the above division method the place value is based on 10³. The value of each place is 1/1000 the value of the place to the left. Dividing the number 864 by 10³ results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 864 ÷ 1000 = 0.864.

Question 20.
0.52 ÷ 10¹
Answer:
0.52 ÷ 10 = 0.052
Explanation:
In the above division method the place value is based on 10¹. The value of each place is 1/10 the value of the place to the left. Dividing the number 0.52 by 10¹ results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 0.52 ÷ 10 = 0.052.

Question 21.
15.7 ÷ 1,000
Answer:
15.7 ÷ 1,000 = 0.157
Explanation:
In the above division method the place value is based on 1000. Dividing the number 15.7 by 1000 results in moving each digit three places to the right. This looks the same as moving the decimal point three places to the left. The quotient for 15.7 ÷ 1,000 = 0.157.

Question 22.
7,700 ÷ 10²
Answer:
7,700 ÷ 100 = 77
Explanation:
In the above division method the place value is based on 100. Dividing the number 7,700 by 100 results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 7,700 ÷ 100 = 77.

Question 23.
770 ÷ 10²
Answer:
770 ÷ 100 = 7.7
Explanation:
In the above division method the place value is based on 10². The value of each place is 1/100 the value of the place to the left. Dividing the number 770 by 100 results in moving each digit two places to the right. This looks the same as moving the decimal point two places to the left. The quotient for 770 ÷ 100 = 7.7.

Question 24.
77 ÷ 10¹
Answer:
77 ÷ 10 = 7.7
Explanation:
In the above division method the place value is based on 10¹. The value of each place is 1/10 the value of the place to the left. Dividing the number 77 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 77 ÷ 10 = 7.7.

Question 25.
7.7 ÷ 10¹
Answer:
7.7 ÷ 10 = 0.77
Explanation:
In the above division method the place value is based on 10¹. The value of each place is 1/10 the value of the place to the left. Dividing the number 7.7 by 10 results in moving each digit one place to the right. This looks the same as moving the decimal point one place to the left. The quotient for 7.7 ÷ 10 = 0.77.

Problem Solving

For 26-28, use the table that shows the winning times at the Pacific Middle School swim meet.

Question 26.
What was the difference between the winning butterfly time and the winning backstroke time?
Answer:
The difference between the winning butterfly time and the winning backstroke time is 4.66 seconds.
Explanation:
The winning butterfly time is 58.49 seconds. The winning backstroke time is 53.83 seconds. Subtract the winning backstroke time from winning butterfly time then the difference is 4.66 seconds.

Question 27.
The winning time for the 100-yard freestyle was twice the time for the 50-yard freestyle. What was the winning time for the 100-yard freestyle?
Answer:
The winning time for the 100-yard freestyle is 44.34 seconds.
Explanation:
The winning time for the 100-yard freestyle was twice the time for the 50-yard freestyle. The winning time for 50-yard freestyle is 22.17 seconds. So add 22.17 seconds with 22.17 seconds then the sum is 44.34 seconds. The winning time for the 100-yard freestyle is 44. 34 seconds.

Question 28.
What was the difference between the winning 100-yard freestyle time and the winning butterfly time?
Answer:
The difference between the winning 100-yard freestyle time and the winning butterfly time is 14.15 seconds.
Explanation:
The winning 100-yard freestyle time is 44.34 seconds. The winning 100-yard butterfly time is 58.49 seconds. Subtract 100-yard freestyle winning time from 100-yard butterfly winning time then the difference is 14.15 seconds.

Question 29.
Reasoning A pickup truck carrying 10³ identical bricks weighs 6,755 pounds. If the empty truck weighs 6,240 pounds, what is the weight of each brick? Explain how to solve the problem.
Answer:

Question 30.
Higher Order Thinking Katie noticed a pattern in the answers for each of the expressions below. What do you notice?

Answer:
14.6 x  0.1 = 1.46          14.6 ÷ 10 = 1.46
146 x 0.01 = 1.46          146 ÷ 100 = 1.46
146 x 0.001 = 0.146       146 ÷ 1,000 = 0.146
Explanation:
In first expressions I noticed that if we are multiplying 14.6 x  0.1 results the product as 1.46. When we are dividing 14.6 ÷ 10 results the quotient as 1.46.
In second expressions I noticed that if we are multiplying 146 x  0.01 results the product as 1.46. When we are dividing 146 ÷ 100 results the quotient as 1.46.
In third expressions I noticed that if we are multiplying 146 x  0.001 results the product as 0.146. When we are dividing 146 ÷ 1,000 results the quotient as 0.146.

Assessment Practice

Question 31.
Choose the equations in which n = 1,000 makes the equation true.
0 2.5 ÷ n = 0.025
947.5 ÷ n = 0.9475
8,350 ÷ n = 8.35
16.4 ÷ n = 0.0164
0.57 ÷ n = 0.0057
Answer:

Explanation:
If we put n = 1,000 in first equation 0.25 ÷ 1,000 = 0.0025. The First equation is not true.
If we put n = 1,000 in second equation 947.5 ÷ 1,000 = 0.9475. The Second equation is true.
If we put n = 1,000 in third equation 8,350 ÷ 1,000 = 8.35. The third equation is true.
If we put n = 1,000 in fourth equation 16.4 ÷ 1,000 = 0.0164. The fourth equation is true.
If we put n = 1,000 in fifth equation 0.57 ÷ 1,000 = 0.00057. The fifth equation is not true.

Question 32.
Choose the equations in which d = 10² makes the equation true.
386.2 ÷ d = 3.862
4,963.6 ÷ d = 4.9636
0.6 ÷ d = 0.006
5.8 ÷ d = 0.58
15.3 ÷ d = 0.153
Answer:

Explanation:
If we put d = 100 in first equation 386.2 ÷ 100 = 3.862. The First equation is true.
If we put d = 100 in second equation 4,963.6 ÷ 100 = 49.636. The Second equation is not true.
If we put d = 100 in third equation 0.6 ÷ 100 = 0.006. The third equation is true.
If we put d = 100 in fourth equation 5.8 ÷ 100 = 0.058. The fourth equation is not true.
If we put d = 100 in fifth equation 15.3 ÷ 100 = 0.153. The fifth equation is true.

Lesson 6.2 Estimate Decimal Quotients

Activity

Slove&Share

A 135.8-foot piece of construction material needs to be cut into pieces that are each 16 feet long. About how many pieces can be cut? Solve this problem any way you choose.

Answer:

135 ÷ 15 = 9
The construction material can be cut into 9 pieces.
Explanation:
A 135.8-foot piece of construction material is about 135. We need to cut the material into pieces that are each 16 feet long. The 16 pieces material is rounded to 15. Apply division method to solve the problem. Divide 135 with 15 then the result is 9. The construction material can be cut into 9 pieces.

You can use reasoning to estimate decimal quotients.

Look Back! Reasoning Can you find a different way to estimate the answer for the problem above? Explain.

Visual Learning Bridge

Essential Question
How Can You Use Estimation to Find Quotients?

A.
Diego borrowed money from his parents to purchase a video gaming system for $473.89 (including tax). About how much are his monthly payments to his parents if he wants to pay this off in one year?

You can use division to find equal groups.

B.
One Way
Estimate $473.89 ÷ 12. Use rounding.
Round to the nearest ten: 473.89 rounds to 470; 12 rounds to 10
$473.89 ÷ 12 is about $470 ÷ 10 = $47.
Each monthly payment will be about $47.

C.
Another Way
Estimate $473.89 ÷ 12. Use compatible numbers.
Look for compatible numbers.
$473.89 ÷ 12 is close to $480 ÷ 12 = $40.

You know 48 ÷ 12 = 4.

Each monthly payment will be about $40.

Convince Me! Construct Arguments in the example above, which estimate is closer to the exact answer? Tell how you decided.
Answer:
We use compatible numbers to make the problem easier to solve in our head by rounding each number to the nearest ten, twenty, fifty or hundred. But if we make the numbers compatible and round up to the nearest hundred or ten spot, 300 and 350 are much easier to compute in our heads.

Guided Practice

Do You Understand?

Question 1.
Number Sense Leo is estimating 53.1 ÷ 8.4. Do you think he should use 53 ÷ 8 or 54 ÷ 9 to estimate? Why?
Answer:
Estimate 53.1 ÷ 8.4. Use compatible numbers.
Look for compatible numbers.
53.1 ÷ 8.4 is close to 54 ÷ 9 = 6.
53 ÷ 8 is not easy to find and 54 ÷ 9 is easy to find because 54 is multiple of 9.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 53.1 ÷ 8.4 is closes to 54 ÷ 9. The actual dividend 53.1 is compatible to 54. Perform division operation 54 ÷ 9 = 6. The Estimated quotient is 6. Here 54 is multiple of 9 so we can easily find out the quotient. 53 ÷ 8 = 6.625 so it is difficult to find.

Question 2.
Is each quotient greater than or less than 1?
A. 0.2 ÷ 4
B. 1.35 ÷ 0.6
Answer:
A. 0.2 ÷ 4 = 0.05
0.05 < 1
B. 1.35 ÷ 0.6 = 2.25
2.25 > 1
Explanation:
A. Divide 0.2 by 4 then the quotient is 0.05. 0.05 is less than 1.
B. Divide 1.35 by 0.6 then the quotient is 2.25. 2.25 is greater than 1.

How do you know?

In 3-8, estimate each quotient. Use rounding or compatible numbers.

Question 3.
42 ÷ 6.8
Answer:
Estimate 42 ÷ 6.8. Use compatible numbers.
Look for compatible numbers.
42 ÷ 6.8 is closes to 42 ÷ 7 = 6.
The Estimated quotient is 6.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 42 ÷ 6.8 is closes to 42 ÷ 7. The actual divisor 6.8 is compatible to 7. Perform division operation 42 ÷ 7 = 6. The Estimated quotient is 6.

Question 4.
102 ÷ 9.6
Answer:
Estimate 102 ÷ 9.6. Use rounding.
Round to the nearest ten: 102 rounds to 100; 9.6 rounds to 10
102 ÷ 9.6 is about 100 ÷ 10 = 10.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 102 ÷ 9.6. Round the numbers to the nearest ten or hundreds. Here 102 is rounded to 100 and 9.6 is rounded to 10. Now perform division operation on 100 ÷ 10 = 10. The estimated quotient is 10.

Question 5.
48.9 ÷ 4
Answer:
Estimate 48.9 ÷ 4. Use compatible numbers.
Look for compatible numbers.
48.9 ÷ 4 is closes to 50 ÷ 5 = 10.
The Estimated quotient is 10.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 48.9 ÷ 4 is closes to 50 ÷ 5. The actual dividend is 48.9 is compatible to 50. The actual divisor 4 is compatible to 5. Perform division operation 50 ÷ 5 =10. The Estimated quotient is 10.

Question 6.
72.59 ÷ 7
Answer:
Estimate 72.59 ÷ 7. Use rounding.
Round to the nearest ten: 72.59 rounds to 70; 7 rounds to 10
72.59 ÷ 7 is about 70 ÷ 10 = 7.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 72.59 ÷ 7. Round the numbers to the nearest ten or hundreds. Here 72.59 is rounded to 70 and 7 is rounded to 10. Now perform division operation on 70 ÷ 10 = 7. The estimated quotient is 7.

Question 7.
15.4 ÷ 1.9
Answer:
Estimate 15.4 ÷ 1.9. Use compatible numbers.
Look for compatible numbers.
15.4 ÷ 1.9 is closes to 16 ÷ 2 = 8.
The Estimated quotient is 8.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 15.4 ÷ 1.9 is closes to 16 ÷ 2. The actual dividend is 15.4 is compatible to 16. The actual divisor 1.9 is compatible to 2. Perform division operation 16 ÷ 2 =8. The Estimated quotient is 8.

Question 8.
44.07 ÷ 6.3
Answer:
Estimate 44.07 ÷ 6.3. Use compatible numbers.
Look for compatible numbers.
44.07 ÷ 6.3 is closes to 42 ÷ 6 = 7.
The Estimated quotient is 7.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 44.07 ÷ 6.3 is closes to 42 ÷ 6. The actual dividend is 44.07 is compatible to 42. The actual divisor 6.3 is compatible to 6. Perform division operation 42 ÷ 6 =7. The Estimated quotient is 7.

Independent Practice

Leveled Practice In 9 and 10, complete the work to estimate each quotient.

Question 9.

Answer:
Estimate 64.5 ÷ 12.3. Use rounding.
Round to the nearest ten: 64.5 rounds to 65 ; 12.3 rounds to 10
64.5 ÷ 12.3 is about 65 ÷ 10 = 6.5.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 64.5 ÷ 12.3. Round the numbers to the nearest ten or hundreds. Here 64.5 is rounded to 65 and 12.3 is rounded to 10. Now perform division operation on 65 ÷ 10 = 6.5. The estimated quotient is 6.5.

Question 10.
Estimate 64.5 ÷ 12.3 using compatible numbers.
65 ÷ 10 = _____
Answer:
Estimate 64.5 ÷ 12.3. Use compatible numbers.
Look for compatible numbers.
64.5 ÷ 12.3 is closes to 65 ÷ 10 = 6.5.
The Estimated quotient is 6.5.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 64.5 ÷ 12.3 is closes to 65 ÷ 10. The actual dividend is 64.5 is compatible to 65. The actual divisor 12.3 is compatible to 10. Perform division operation 65 ÷ 10 =6.5. The Estimated quotient is 6.5.

In 11-19, estimate each quotient.

Question 11.
7 ÷ 0.85
Answer:
Estimate 7 ÷ 0.85. Use compatible numbers.
Look for compatible numbers.
7 ÷ 0.85 is closes to 7 ÷ 1 = 7.
The Estimated quotient is 7.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 7 ÷ 0.85 is closes to 7 ÷ 1. The actual divisor 0.85 is compatible to 1. Perform division operation 7 ÷ 1 = 7. The Estimated quotient is 7.

Question 12.
9.6 ÷ 0.91
Answer:
Estimate 9.6 ÷ 0.91. Use compatible numbers.
Look for compatible numbers.
9.6 ÷ 0.91 is closes to 10 ÷ 1 = 10.
The Estimated quotient is 10.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 9.6 ÷ 0.91 is closes to 10 ÷ 1. The actual dividend 9.6 is compatible to 10.The actual divisor 0.91 is compatible to 1. Perform division operation 10 ÷ 1 = 10. The Estimated quotient is 10.

Question 13.
17.7 ÷ 3.2
Answer:
Estimate 17.7 ÷ 3.2. Use compatible numbers.
Look for compatible numbers.
17.7 ÷ 3.2 is closes to 18 ÷ 3 = 6.
The Estimated quotient is 6.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 17.7 ÷ 3.2 is closes to 18 ÷ 3. The actual dividend 17.7 is compatible to 18.The actual divisor 3.2 is compatible to 3. Perform division operation 18 ÷ 3 = 6. The Estimated quotient is 6.

Question 14.
91.02 ÷ 4.9
Answer:
Estimate 91.02 ÷ 4.9. Use compatible numbers.
Look for compatible numbers.
91.02 ÷ 4.9 is closes to 90 ÷ 5 = 18.
The Estimated quotient is 18.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 91.02 ÷ 4.9 is closes to 90 ÷ 5. The actual dividend 91.02 is compatible to 90.The actual divisor 4.9 is compatible to 5. Perform division operation 90 ÷ 5 = 18. The Estimated quotient is 18.

Question 15.
45.64 ÷ 6.87
Answer:
Estimate 45.64 ÷ 6.87. Use compatible numbers.
Look for compatible numbers.
45.64 ÷ 6.87 is closes to 49 ÷ 7 = 7.
The Estimated quotient is 7.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 45.64 ÷ 6.87 is closes to 49 ÷ 7. The actual dividend 45.64 is compatible to 49.The actual divisor 6.87 is compatible to 7. Perform division operation 49 ÷ 7 = 7. The Estimated quotient is 7.

Question 16.
821.22 ÷ 79.4
Answer:
Estimate 821.22 ÷ 79.4. Use rounding.
Round to the nearest ten: 821.22 rounds to 800 ; 79.4 rounds to 80
821.22 ÷ 79.4 is about 800 ÷ 80 = 10.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 821.22 ÷ 79.4. Round the numbers to the nearest ten or hundreds. Here 821.22 is rounded to 800 and 79.4 is rounded to 80. Now perform division operation on 800 ÷ 80 = 10. The estimated quotient is 10.

Question 17.
22.5 ÷ 3
Answer:
Estimate 22.5 ÷ 3. Use compatible numbers.
Look for compatible numbers.
22.5 ÷ 3 is closes to 24 ÷ 3 = 8.
The Estimated quotient is 8.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 22.5 ÷ 3 is closes to 24 ÷ 3. The actual dividend 22.5 is compatible to 24. Perform division operation 24 ÷ 3 = 8. The Estimated quotient is 8.

Question 18.
15.66 ÷ 9.3
Answer:
Estimate 15.66 ÷ 9.3. Use rounding.
Round to the nearest ten: 15.66 rounds to 20 ; 9.3 rounds to 10.
15.66 ÷ 9.3 is about 20 ÷ 10 = 2.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 15.66 ÷ 9.3. Round the numbers to the nearest ten or hundreds. Here 15.66 is rounded to 20 and 9.3 is rounded to 10. Now perform division operation on 20 ÷ 10 = 2. The estimated quotient is 2.

Question 19.
156.3 ÷ 14.5
Answer:
Estimate 156.3 ÷ 14.5. Use rounding.
Round to the nearest ten: 156.3 rounds to 160 ; 14.5 rounds to 20.
156.3 ÷ 14.5 is about 160 ÷ 20 = 8.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 156.3 ÷ 14.5. Round the numbers to the nearest ten or hundreds. Here 156.3 is rounded to 160 and 14.5 is rounded to 20. Now perform division operation on 160 ÷ 20 = 8. The estimated quotient is 8.

Problem Solving

Question 20.
Luci’s mother gave her $7.50 to buy 8 spiral notebooks. With tax, the cost of each notebook is $1.05. Does Luci have enough money? Use compatible numbers and estimation to help you decide.
Answer:

Question 21.
Critique Reasoning Kerri said that the quotient of 4.2 ÷ 5 is about 8 tenths because 4.2 ÷ 5 is close to 40 tenths ÷ 5. Do you agree with Kerri’s reasoning? Explain.
Answer:

Question 22.
Higher Order Thinking Write a decimal division problem that has an estimated quotient of 4. Explain how to get that estimate.
Answer:

Question 23.
Lia’s car averages 14.5 miles per gallon while Roman’s car averages 28.5 miles per gallon. Use estimation to find how many times as many miles per gallon Roman’s car gets compared to Lia’s car.
Answer:

In 24-26, use the table.

Question 24.
enVision® STEM Which sample from the experiment had the least mass? Which had the lowest temperature?
Answer:
In the above table we can observe Sample 3 had the least mass 0.058 g from the experiment. Sample 1 had the lowest temperature as 37.57°C.

Question 25.
Sample 3 was used in another experiment. A temperature of 82.14°C was recorded. How many degrees did the temperature change?
Answer:
In the above table we can observe sample 3 had the temperature 75.50°C. Sample 3 was used in another experiment. A temperature of 82.14°C was recorded. The difference of these two temperatures are 6.64°C

Question 26.
What is the difference in mass between Sample 1 and Sample 2?
Answer:
Sample 1 has the mass 0.98 g.
Sample 2 has the mass 0.58 g.
The difference in mass between Sample 1 and Sample 2 is 0.4.

Assessment Practice

Question 27.
Mauricio scored a total of 34.42 points in five gymnastic events. Which equation shows the best way to estimate Mauricio’s score for each event?
A. 35 ÷ 5 = 7
B. 35 ÷ 7 = 5
C. 30 ÷ 10 = 3
D. 40 ÷ 10 = 4
Answer:
Option A 35 ÷ 5 = 7 is correct.
35 ÷ 5 = 7 is the best way to estimate Mauricio’s score for each event.
Explanation:
Mauricio scored a total of 34.42 points in five gymnastic events. Use compatible method. In the above options option A is correct. The equation 34.42 ÷ 5 is closes to 35 ÷ 5. The actual dividend 34.42 is compatible to 35. Perform division operation 35 ÷ 5 = 7. The Estimated score for each event is 8.

Question 28.
Terry paid $117.50 for 18 identical flash drives. Which is the best estimate for the cost of each flash drive?
A. $6
B. $10
C. $12
D. $60
Answer:
Option A $6 is correct.
$117.50 ÷ 18
$120 ÷ 20 = $6.
The estimated cost of each flash drive is 6.
Explanation:
Terry paid $117.50 for 18 identical flash drives. Use rounding method. Rounding means replacing a number with an approximate value. In the above division method $117.50 ÷ 18. Round the numbers to the nearest ten or hundreds. Here $117.50 is rounded to $120 and 18 is rounded to 20. Now perform division operation on $120 ÷ 20 = $6. The estimated cost of each flash drive is $6.

Lesson 6.3 Use Models to Divide by a 1-Digit Whole Number

Activity

Solve&Share
Chris paid $3.60 for 3 colored pens. Each pen costs the same amount. How much did each pen cost? Solve this problem any way you choose.

You can use appropriate tools such as drawings, money, or place-value blocks to help you divide. Show your work!

Answer:

Each pen cost is $1.20.
Explanation:
Chris paid $3.60 for 3 colored pens. Each pen costs the same amount. Divide $3.60 with 3 colored pens then the quotient is $1.20. Each pen cost is $1.20.

Look Back! Without dividing, how do you know that the answer to the problem above must be greater than 1?
Answer:
The answer to the above problem must be greater than 1. Because each pen costs the same amount. we can clearly see that Chris paid $3.60 for 3 colored pens. So we can say without dividing method the answer to the above problem is greater than 1

Visual Learning Bridge

Essential Question How Can You Use Models to Find a Decimal Quotient?

A.
Three friends received $2.58 for aluminum cans they recycled. They decided to share the money equally. How much will each friend get?

You can use place value blocks. Let a 100 square = $1.00, a tenth bar = $0.10, and a hundredth cube = $0.01.

Find 2.58 ÷ 3.

B.
There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. You can see that there are 25 tenths in 2.58. Divide the 25 tenths into 3 equal groups.

C.
Trade the one extra tenth for 10 hundredths to get 18 hundredths. Divide the 18 hundredths into 3 equal groups. Each group gets 6 hundredths.

Each of the 3 friends will get $0.86.

Convince Me! Reasoning The next week, 4 friends got $8.24 for the cans they collected. How much money will each friend get? Estimate using compatible numbers and then use a strategy to find the answer.

Guided Practice

Do You Understand?

Question 1.
What is a reasonable estimate for 8.24 ÷ 4? Explain.
Answer:
Estimate $8.24 ÷ 4. Use compatible numbers.
Look for compatible numbers.
$8.24 ÷ 4 is closes to $8 ÷ 4 = $2.
The Estimated quotient is $2.
Each friend get $2.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. The next week, 4 friends got $8.24 for the cans they collected. In the above division problem $8.24 ÷ 4 is closes to 8 ÷ 4. The actual dividend 8.24 is compatible to 8. Perform division operation 8 ÷ 4 = 2. The Estimated quotient is 2. Each friend get $2.

Question 2.
How is dividing a decimal by a whole number similar to dividing a whole number by a whole number? Explain.
Answer:

Do You Know How?

Question 3.
Use models to help you divide 2.16 ÷ 4. Complete the division calculation.

Answer:

2.16 ÷ 4 = 0.54.
Explanation:
In the above image we can observe the division of 2.16 ÷ 4 = 0.54. There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. Divide 20 tenths into 4 equal groups. Each group gets 5 tenths. Four groups of 0.5 = 2.0.
Trade the one extra tenth for 10 hundredths to get 16 hundredths. Divide the 16 hundredths into 4 equal groups. Each group gets 4 hundredths. Four groups of 0.04 = 0.16.

Independent Practice

Leveled Practice In 4-9, divide. Use or draw models to help.

Question 4.

Answer:

1.35 ÷ 3 = 0.45
Explanation:
In the above image we can observe the division of 1.35 ÷ 3 = 0.45. There are not enough ones to put 1 in each group, so regroup the 1 ones into 10 tenths. We can see that there are 13 tenths in 1.35. Divide the 13 tenths into 3 equal groups. Each group gets 4 tenths. Three groups of 0.4 = 1.2.
Trade the one extra tenth for 10 hundredths to get 15 hundredths. Divide the 15 hundredths into 3 equal groups. Each group gets 5 hundredths. Three groups of 0.05 = 0.15.

Question 5.

Answer:

5.72 ÷ 4 = 1.43
Explanation:
In the above image we can observe the division of 5.72 ÷ 4 = 1.43. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 5 ones into 4 equal groups. Each group gets 1 ones. Four groups of 1 = 4. Regroup of the 1 ones into 10 tenths. We can see that there are 17 tenths in 5.72. Divide the 17 tenths into 4 equal groups. Each group gets 4 tenths. Four groups of 0.4 = 1.6.
Trade the one extra tenth for 10 hundredths to get 12 hundredths. Divide the 12 hundredths into 4 equal groups. Each group gets 3 hundredths. Four groups of 0.03 = 0.12.

Question 6.
2.38 ÷ 7
Answer:

2.38 ÷ 7 = 0.34.
Explanation:
In the above image we can observe the division of 2.38 ÷ 7 = 0.34. There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. We can see that there are 23 tenths in 2.38. Divide the 23 tenths into 7 equal groups. Each group gets 3 tenths. Seven groups of 0.3 = 2.1.
Trade the two extra tenth for 20 hundredths to get 28 hundredths. Divide the 28 hundredths into 7 equal groups. Each group gets 4 hundredths. Seven groups of 0.04 = 0.28.

Question 7.
4.71 ÷ 3
Answer:

4.71 ÷ 3 = 1.57.
Explanation:
In the above image we can observe the division of 4.71 ÷ 3 = 1.57. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 3 ones into 3 equal groups. Each group gets 1 ones. Three groups of 1 = 3. Regroup of the 1 ones into 10 tenths. We can see that there are 17 tenths in 4.71. Divide the 17 tenths into 3 equal groups. Each group gets 5 tenths. Three groups of 0.5 = 1.5.
Trade the two extra tenth for 20 hundredths to get 21 hundredths. Divide the 21 hundredths into 3 equal groups. Each group gets 7 hundredths. Three groups of 0.07 = 0.21.

Question 8.
1.76 ÷ 8
Answer:

1.76 ÷ 8 = 0.22.
Explanation:
In the above image we can observe the division of 1.76 ÷ 8 = 0.22. There are not enough ones to put 1 in each group, so regroup the 1 ones into 10 tenths. We can see that there are 17 tenths in 1.76. Divide the 17 tenths into 8 equal groups. Each group gets 2 tenths. Eight groups of 0.2 = 1.6.
Trade the one extra tenth for 10 hundredths to get 16 hundredths. Divide the 16 hundredths into 8 equal groups. Each group gets 2 hundredths. Eight groups of 0.02 = 0.16.

Question 9.
5.36 ÷ 2
Answer:

5.36 ÷ 2 = 2.68.
Explanation:
In the above image we can observe the division of 5.36 ÷ 2 = 2.68. There are enough ones to put 2 in each group, and extra ones is regrouped. Divide the 5 ones into 2 equal groups. Each group gets 2 ones. Two groups of 2 = 4. Regroup of the 1 ones into 10 tenths. We can see that there are 13 tenths in 5.36. Divide the 13 tenths into 2 equal groups. Each group gets 6 tenths. Two groups of 0.6 = 1.2.
Trade the one extra tenth for 10 hundredths to get 16 hundredths. Divide the 16 hundredths into 2 equal groups. Each group gets 8 hundredths. Two groups of 0.08 = 0.16.

Problem Solving

Question 10.
Reasoning Alan is modeling 2.65 ÷ 5. How should he exchange the place-value blocks so he can make 5 equal shares?

Answer:

2.65 ÷ 5 = 0.53
Explanation:
In the above image we can observe the division of 2.65 ÷ 5 = 0.53. There are not enough ones to put 1 in each group, so regroup the 2 ones into 20 tenths. We can see that there are 26 tenths in 2.65. Divide the 26 tenths into 5 equal groups. Each group gets 5 tenths. Five groups of 0.5 = 2.5.
Trade the one extra tenth for 10 hundredths to get 15 hundredths. Divide the 15 hundredths into 5 equal groups. Each group gets 3 hundredths. Five groups of 0.03 = 0.15.

Question 11.
Algebra Abby wants to know the value of n in the equation 7.913 × n = 791.3. What value for n makes the equation true?
Answer:
7.913 × n = 791.3
7.913 × 100 = 791.3
If n= 100 makes the equation true.

Question 12.
To find 5.16 ÷ 6, should you divide the ones first or the tenths first? Why?
Answer:

First we have to divide the ones first.
5.16 ÷ 6 = 0.86
Explanation:
In the above image we can observe the division of 5.16 ÷ 6 = 0.86. There are not enough ones to put 1 in each group, so regroup the 5 ones into 50 tenths. We can see that there are 51 tenths in 5.16. Divide the 51 tenths into 6 equal groups. Each group gets 8 tenths. Six groups of 0.8 = 4.8.
Trade the one extra tenth for 10 hundredths to get 36 hundredths. Divide the 36 hundredths into 6 equal groups. Each group gets 6 hundredths. Six groups of 0.06 = 0.36.

Question 13.
There are 264 children going on a field trip. Are 5 buses enough if each bus holds 52 children? Tell how you decided.
Answer:
264 ÷ 5 = 52.8
5 buses are not enough to hold 52 children in each bus.
Explanation:
There are 264 children going on a field trip. Divide 264 by 5 then the quotient is 52.8. 5 buses are not enough to hold 52 children in each bus.

Question 14.
Higher Order Thinking Ginny earned $49.50 for 6 hours of gardening and $38.60 for 4 hours of babysitting. For which job did she earn more money per hour? How much more per hour did she earn? Explain how you found the answers.

Think about what information in the problem you need to compare.

Answer:
Ginny earned $49.50 for 6 hours of gardening.
$49.50 ÷ 6 = $8.25.
Ginny earns $8.25 per hour.
Ginny earned $38.60 for 4 hours of babysitting.
$38.60 ÷ 4 = $9.65.
Ginny earns $9.65 per hour.
$9.65 – $8.25 = $1.4.
She earns more $1.4 per hour.
Explanation:
Ginny earned $49.50 for 6 hours of gardening. Perform division operation on $49.50 ÷ 6 = $8.25. Ginny earns $8.25 per hour. Ginny earned $38.60 for 4 hours of babysitting. Perform division operation on $38.60 ÷ 4 = $9.65. Ginny earns $9.65 per hour. Now we have to calculate how much more money she is earning. Subtract
$9.65 – $8.25 = $1.4. She earns more $1.4 per hour.

Assessment Practice

Question 15.
Tia drew the model below for 1.35 ÷ 3.

Part A
Explain the mistake Tia made.
Answer:
1.35 ÷ 3 = 0.45.
Explanation:
In the above image we can observe the 4 groups. Tia made a mistake of drawing the model above. She has to draw 3 groups. She drew one extra group of 4 tenths and 5 hundredths.
Part B
Draw the correct model and find the quotient.
Answer:

1.35 ÷ 3 = 0.45.
The quotient is 0.45.
Explanation:
In the above image we can observe the division of 1.35 ÷ 3 = 0.45. There are not enough ones to put 1 in each group, so regroup the 1 ones into 10 tenths. We can see that there are 13 tenths in 1.35. Divide the 13 tenths into 3 equal groups. Each group gets 4 tenths. Three groups of 0.4 = 1.2.
Trade the one extra tenth for 10 hundredths to get 15 hundredths. Divide the 15 hundredths into 3 equal groups. Each group gets 5 hundredths. Three groups of 0.05 = 0.15.

Lesson 6.4 Divide by a 2-Digit Whole Number

Activity

Solve&Share

Stan has a rectangular piece of carpet with an area of 23.4 square meters. The piece of carpet is 13 meters long. What is the width of the piece of carpet? Solve this problem any way you choose.

Model with Math You can write an equation to model the problem.

Look Back! How could you estimate the width of the piece of carpet?
Answer:
23.4 ÷ 13 = ?
23.4 ÷ 13 = 1.8
The width of the piece of carpet is 1.8 meters.
Explanation:
Stan has a rectangular piece of carpet with an area of 23.4 square meters. The piece of carpet is 13 meters long. Perform division operation 23.4 ÷ 13 = 1.8. The width of the piece of carpet is 1.8 meters.

Visual Learning Bridge

Essential Question How Do You Divide Decimals Question by 2-Digit Numbers?

A.
Erin’s garden has an area of 84.8 square feet. She knows the length is 16 feet. What is the width of Erin’s garden? How can you solve 84.8 ÷ 16 = w?

You can use what you know about dividing whole numbers to help.

B.
The total area is 84.8. The pieces of the model represent the areas for the partial quotients.

Convince Me! Reasoning How could Amy use estimation to make sure the decimal point is in the correct place in the quotient?

Guided Practice

Do You Understand?
In 1 and 2, use the example on the previous page.

Question 1.
Where is 5.3 shown in the diagram?
Answer:

Question 2.
How can you check that the quotient 5.3 is reasonable? Explain.
Answer:

Do You Know How?

In 3 and 4, complete the division problem.

Question 3.

Answer:

306.25 ÷ 49 = 6.25
Explanation:
In the above image we can observe the division operation  306.25 ÷ 49 = 6.25. The nearest possible multiple value of 49 is 294(49 x 6). Subtract 294 from 306.25 so as to get the remainder 12.25. 49 cannot be a multiple of 12.25 and so we have kept a decimal in the quotient and now 49 has the least possible multiple value of 9.8(49 x 0.2) near to 12.25. After subtracting 9.8 from 12.25, we are now having 6.2 as quotient and 2.45 as remainder. Now the possible multiple value of 49 near to 2.45 is 2.45 itself(49 x 0.05 = 2.45). Now the remainder is zero and the final quotient is 6.25.

Question 4.

Answer:

28.5 ÷ 15 = 1.9
Explanation:
In the above image we can observe the division operation  28.5 ÷ 15 = 1.9. The nearest possible multiple value of 15 is 15(15 x 1). Subtract 15 from 28.5 so as to get the remainder 13.5. 15 cannot be a multiple of 13.5 and so we have kept a decimal in the quotient and now the possible multiple value of 15 near to 13.5 is 13.5 itself(15 x 0.9 = 13.5). Now the remainder is zero and the final quotient is 1.9.

Independent Practice

Leveled Practice In 5-6, find each quotient and label the model.

Question 5.

Answer:

78.2 ÷ 17 = 4.6
Explanation:
In the above image we can observe the division operation  78.2 ÷ 17 = 4.6. The nearest possible multiple value of 17 is 68(17 x 4). Subtract 68 from 78.2 so as to get the remainder 10.2. 17 cannot be a multiple of 10.2 and so we have kept a decimal in the quotient and now the possible multiple value of 17 near to 10.2 is 10.2 itself(17 x 0.6 = 10.2). Now the remainder is zero and the final quotient is 4.6.

Question 6.

Answer:

304.75 ÷ 53 = 5.75
Explanation:
In the above image we can observe the division operation  304.75÷ 53 = 5.75. The nearest possible multiple value of 53 is 265(53 x 5). Subtract 265 from 304.75 so as to get he remainder 39.75. 53 cannot be a multiple of 39.75 and so we have kept a decimal in the quotient and now 53 has the least possible multiple value of 37.10(53 x 0.7) near to 39.75. After subtracting 37.10 from 39.75, we are now having 5.7 as quotient and 2.65 as remainder. Now the possible multiple value of 53 near to 2.65 is 2.65 itself(53 x 0.05 = 2.65). Now the remainder is zero and the final quotient is 5.75.

In 7-10, find each quotient.

Question 7.

Answer:

91.8 ÷ 27 = 3.4
The quotient is 3.4
Explanation:
In the above image we can observe the division operation  91.8 ÷ 27 = 3.4. The nearest possible multiple value of 27 is 81(27 x 3). Subtract 81 from 91.8 so as to get the remainder as 10.8. 27 cannot be a multiple of 10.8 and so we have kept a decimal in the quotient and now the possible multiple value of 27 near to 10.8 is 10.8 itself(27 x 0.4 = 10.8). Now the remainder is zero and the final quotient is 3.4.

Question 8.

Answer:

3.9 ÷ 15 = 0.26
The quotient is 0.26
Explanation:
In the above image we can observe the division operation  3.9 ÷ 15 = 0.26. 15 cannot be a multiple of 3.9 so we have kept a decimal in the quotient and now 15 has the least possible multiple value of 3.0(15 x 0.2) near to 3.9. Subtract 3.0 from 3.9 then the remainder is 0.9.  Now the possible multiple value of 15 near to 0.9 is 0.9 itself(15 x 0.06 = 0.9). Now the remainder is zero and the final quotient is 0.26.

Question 9.

Answer:

39.6 ÷ 12 = 3.3
The quotient is 3.3
Explanation:
In the above image we can observe the division operation  39.6 ÷ 12 = 3.3. The nearest possible multiple value of 12 is 36(12 x 3). Subtract 36 from 39.6 so as to get the remainder as 3.6. 12 cannot be a multiple of 3.6 and so we have kept a decimal in the quotient and now the possible multiple value of 12 near to 3.6 is 3.6 itself(12 x 0.3 = 3.6). Now the remainder is zero and the final quotient is 3.3.

Question 10.

Answer:

247.5 ÷ 50 = 4.95
Explanation:
In the above image we can observe the division operation  247.5 ÷ 50 = 4.95. The nearest possible multiple value of 50 is 200(50 x 4). Subtract 200 from 247.5 so as to get the remainder 47.5. 50 cannot be a multiple of 47.5 and so we have kept a decimal in the quotient and now 50 has the least possible multiple value of 45.0(50 x 0.9) near to 47.5. After subtracting 45.0 from 47.5, we are now having 4.9 as quotient and 2.5 as remainder. Now the possible multiple value of 50 near to 2.5 is 2.5 itself(50 x 0.05 = 2.5). Now the remainder is zero and the final quotient is 4.95.

Problem Solving

Question 11.
Sharon pays $98.75 for twenty-five 14-ounce boxes of Yummy Flakes cereal. How much does one box of cereal cost?
Answer:

Question 12.
Javier bought a new TV for $479.76. He will make equal payments each month for 2 years. How can Javier use compatible numbers to estimate each payment?
Answer:
Estimate $479.76 ÷ 24. Use compatible numbers.
Look for compatible numbers.
$479.76 ÷ 24 is closes to $480 ÷ 24 = $20.
The Estimated quotient is $20.
Javier pays each month $20.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. Javier bought a new TV for $479.76. He will make equal payments each month for 2 years. 2years means 24 months. In the above division problem $479.76 ÷ 24 is closes to 480 ÷ 24. The actual dividend $479.76 is compatible to 480. Perform division operation 480 ÷ 24 = 20. The Estimated quotient is 20. Javier pays each month $20.

Question 13.
Higher Order Thinking The area of the rectangular flower bed shown is 20.4 square meters. How many meters of edging are needed to go around the flower bed? Explain.

Answer:

Question 14.
Make Sense and Persevere Ms. Wang is shopping for a new refrigerator. Brand A costs $569 and uses 635 kilowatt-hours per year. Brand B costs $647 and uses 582 kilowatt-hours per year. If electricity costs $0.18 per kilowatt-hour, how much would Ms. Wang save on electricity per year by buying Brand B?
Answer:

Question 15.
Pat is driving from Seattle to Los Angeles. The distance is 1,135 miles. For the first 250 miles, it costs Pat $0.29 a mile to drive. After that, her driving cost is $0.16 a mile. What is Pat’s total driving cost?
Answer:

Assessment Practice

Question 16.
Which is equal to 27.3 divided by 13?
A. 0.21
B. 2.01
C. 2.1
D. 21
Answer:

27.3 ÷ 13 = 2.1
Option C is correct.
Explanation:
Divide 27.3 by 13 then the quotient is 2.1. So option C is correct.

Question 17.
Which is equal to 73.5 divided by 21?
A. 0.35
B. 3.05
C. 3.5
D. 30.5
Answer:

73.5 ÷ 21 = 3.5
Option C is correct.
Explanation:
Divide 73.5 by 21 the quotient is 3.5. So option C is correct.

Lesson 6.5 Divide by a Decimal

Activity

Solve & Share
Aaron buys erasers for his pencils. Each eraser costs $0.20. The total cost is $1.20. How many erasers does Aaron buy? Solve this problem any way you choose.

You can model the problem using hundredth grids or other drawings. Show your work!

Look Back! Reasoning How do you know your answer makes sense?
Answer:
$1.20 ÷ ? = $0.20
$1.20 ÷ 6 = $0.20
Aaron buys 6 erasers for his pencils.
Explanation:
Aaron buys erasers for his pencils. Each eraser costs $0.20. The total cost is $1.20. Divide $1.20 by $0.20 then the answer is 6. Aaron buys 6 erasers for his pencils.

Visual Learning Bridge

Essential Question How Can You Divide a Preston Decimal by a Decimal?

A.
Michelle purchases several bottles of water. Before tax is added, the total cost is $3.60 and the cost of each bottle is $1.20. How many bottles did she buy?
Divide $3.60 by $1.20.

You can use what you know about division with whole numbers to find how many groups of $1.20 are in $3.60.

B.
One Way
Think: $3.60 is the same as 36 dimes. $1.20 is the same as 12 dimes.

How many 12s are in 36?

She bought 3 bottles.

C.
Another Way
Think multiplication:
To find 3.60 ÷ 1.20, use the relationship between multiplication and division.
1.20 × ? = 3.60
Writing this another way:
120 hundredths ×? = 360 hundredths
? = 3
She bought 3 bottles.

Convince Me! Construct Arguments Is 3.6 ÷ 1.2 equal to, less than, or greater than 36 ÷ 12? Explain.

Guided Practice

Do You Understand?

Question 1.
How is dividing by a decimal like dividing by a whole number?
Answer:

Question 2.
How can you use multiplication to find 2.8 ÷ 0.7?
Answer:

Do You Know How?

In 3-6, use what you know about decimal division and mental math to find each quotient.

Question 3.
2 ÷ 0.5
Answer:
To find 2 ÷ 0.5, use the relationship between multiplication and division.
0.5 × ? = 2
? = 4
2 ÷ 0.5 = 4
The quotient is 4.
Explanation:
Multiply the divisor 0.5 with 4 then the product is 2. Divide the dividend 2 with the divisor 0.5 then the quotient is 4.

Question 4.
1.25 ÷ 0.25
Answer:
To find 1.25 ÷ 0.25, use the relationship between multiplication and division.
0.25 × ? = 1.25
? = 5
1.25 ÷ 0.25 = 5
The quotient is 5.
Explanation:
Multiply the divisor 0.25 with 5 then the product is 1.25. Divide the dividend 1.25 with the divisor 0.25 then the quotient is 5.

Question 5.
2.1 ÷ 0.7
Answer:
To find 2.1 ÷ 0.7, use the relationship between multiplication and division.
0.7 × ? = 2.1
? = 3
2.1 ÷ 0.7 = 3
The quotient is 3.
Explanation:
Multiply the divisor 0.7 with 3 then the product is 1.25. Divide the dividend 2.1 with the divisor 0.7 then the quotient is 3.

Question 6.
6.6 ÷ 0.3
Answer:
To find 6.6 ÷ 0.3, use the relationship between multiplication and division.
0.3 × ? = 6.6
? = 3
6.6 ÷ 0.3 = 22
The quotient is 22.
Explanation:
Multiply the divisor 0.3 with 22 then the product is 6.6. Divide the dividend 6.6 with the divisor 0.3 then the quotient is 22.

Think about how the dividend, divisor, and quotient are related.

Independent Practice

In 7-10, use what you know about multiplication, division, place value, and partial quotients to divide.

Question 7.
2.56 ÷ 0.04
Answer:
To find 2.56 ÷ 0.04, use the relationship between multiplication and division.
0.04 × ? = 2.56
Writing this another way:
4 hundredths × ? = 256 hundredths
? = 64
2.56 ÷ 0.04 = 64
Explanation:
We have to use the relationship between multiplication and division. Multiply the divisor 0.04 with 64 then the product is 2.56. By dividing 2.56 with 0.04 then the quotient is 64.

Question 8.
25.6 ÷ 0.4
Answer:
To find 25.6 ÷ 0.4, use the relationship between multiplication and division.
0.4 × ? = 25.6
Writing this another way:
4 tenths × ? = 256 tenths
? = 64
25.6 ÷ 0.4 = 64
Explanation:
We have to use the relationship between multiplication and division. Multiply the divisor 0.4 with 64 then the product is 25.6. By dividing 25.6 with 0.4 then the quotient is 64.

Question 9.
256 ÷ 4
Answer:
To find 256 ÷ 4, use the relationship between multiplication and division.
4 × ? = 256
Writing this another way:
4 ones × ? = 256 ones
? = 64
256 ÷ 4 = 64
Explanation:
We have to use the relationship between multiplication and division. Multiply the divisor 4 with 64 then the product is 256. By dividing 256 with 4 then the quotient is 64.

Question 10.
Describe the relationship among Problems 7, 8, and 9.
Answer:
The relationship among problems 7, 8, and 9. The quotient is same in all problems. In problem 7 hundredths place value is used. In problem 8 tenths place value is used. In problem 9 ones place value is used.

In 11-18, find each quotient.

Question 11.

Answer:

4.75 ÷ 0.25 = 19
The quotient is 19.
Explanation:
In this division operation 4.75 ÷ 0.25. The dividend is 4.75 and the divisor is 0.25. By dividing dividend 4.75 with the divisor 0.25 then the quotient is 19.

Question 12.

Answer:

4.56 ÷ 0.04 = 114
The quotient is 114.
Explanation:
In this division operation 4.56 ÷ 0.04. The dividend is 4.56 and the divisor is 0.04. By dividing dividend 4.56 with the divisor 0.04 then the quotient is 114.

Question 13.

Answer:

1.05 ÷ 0.05 = 21
The quotient is 21.
Explanation:
In this division operation 1.05 ÷ 0.05. The dividend is 1.05 and the divisor is 0.05. By dividing dividend 1.05 with the divisor 0.05 then the quotient is 21.

Question 14.

Answer:

182.8 ÷ 0.1 = 1828
The quotient is 1828.
Explanation:
In this division operation 182.8 ÷ 0.1. The dividend is 182.8 and the divisor is 0.1. By dividing dividend 182.8 with the divisor 0.1 then the quotient is 1828.

Question 15.

Answer:

17.25 ÷ 0.03 = 575
The quotient is 575.
Explanation:
In this division operation 17.25 ÷ 0.03. The dividend is 17.25 and the divisor is 0.03. By dividing dividend 17.25 with the divisor 0.03 then the quotient is 575.

Question 16.

Answer:

5.68 ÷ 0.8 = 71
The quotient is 71.
Explanation:
In this division operation 5.68 ÷ 0.8. The dividend is 5.68 and the divisor is 0.8. By dividing dividend 5.68 with the divisor 0.8 then the quotient is 71.

Question 17.

Answer:

6.24 ÷ 0.06 = 104
The quotient is 104.
Explanation:
In this division operation 6.24 ÷ 0.06. The dividend is 6.24 and the divisor is 0.06. By dividing dividend 6.24 with the divisor 0.06 then the quotient is 104.

Question 18.

Answer:

27.5 ÷ 2.5 = 11
The quotient is 11
Explanation:
In this division operation 27.5 ÷ 2.5. The dividend is 27.5 and the divisor is 2.5. By dividing dividend 27.5 with the divisor 2.5 then the quotient is 11.

Problem Solving

Question 19.
Make up a money story for the equation 3.75 ÷ 0.25 = 15.
Answer:

Question 20.
Carol bought 5 pork chops and 3 steaks. Each pork chop weighed 0.32 pound and each steak weighed 0.8 pound. How many pounds of meat did Carol buy in all?
Answer:

Question 21.
Tim estimates that 60 ÷ 5.7 is about 10. Will the actual quotient be greater than or less than 10? Explain.
Answer:
Estimate 60 ÷ 5.7. Use compatible numbers.
Look for compatible numbers.
60 ÷ 5.7 is close to 60 ÷ 6 = 10.
Tim estimates that 60 ÷ 5.7 is about 10.
60 ÷ 5.7 = 10.53
The actual quotient is 10.53.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 60 ÷ 5.7 is closes to 60 ÷ 10. The actual divisor 5.7 is compatible to 6. Perform division operation 60 ÷ 6 = 10. The Estimated quotient is 10. The actual quotient is 10.53. The actual quotient is greater than 10.

Question 22.
Dex estimates that 4,989 ÷ 0.89 is about 500. Is his estimate reasonable? Why or why not?
Answer:
Estimate 4,989 ÷ 0.89. Use compatible numbers.
Look for compatible numbers.
4,989 ÷ 0.89 is close to 4,990 ÷ 1 = 4,990.
Dex estimates that 4,989 ÷ 0.89 is about 500.
His Estimation is not reasonable.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 4,989 ÷ 0.89 is closes to 4,990 ÷ 1. The actual dividend 4,989 is compatible to 4,990. The actual divisor 0.89 is compatible to 1. Perform division operation 4,990 ÷ 1 = 4,990. The Estimated quotient is 4,990. His Estimation is not reasonable.

Question 23.
Higher Order Thinking Susan solves 1.4 ÷ 0.2 using the diagram at the right. Is her reasoning correct? Explain her thinking.

Answer:

Question 24.
Use Structure The same dividend is divided by 0.1 and 0.01. How do the quotients compare? Explain your thinking.
Answer:

Question 25.
A-Z Vocabulary Give three examples of a power of 10. Explain why one of your examples is a power of 10.
Answer:

Assessment Practice

Question 26.
Select the expressions that have a quotient of 4.
2.8 ÷ 0.7
0.28 ÷ 7
2.8 ÷ 0.07
0.28 ÷ 0.07
Answer:

Explanation:
In the above image we can observe the expressions that have a quotient of 4. Option 1 and option 4 is correct.
1. When 2.8 is divided by 0.7 then the quotient is 4. So option 1 is correct.
2. When 0.28 is divided by 7 then the quotient is 0.04. So option 2 is not correct.
3. When 2.8 is divided by 0.07 then the quotient is 40. So option 3 is not correct.
4. When 0.28 is divided by 0.07 then the quotient is 4. So option 4 is correct.

Question 27.
Select the expressions that have a quotient of 9.
1.35 ÷ 1.5
1.35 ÷ 0.15
13.5 ÷ 1.5
13.5 ÷ 0.15
Answer:

Explanation:
In the above image we can observe the expressions that have a quotient of 9. Option 2 and option 3 is correct.
1. When 1.35 is divided by 1.5 then the quotient is 0.9. So option 1 is not correct.
2. When 1.35 is divided by 0.15 then the quotient is 9. So option 2 is correct.
3. When 13.5 is divided by 1.5 then the quotient is 9. So option 3 is  correct.
4. When 13.5 is divided by 0.15 then the quotient is 90. So option 4 is not correct.

Lesson 6.6 Reasoning

Activity

Problem Solving

Reasoning

Solve & Share
Aaron has three slabs of beeswax. He plans to melt them and use all of the wax to form 36 candles. If all the candles are the same size and weight, how much will each candle weigh? Use reasoning to decide.

Thinking Habits
Be a good thinker! These questions can help you.
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Suppose Aaron wants each candle to weigh 0.5 pound. How many candles could he make with the beeswax?

Visual Learning Bridge

Essential Question How Can You Use Reasoning to Solve Problems?

A.
Ms. Watson is mixing mint green paint for her art class. She combines full bottles of blue, yellow, and white paint. How many 8-fluid ounce jars can she fill? Use reasoning to decide.

What do I need to do to solve this problem?
I need to add the three quantities of paint. Then I need to divide the sum by the capacity of a jar.

B.
How can I use reasoning to solve this problem?
I can
• identify the quantities I know
• draw a bar diagram to show relationships.
• give the answer using the correct unit.

Here’s my thinking…

C.
Use bar diagrams to show how the quantities are related.
First, find the sum of the three quantities of paint in the mixture.

Then, divide 93.6 by 8 to find the 11.7 number of jars that can be filled.

Ms. Watson can fill 11 jars. The 12th jar will be only partially filled.

Convince Me! Reasoning Ms. Watson is mixing 34.6 fluid Ounces of red paint and 18.2 fluid ounces of yellow paint to make orange paint. How many 12-fluid Ounce jars can she fill? Use reasoning to decide.

Guided Practice

Reasoning
Miranda mixed 34.5 fluid Ounces of blue paint, 40.5 fluid ounces of red paint, and 2 fluid Ounces of black paint to make purple paint. She poured the same amount of the purple paint into each of 14 jars. How much paint did she pour in each jar?

Use reasoning to decide how the quantities in the problem are related.

Question 1.
Explain what each of the quantities in the problem means.
Answer:

Question 2.
Describe one way to solve the problem.
Answer:

Question 3.
What is the solution to the problem? Explain.
Answer:

Independent Practice

Reasoning
Sue made chicken soup by combining the entire can of soup shown with a full can of water. How many 10-fluid Ounce bowls can she fill with the soup? How much soup will be left over?

Question 4.
Explain what each of the quantities in the problem means.
Answer:

Question 5.
Describe one way to solve the problem.
Answer:

Question 6.
What is the solution to the problem? Explain.
Answer:

Problem Solving

Performance Task
Cooking Competition
Lucas’s cooking class is having a cooking competition. There are 6 teams. Each student brought supplies that will be shared equally among the teams. The table shows the supplies Lucas brought. If the supplies are shared equally among the teams, how much of each supply will each team get?

Question 7.
Make Sense and Persevere Do you need all of the information given above to solve the problem? Explain.
Answer:

Question 8.
Reasoning Describe how to solve the problem.
Answer:

Use reasoning to think about what the quantities in the table represent.

Question 9.
Model with Math Write equations to represent how much of each supply each team will get.
Answer:

Question 10.
Be Precise What is the solution to the problem? Explain.
Answer:

Question 11.
Critique Reasoning Lucas says that to find the total cost of the rice, you should multiply 3.5 by $1.89. Do you agree? Explain.
Answer:

Topic 6 Fluency Practice

Activity

Follow the path
Solve each problem. Follow products that are multiples of 20 to shade a path from START to FINISH. You can only move up, down, right, or left.

Answer:

In the above image we can observe some multiplication problems. Products that are multiples of 20 to shade a path from START to FINISH. The products that are shaded with green color are multiples of 20.

Topic 6 Vocabulary Review

Glossary

Understand Vocabulary

Write always, sometimes, or never.

Word List
• estimate
• exponent
• hundredths
• power
• quotient
• rounding
• tenths
• thousandths

Question 1.
A digit in the hundredths place has \(\frac{1}{10}\) the value of the same digit in the tenths place. ______
Answer:
A digit in the hundredths place has \(\frac{1}{10}\) the value of the same digit in the tenths place. Sometimes.

Question 2.
The answer to a division problem is less than the divisor. ______
Answer:
The answer to a division problem is less than the divisor. Sometimes

Question 3.
A whole number divided by a decimal number is a whole number. ____
Answer:
A whole number divided by a decimal number is a whole number. Sometimes

Question 4.
Dividing by 10³ moves the decimal point in the dividend three places to the left. ____
Answer:
Dividing by 10³ moves the decimal point in the dividend three places to the left. Always

Question 5.
Multiplying the dividend and the divisor by the same power of 10 changes the quotient. ____
Answer:
Multiplying the dividend and the divisor by the same power of 10 changes the quotient. Never

Question 6.
The answer to a division problem is greater than the divisor. ______
Answer:
The answer to a division problem is greater than the divisor. Sometimes

Write T for true or F for false.

_____ Question 7.
3.65 ÷ 5.2 < 1
Answer: _____
3.65 ÷ 5.2 < 1
0.70 < 1
True
Explanation:
Perform division operation on 3.65 ÷ 5.2 = 0.70. The quotient is 0.70. The quotient 0.70 is less than 1. So the above expression is True.

Question 8.
48 ÷ 0.6 = 0.8
Answer:
48 ÷ 0.6 = 0.8
48 ÷ 0.6 = 80
The answer for above division operation is not correct.  So the answer is False.
Explanation:
Perform division operation on 48 ÷ 0.6 = 80. The quotient is 80.  In the above division operation the quotient is 0.8. So the above expression is False.

_____ Question 9.
2.42 ÷ 2.1 > 1.
Answer:
2.42 ÷ 2.1 > 1.
1.15 > 1
The answer for above division operation is 1.15 is greater than 1. So the answer is True.
Explanation:
Perform division operation on 2.42 ÷ 2.1 = 1.15. The quotient is 1.15. The quotient 1.15 is greater than 1. So the above expression is True.

_____ Question 10.
4.9 ÷ 0.8 < 4.9
Answer:
4.9 ÷ 0.8 < 4.9
6.125 < 4.9
The answer for above division operation is 6.125 is not less than 4.9. So the answer is False.
Explanation:
Perform division operation on 4.9 ÷ 0.8 = 6.125. The quotient is 6.125. The quotient 6.125 is  not less than 4.9. So the above expression is False.

Use Vocabulary in Writing

Question 11.
Mary says the digits in the quotient of 381.109 0.86 are 4 4 315, but she doesn’t know where to place the decimal point. How can Mary use number sense to place the decimal point? Use at least three terms from the Word List in your answer.
Answer:

Topic 6 Reteaching

Set A
pages 229-232
Find 340.5 ÷ 100.
Dividing by 10, or 10¹, means moving the decimal point one place to the left.
Dividing by 100, or 10², means moving the decimal point two places to the left.
Dividing by 1,000, or 10³, means moving the decimal point three places to the left.

Remember that when dividing decimals by a power of 10, you may need to use one or more zeros as placeholders.

Use mental math to find each quotient.

Question 1.
34.6 ÷ 10¹
Answer:
34.6 ÷ 10¹
34.6 ÷ 10 = 3.46
The quotient is 3.46.
Explanation:
Dividing by 10, or 10¹, means moving the decimal point one place to the left. Move the dividend decimal point 34.6 one place to the left then the result is 3.46. The quotient is 3.46.

Question 2.
6,483 ÷ 10²
Answer:
6,483 ÷ 10²
6,483 ÷ 100 = 64.83
The quotient is 64.83.
Explanation:
Dividing by 100, or 10², means moving the decimal point two places to the left. Move the dividend decimal point 6,483 two places to the left then the result is 64.83. The quotient is 64.83.

Question 3.
148.3 ÷ 100
Answer:
148.3 ÷ 100 = 1.483
The quotient is 1.483.
Explanation:
Dividing by 100, or 10², means moving the decimal point two places to the left. Move the dividend decimal point 148.3 two places to the left then the result is 1.483. The quotient is 1.483.

Question 4.
29.9 ÷ 10¹
Answer:
29.9 ÷ 10¹
29.9 ÷ 10 = 2.99
The quotient is 2.99
Explanation:
Dividing by 10, or 10¹, means moving the decimal point one place to the left. Move the dividend decimal point 29.9 one place to the left then the result is 2.99. The quotient is 2.99.

Question 5.
70.7 ÷ 10
Answer:
70.7 ÷ 10 = 7.07
The quotient is 7.07.
Explanation:
Dividing by 10, or 10¹, means moving the decimal point one place to the left. Move the dividend decimal point 70.7 one place to the left then the result is 7.07. The quotient is 7.07.

Question 6.
5,913 ÷ 10³
Answer:
5,913 ÷ 10³
5,913 ÷ 1000 = 5.913
The quotient is 5.913.
Explanation:
Dividing by 1,000, or 10³, means moving the decimal point three places to the left. Move the dividend decimal point 5,913 three place to the left then the result is 5.913. The quotient is 5.913.

Set B
pages 233-236
Estimate 27.3 ÷ 7.1. Use compatible numbers.

So, 27.3 ÷ 7.1 is about 4.
Estimate 42.5 ÷ 11. Use rounding.

So, 42.5 ÷ 11 is about 4.

Remember that compatible numbers are numbers that are easy to compute in your head.

Write a number sentence that shows a way to estimate each quotient.

Question 1.
26.2 ÷ 5
Answer:
Estimate 26.2 ÷ 5. Use compatible numbers.
Look for compatible numbers.
26.2 ÷ 5 is closes to 25 ÷ 5 = 5.
So, 26.2 ÷ 5 is about 5.
The Estimated quotient is 5.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 26.2 ÷ 5 is closes to 25 ÷ 5. The actual dividend 26.2 is compatible to 25. Perform division operation 25 ÷ 5 = 5. The Estimated quotient is 5.

Question 2.
49.6 ÷ 7.8
Answer:
Estimate 49.6 ÷ 7.8. Use compatible numbers.
Look for compatible numbers.
49.6 ÷ 7.8 is closes to 49 ÷ 7 = 7.
So, 49.6 ÷ 7.8 is about 7.
The Estimated quotient is 7.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 49.6 ÷ 7.8 is closes to 49÷ 7. The actual dividend 49 is compatible to 25. The actual divisor 7.8 is compatible to 7. Perform division operation 25 ÷ 5 = 5. The Estimated quotient is 7.

Question 3.
121 ÷ 12.75
Answer:
Estimate 121 ÷ 12.75. Use compatible numbers.
Look for compatible numbers.
121 ÷ 12.75 is closes to 120 ÷ 12 = 10.
So, 121 ÷ 12.75 is about 10.
The Estimated quotient is 10.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 121 ÷ 12.75 is closes to 120 ÷ 12. The actual dividend 121 is compatible to 120. The actual divisor 12.75 is compatible to 12. Perform division operation 120 ÷ 12 = 10. The Estimated quotient is 10.

Question 4.
32.41 ÷ 10.9
Answer:
Estimate 32.41 ÷ 10.9. Use rounding.
Round to the nearest ten: 32 rounds to 30; 10.9 rounds to 10.
32.41 ÷ 10.9 is about 30 ÷ 10 = 3.
Explanation:
Rounding means replacing a number with an approximate value. In the above division method 32.41 ÷ 10.9. Round the numbers to the nearest ten or hundreds. Here 32.41 is rounded to 30 and 10.9 is rounded to 10. Now perform division operation on 30 ÷ 10 = 3. The estimated quotient is 3.

Question 5.
82.4 ÷ 3.7
Answer:
Estimate 82.4 ÷ 3.7. Use compatible numbers.
Look for compatible numbers.
82.4 ÷ 3.7 is closes to 80 ÷ 4 = 20.
So, 82.4 ÷ 3.7 is about 20.
The Estimated quotient is 20.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 82.4 ÷ 3.7 is closes to 80 ÷ 4. The actual dividend 82.4 is compatible to 80. The actual divisor 3.7 is compatible to 4. Perform division operation 80 ÷ 4 = 20. The Estimated quotient is 20.

Question 6.
28.5 ÷ 0.94
Answer:
Estimate 28.5 ÷ 0.94. Use compatible numbers.
Look for compatible numbers.
28.5 ÷ 0.94 is closes to 30 ÷ 1 = 30.
So, 28.5 ÷ 0.94 is about 30.
The Estimated quotient is 30.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 28.5 ÷ 0.94 is closes to 30 ÷ 1. The actual dividend 28.5 is compatible to 30. The actual divisor 0.94 is compatible to 1. Perform division operation 30 ÷ 1 = 30. The Estimated quotient is 30.

Set C
pages 237-240
Find 1.14 ÷ 3.

Remember to use estimation to check the placement of the decimal point in the quotient. Divide. Use models to help.

Question 1.
6.58 ÷ 7
Answer:

6.58 ÷ 7 = 0.94
Explanation:
In the above image we can observe the division of 6.58 ÷ 7 = 0.94. There are not enough ones to put 1 in each group, so regroup the 6 ones into 60 tenths. Divide 65 tenths into 7 equal groups. Each group gets 9 tenths. Seven groups of 0.9 = 6.3.
Trade the two extra tenth for 20 hundredths to get 28 hundredths. Divide the 28 hundredths into 7 equal groups. Each group gets 4 hundredths. Seven groups of 0.04 = 0.28.

Question 2.
156 ÷ 8
Answer:

156 ÷ 8 = 19.5
Explanation:
In the above image we can observe the division of 156 ÷ 8 = 19.5. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 156 ones into 8 equal groups. Each group gets 19 ones. Eight groups of 19 = 152. Regroup of the 4 ones into 40 tenths.  Divide the 40 tenths into 8 equal groups. Each group gets 5 tenths. Eight groups of 0.5 = 4.

Question 3.
34.2 ÷ 3
Answer:

34.2 ÷ 3 = 11.4
Explanation:
In the above image we can observe the division of 34.2 ÷ 3 = 11.4. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 34 ones into 3 equal groups. Each group gets 11 ones. Three groups of 11 = 33. Regroup of the 1 one into 10 tenths.  Divide the 12 tenths into 3 equal groups. Each group gets 4 tenths. Three groups of 0.4 = 1.2.

Question 4.
5.84 ÷ 4
Answer:

5.84 ÷ 4 = 1.46
Explanation:
In the above image we can observe the division of 5.84 ÷ 4 = 1.46. There are enough ones to put 1 in each group, and extra ones is regrouped. Divide the 5 ones into 4 equal groups. Each group gets 1 ones. Four groups of 1 = 4. Regroup of the 1 ones into 10 tenths. We can see that there are 18 tenths in 5.84. Divide the 18 tenths into 4 equal groups. Each group gets 4 tenths. Four groups of 0.4 = 1.6.
Trade the one extra tenth for 10 hundredths to get 24 hundredths. Divide the 24 hundredths into 4 equal groups. Each group gets 6 hundredths. Four groups of 0.06 = 0.24.

Question 5.
Michelle pays $66.85 for a costume pattern and 8 yards of fabric. The costume pattern costs $4.85. How much does each yard of the fabric cost?
Answer:

Set D
pages 241-244

Find 94.5 ÷ 15.
Estimate first
94.5 ÷ 15 is close to 100 ÷ 20 = 5, so start dividing with the ones place.

So, 94.5 ÷ 15 = 6.3

Remember that you can check your calculation by multiplying the quotient by the divisor.

Find each quotient.

Question 1.
91.2 ÷ 16
Answer:

91.2 ÷ 16 = 5.7
Explanation:
In the above image we can observe the division operation  91.2 ÷ 16 = 5.7. The nearest possible multiple value of 16 is 80(16 x 5). Subtract 80 from 91.2 so as to get the remainder 11.2. 16 cannot be a multiple of 11.2 and so we have kept a decimal in the quotient and now the possible multiple value of 16 near to 11.2 is 11.2 itself(16 x 0.7 = 11.2). Now the remainder is zero and the final quotient is 5.7.

Question 2.
361.5 ÷ 15
Answer:

361.5 ÷ 15 = 24.1
Explanation:
In the above image we can observe the division operation  361.5 ÷ 15 = 24.1. The nearest possible multiple value of 15 is 360(15 x 24). Subtract 360 from 361.5 so as to get the remainder 1.5. 15 cannot be a multiple of 1.5 and so we have kept a decimal in the quotient and now the possible multiple value of 15 near to 1.5 is 1.5 itself(15 x 0.1 = 1.5). Now the remainder is zero and the final quotient is 24.1.

Question 3.
29.04 ÷ 22
Answer:

29.04 ÷ 22 = 1.32
Explanation:
In the above image we can observe the division operation  29.04 ÷ 22 = 1.32. The nearest possible multiple value of 22 is 22(22 x 1). Subtract 22 from 29.04 so as to get the remainder 7.04. 22 cannot be a multiple of 7.04 and so we have kept a decimal in the quotient and now 22 has the least possible multiple value of 6.60(22 x 0.3) near to 7.04. After subtracting 6.6 from 7.04, we are now having 1.3 as quotient and 0.44as remainder. Now the possible multiple value of 22 near to 0.44 is 0.44 itself(22 x 0.02 = 0.44). Now the remainder is zero and the final quotient is 1.32.

Question 4.
144 ÷ 45
Answer:

144 ÷ 45 = 3.2
Explanation:
In the above image we can observe the division operation  144 ÷ 45= 3.2. The nearest possible multiple value of 45 is 135(45 x 3). Subtract 135 from 144 so as to get the remainder 9. 45 cannot be a multiple of 9 and so we have kept a decimal in the quotient and now the possible multiple value of 45 near to 9.0 is 9.0 itself(45 x 0.2 = 9.0). Now the remainder is zero and the final quotient is 3.2.

Question 5.
A 12-ounce bottle of shampoo costs $4.20. A 16-ounce bottle costs $6.88. Which shampoo costs less per ounce? How do you know?
Answer:
A 12-ounce bottle of shampoo costs $4.20.
$4.20 ÷ 12 = $0.35.
A 16-ounce bottle costs $6.88.
$6.88 ÷ 16 = $0.43
12- ounce bottle shampoo costs less per ounce is $0.35.
Explanation:
A 12-ounce bottle of shampoo costs $4.20. Divide $4.20 ÷ 12 = $0.35. A 16-ounce bottle costs $6.88.  Divide $6.88 ÷ 16 = $0.43. Compare these 12- ounce and 16- ounce bottle of shampoos. The 12-ounce bottle shampoo costs less per ounce is $0.35.

Set E
pages 245-248

Find 4.8 ÷ 0.6.

48 tenths ÷ 6 tenths
6 tenths × ? = 48 tenths
? = 8
So, 4.8 ÷ 6 = 8

Remember to use estimation Dates to check the quotient for reasonableness.

Question 1.
6.4 ÷ 3.2
Answer:
6.4 ÷ 3.2
3.2 x 2 = 6.4
6.4 ÷ 3.2 = 2
The quotient is 2.
Explanation:
Multiply 3.2 with 2 then the product is 6.4. Dividing 6.4 by 3.2 then the quotient is 2.

Question 2.
6.4 ÷ 0.32
Answer:
0.32 x 20 = 6.4
6.4 ÷ 0.32 = 20
The quotient is 20.
Explanation:
Multiply 0.32 with 20 then the product is 6.4. Dividing 6.4 by 0.32 then the quotient is 20.

Question 3.
9.6 ÷ 0.8
Answer:
12 x 8 = 96
12 x 0.8 = 9.6
9.6 ÷ 0.8 = 12
The quotient is 12.
Explanation:
Multiply 0.8 with 12 then the product is 9.6. Dividing 9.6 by 0.8 then the quotient is 12.

Question 4.
0.96 ÷ 0.08
Answer:
12 x 8 = 96
12 x 0.08 = 0.96
0.96 ÷ 0.08 = 12
The quotient is 12.
Explanation:
Multiply 0.08 with 12 then the product is 0.96. Dividing 0.96 by 0.08 then the quotient is 12.

Question 5.
41.8 ÷ 2.2
Answer:
19 x 2.2 = 41.8
41.8 ÷ 2.2 = 19
The quotient is 19.
Explanation:
Multiply 2.2 with 19 then the product is 41.8. Dividing 41.8 by 2.2 then the quotient is 19.

Question 6.
4.18 ÷ 0.22
Answer:
0.22 x 19 = 4.18
4.18 ÷ 0.22 = 19
The quotient is 19.
Explanation:
Multiply 0.22 with 19 then the product is 4.18. Dividing 4.18 by 0.22 then the quotient is 19.

Question 7.
81.4 ÷ 7.4
Answer:
11 x 7.4 = 81.4
81.4 ÷ 7.4 = 11
The quotient is 11.
Explanation:
Multiply 7.4 with 11 then the product is 81.4. Dividing 81.4 by 7.4 then the quotient is 11.

Question 8.
814 ÷ 74
Answer:
814 ÷ 74 = 11
The quotient is 11.
Explanation:
By Dividing 814 by 74 then the quotient is 11.

Question 9.
9.6 ÷ 0.03
Answer:
9.6 ÷ 0.03 = 320
The quotient is 320.
Explanation:
By Dividing 9.6 by 0.03 then the quotient is 320.

Question 10.
9.6 ÷ 0.3
Answer:
9.6 ÷ 0.3 = 32
The quotient is 32.
Explanation:
By Dividing 9.6 by 0.3 then the quotient is 32.

Set F
pages 249-252

Think about these questions to help you reason abstractly and quantitatively.

Thinking Habits
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Zoey has a goal of saving $750 for a vacation. Her vacation will last 6 days. She wants to save the same amount each week for 12 weeks to reach her goal. How much should she save each week?
Which quantities do you need to solve the problem?
The savings goal is $750; Zoey will save for 12 weeks.

Will Zoey need to save more than or less than $80 each week? Explain your reasoning.
Less than; 12 × $80 = $960, but she only needs to save $750.
How much should she save each week? Write an equation to represent the problem.
$62.50; $750 :12 = $62.50

Remember to check the reasonableness of a solution by making sure your calculations are correct, and that you answered all of the questions that were asked.
lan uses 4 feet of ribbon to wrap each package. How many packages can he wrap with 5.6 yards of ribbon?

Remember there are 3 feet in a yard.

Question 1.
Describe one way to solve the problem.
Answer:

Question 2.
What is the solution to the problem? Show your work.
Answer:

A bushel of apples weighs about 42 pounds. There are 4 pecks in a bushel. It takes 2 pounds of apples to make one pie. How many pies can you make with one peck of apples?

Question 3.
How are the numbers in the problem related?
Answer:

Question 4.
Describe one way to solve the problem.
Answer:

Question 5.
Solve the problem. Show your work.
Answer:

Topic 6 Assessment Practice

Question 1.
Mr. Dodd filled the gas tank on his lawn mower with 3.8 gallons of gas. He mowed his yard 10 times on the same tank of gas. He used the same amount of gas each time. How much gas did he use each time? Write an equation to show your work. Explain how the decimal point moves.
Answer:

Question 2.
Kimberly scored a total of 35.08 points in four events for her gymnastic competition. If she scored the same number of points in each event, how many points did she score in each? Write an equation to show your work.
Answer:
35.08 points ÷  4 = 8.77 points.
She scored 8.77 points in each event.
Explanation:
Kimberly scored a total of 35.08 points in four events for her gymnastic competition. If she scored the same number of points in each event. Divide 35.08 by 4 then the quotient is 8.77. She scored 8.77 points in each event.

Question 3.
Choose the correct quotient for each expression. Use number sense and estimation to help.

Answer:

Explanation:
Perform division operation on 21.6 ÷ 1.8 = 12. The quotient is 12. Put a tick mark below the number 12.
Perform division operation on 10.23 ÷ 0.55 = 18.6. The quotient is 18.6. Put a tick mark below the number 18.6.
Perform division operation on 78.75 ÷ 3.5 = 22.5. The quotient is 22.5. Put a tick mark below the number 22.5.
Perform division operation on 29.67 ÷ 4.6 = 18.6. The quotient is 18.6. Put a tick mark below the number 18.6.

Question 4.
What is the value of the missing exponent in the equation?

A. 1
B. 2
C. 3
D. 4
Answer:

80.5 ÷ 10² = 0.805
The missing exponent in the equation is 2.

Question 5.
The chef at a restaurant bought 37 pounds of salad for $46.25. How much did she pay for each pound of salad?
A. 0.125
B. $1.25
C. $1.3
D. $12.50
Answer:

$46.25 ÷ 37 = $1.25
She pays $1.25 for each pound of salad.
Explanation:
The chef at a restaurant bought 37 pounds of salad for $46.25. Divide $46.25 by 37 pounds then the quotient is $1.25. She pays $1.25 for each pound of salad.

Question 6.
Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same amount.
A. Estimate the cost of each ticket. Write an equation to show your work.
B. Find the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.
Answer:
A. $231 ÷ 12 = ?
Estimate $231 ÷ 12 closes to 230 ÷ 12 = $19.16.
The estimated cost of each ticket is $19.16.
Explanation:
Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same amount. Divide 230 by 12 then the quotient is $19.16. The estimated cost of each ticket is $19.16.
B. $231 ÷ 12 = $19.25
The actual cost of each ticket is $19.25.
Explanation:
The estimated cost of each ticket is $19.16 and the actual cost of each ticket is $19.25.  Both estimated answer and actual answer are reasonable.

Question 7.
Select all of the following equations that are true when 12.5 is used. Use number sense to help.

Answer:

Explanation:
In the above image we can observe the equations that are true when 12.5 is used. Option 1 and option 3, option 5 is correct.
1. When 12.5 is divided by 10 then the quotient is 1.25. So option 1 is correct.
2. When 12.5 is divided by 1 then the quotient is 12.5. So option 2 is not correct.
3. When 12.5 is divided by 1 then the quotient is 12.5. So option 3 is correct.
4. When 12.5 is divided by 100 then the quotient is 0.125. So option 4 is not correct.
5. When 12.5 is divided by 100 then the quotient is 0.125. So option 5 is correct.

Question 8.
Which division problem does the model Tess made represent?

A. 1.35 ÷ 3 = 0.45
B. 1.35 ÷ 3 = 0.54
C. 1.62 ÷ 3 = 0.45
D. 1.62 ÷ 3 = 0.54
Answer:

Option D 1.62 ÷ 3 = 0.54 is correct.
Explanation:
In the above image we can observe 5 tenths and 4 hundredths. By dividing 1.62 by 3 then the quotient is 0.54. The division problem answer option D represents the above image.

Question 9.
If 8 ounces of canned pumpkin has 82 calories, how many calories are in 1 ounce? Use your answer to find how many calories are in 6 ounces of pumpkin.
Answer:

10.25 calories are there in 1 ounce.
10.25 calories = 1 ounce
? calories    = 6 ounces
10.25 calories x 6 ounces = 61.5 calories
61.5 calories are in 6 ounces of pumpkin.
Explanation:
8 ounces of canned pumpkin has 82 calories. Perform division operation on 82 ÷ 8 = 10.25. There are 10.25 calories in 1 ounce. We have to find out the how many calories are there in 6 ounces. Perform multiplication operation on these two numbers 10.25 calories and 6 ounces then the product is 61.5 calories. There are 61.5 calories in 6 ounces of pumpkin.

Question 10.
Use the equation 1.6 ÷ n = 0.016.
A. What value of n makes the equation true? Write your answer using an exponent.
B. Explain how you know your answer is correct.
Answer:
A. 1.6 ÷ n = 0.016.
1.6 ÷ 0.01 = 0.016.
1.6 ÷ 10^-2 = 0.016.
The value n = 0.01 makes the equation true. The exponent form of 0.01 is 10^-2 .
B. We can check the answer is correct or not by performing division operation on 0.016 ÷ 1.6 = 0.01.

Question 11.
Eileen bought 8 roses for $45.50. Which is the best way to estimate the cost of one rose?
A. $45 ÷ 5 = $9.00
B. $48 ÷ 8 = $6.00
C. $45 ÷ 10 = $0.45
D. $40 ÷ 8 = $0.50
Answer:
Option B $48 ÷ 8 = $6.00 is the best way to estimate the cost of one rose.

Estimate $45.50÷ 8. Use compatible numbers.
Look for compatible numbers.
$45.50÷ 8 is closes to $48 ÷ 8 = $6.
The Estimated cost of one rose is $6.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. Eileen bought 8 roses for $45.50. In the above division problem $45.50÷ 8 is closes to 48 ÷ 8. The actual dividend $45.50 is compatible to 48. Perform division operation $48 ÷ 8 = 6. The Estimated cost of one rose is $6.

Question 12.
Toby’s faucet dripped a total of 1.92 liters of water in 24 hours. The faucet dripped the same amount each hour.
A. Estimate how many liters his faucet dripped each hour. Write an equation to model your work.
B. Find the exact amount of water that dripped each hour.
C. Compare your estimate to your answer. Is your answer reasonable? Explain.
Answer:
A. 1.92 liters ÷ 24 = ?
Estimate 1.92 liters ÷ 24 closes to 2 liters ÷ 24 = 0.083 liters.
The estimated amount of water dripped each hour is 0.083 liters.
Explanation:
Toby’s faucet dripped a total of 1.92 liters of water in 24 hours. Divide 2liters by 24 then the result is 0.083 liters. The estimated amount of water dripped each hour is 0.083 liters.
B. 1.92 liters ÷ 24 = 0.08 liters.
The exact amount of water that dripped each hour is 0.08 liters.
Explanation:
Perform division operation on 1.92 liters by 24 hours. The quotient is 0.08 liters. The exact amount of water that dripped each hour is 0.08 liters.
c. The estimated amount of water dripped each hour is 0.083 liters.
The exact amount of water that dripped each hour is 0.08 liters. The answer is reasonable.

Topic 6 Assessment Practice

Question 13.
Choose the correct quotient for each expression.

Answer:

Explanation:
Perform division operation on 0.78 ÷ 10 = 0.078. The quotient is 0.078. Put a tick mark below the number 0.078.
Perform division operation on 7,080 ÷ 10³ = 7.08. The quotient is 7.08. Put a tick mark below the number 7.08.
Perform division operation on 70.8 ÷ 10² = 0.708. The quotient is 0.708. Put a tick mark below the number 0.708.
Perform division operation on 780 ÷ 10³ = 0.78. The quotient is 0.78. Put a tick mark below the number 0.78.

Question 14.
Diego is making a large mural. He draws a hexagon with a perimeter of 10.5 meters. Each side of the hexagon is the same length.

A. How many meters long is each side of Diego’s hexagon? Write an equation to model your work.
B. The total cost of the supplies to paint the mural is $38.70. Diego and 9 friends divide the total cost equally. How much does each person pay?
Answer:

Question 15.
Select all of the following equations that are true when 40.3 is used. Use number sense to help.

Answer:

Explanation:
In the above image we can observe the equations in option 2 and option 3 are true when 40.3 is used.
Perform division operation on 40.3 ÷ 10² = 0.403. The quotient is 0.403. So option 2 is correct.
Perform division operation on 40.3 ÷ 10⁰ = 40.3. The quotient is 40.3. So option 3 is correct.

Question 16.
Lou’s Diner spent $12.80 on 8 pounds of potatoes. What was the cost of one pound of potatoes? What would be the total cost if the cost per pound remained the same and the diner bought 7 pounds? Show your work.
Answer:
$12.80 ÷ 8 pounds = $1.6
The cost of one pound of potatoes is $1.6.
? ÷ 7 pounds = $1.6
$1.6 x 7 pounds = $11.2
The total cost is $11.2. If the cost per pound remains same and the dinner bought 7 pounds.
Explanation:
Lou’s Diner spent $12.80 on 8 pounds of potatoes. Divide $12.80 ÷ 8 pounds = $1.6. The cost of one pound of potatoes is $1.6. If the cost per pound remains same and the dinner bought 7 pounds. Multiply $1.6 x 7 pounds = $11.2. The total cost is $11.2.

Question 17.
How many quarters are there in $30? Solve the equation 30 ÷ 0.25 to help you.
A. 12 quarters
B. 20 quarters
C. 120 quarters
D. 200 quarters
Answer:
30 ÷ 0.25 = 120
There are 120 quarters in $30.
Option C is correct.
Explanation:
Perform division operation on 30 ÷ 0.25 = 120 . Here the dividend is 30 and the divisor is 0.25. By dividing the dividend with divisor then the quotient is 120. There are 120 quarters in $30. So option C is correct.

Question 18.
When solving 6.1 ÷ 10², how is the decimal point moved?
A. 1 place to the right
B. 1 place to the left
C. 2 places to the right
D. 2 places to the left
Answer:
6.1 ÷ 10²  = 0.061
Option D is correct .
Explanation:
Perform division operation on 6.1 ÷ 10²  = 0.061 . Here the divisor is 10²  which is 100. So the decimal point is moved two places to the left. The quotient is 0.061. So option D is correct.

Question 19.
A group of 5 friends bought a bag of grapes to share equally. If the bag of grapes weighs 11.25 pounds, how much is each person’s share? How many friends could share the grapes if each person’s share was 1.25 pounds? Write an equation to model your work.
Answer:
11.25 pounds  ÷ 5 = 2.25 pounds.
Each person share is 2.25 pounds.
11.25 pounds ÷ ? = 1.25 pounds.
11.25 pounds ÷ 9 = 1.25 pounds.
9 friends can share the grapes if each person’s share was 1.25 pounds.
Explanation:
A group of 5 friends bought a bag of grapes to share equally. The bag of grapes weighs 11.25 pounds. Perform division operation on 11.25 pounds  ÷ 5 = 2.25 pounds. Each person share is 2.25 pounds.
Divide 11.25 pounds ÷ 1.25 pounds = 9. Nine friends can share the grapes if each person’s share was 1.25 pounds.

Question 20.
When dividing 560.9 by 100, how should the decimal point be moved?
Answer:
560.9 ÷ 100 = 5.609
Explanation:
Dividing by 100, or 10², means moving the decimal point two places to the left. Move the dividend decimal point 560.9 two places to the left then the result is 5.609. The quotient is 5.609.

Question 21.
June says that there should be a decimal point in the quotient below after the 4. Is she correct? Use number sense to explain your answer. 43.94 ÷ 5.2 = 845
Answer:
43.94 ÷ 5.2 = 8.45
She is not correct. The decimal should be placed after 8.
Explanation:
June says that there should be a decimal point in the quotient after the 4. She is not correct because we have to place the decimal point after 8.

Question 22.
Three coworkers decided to buy fruit to share at lunchtime. Antonio spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges.
A. Complete the bar diagram to find out how much they spent in all on fruit.

Answer:

They spent $7.2 in all on fruit.
Explanation:
Three coworkers decided to buy fruit to share at lunchtime. Antonio spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. Add all fruit costs. Add $1.47 with $2.88 and $2.85 then the sum is $7.2. They spent $7.2 in all on fruit.

B. They evenly divided the cost of the 3 types of fruit. How much did each person pay? Complete the bar diagram to help you.

Answer:

Each person has to pay $2.4 for fruits.
Explanation:
The three coworkers evenly divided the cost of the 3 types of fruit. The total cost of three fruits is $7.2. Divide $7.2 by 3 then the quotient is $2.4. Each person has to pay $2.4 for fruits.

C. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1? How can you tell?
Answer:

Topic 6 Performance Task

Cooking Competition
Lydia is organizing a cooking competition at her school. She ordered some basic supplies to share among the teams that are competing. The teams will be bringing other ingredients as well.

Use the list at the right to answer the questions.

Question 1.
If 10 of the teams divide the olive oil equally, how much will each team receive? Write an equation to model your work.

Answer:
5.4 liters ÷ 10 = 0.54 liters.
Each team receives 0.54 liters.
Explanation:
10 of the teams divide the olive oil equally. Here we have total 5.4 liters of olive oil. Perform division operation on 5.4 liters ÷ 10 = 0.54 liters. Each team receives 0.54 liters.

Question 2.
Eight teams agree to share the flour equally.
Part A
About how many grams of flour will each team get? Use compatible numbers to estimate. Write an equation to show how you estimated.
Answer:
738.4 grams ÷ 8  = ?.
Estimate 738.4 grams ÷ 8. Use compatible numbers.
Look for compatible numbers.
738.4 ÷ 8 is closes to 738 ÷ 8 = 92.25 grams.
The Estimated quotient is 92.25.
Each team get 92.25 grams of flour.
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. In the above division problem 738.4 grams ÷ 8 is closes to 738 ÷ 8. The actual dividend738.4 is compatible to 738.  Perform division operation 738 ÷ 8 = 92.25. The Estimated quotient is 92.25. Each team get 92.25 grams of flour.
Part B
Find the actual amount of flour each team will receive. Show your work.
Answer:
738.4 grams ÷ 8  = 92.3 grams.
Each team will receive 92.3 grams of flour.
Explanation:
Perform division operation on 738.4 grams ÷ 8  = 92.3 grams. Each team will receive the actual amount of flour is 92.3 grams.

Question 3.
Several teams agree to share the salt equally. Each team will be given 7.3 grams of salt. How many teams agree to share the salt? Write a division equation to model the problem. Then write an equivalent equation using whole numbers.
Answer:
87.6 grams ÷ ? = 7.3 grams.
87.6 grams ÷ 12 = 7.3 grams.
12 teams agree to share the salt.
Explanation:
Several teams agree to share the salt equally. Each team will be given 7.3 grams of salt. The division equation is 87.6 grams ÷ ? = 7.3 grams. Divide 87.6 with 7.3 then the answer is 12. 12 teams agree to share the salt.

Question 4.
Malcolm calculated how many liters of milk each team would get if 6 teams shared the milk equally. His work is shown at the right, but he forgot to place the decimal point in the quotient. Where should he place the decimal point? Explain.
Answer:

8.25 liters ÷ 6 = 1.375 liters.
Malcolm has to place the decimal point before 3 and after 1.
Each team get 1.375 liters of milk.
Explanation:
Malcolm calculated how many liters of milk each team would get if 6 teams shared the milk equally. His work is shown above, but he forgot to place the decimal point in the quotient. He has to place the decimal point before 3 and after 1. Each team get 1.375 liters of milk.

Question 5.
Lydia decides to provide cheddar cheese for the competition. She buys 4.2 kilograms for $39.90.
Part A
She estimates the cost of 1 kilogram of cheese to be $1. Is her estimate reasonable? Explain.
Answer:
4.2 kilograms ÷ $39.90 = ?
Estimate 4.2 ÷ $40 = $0.105
The cost of 1 kilogram of cheese to be $0.105. Her Estimation is not reasonable.
Explanation:
Lydia decides to provide cheddar cheese for the competition. She buys 4.2 kilograms for $39.90. Perform division operation on 4.2 ÷ $40 = $0.105. The cost of 1 kilogram of cheese to be $0.105. Her Estimation is not reasonable.
Part B
To find the actual cost of 1 kilogram of cheese, Lydia needs to divide $39.90 by 4.2. How can she change the division problem to an equivalent problem using whole numbers? Write and solve the equivalent problem..
Part C
If 7 teams share the cheese equally, how much cheese will each team get?
Answer:
4.2 kilograms ÷  7 = 0.6 kilograms.
Each team get 0.6 kilograms of cheese equally.
Explanation:
The cheese we have is 4.2 kilograms. Seven teams takes the cheese equally. perform division operation on 4.2 kilograms ÷  7 = 0.6 kilograms. Each team get 0.6 kilograms of cheese equally.

Go through the enVision Math Common Core Grade 3 Answer Key Topic 9 Fluently Add and Subtract within 1,000 regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 9 Fluently Add and Subtract within 1,000

Essential Question: What are the procedures for adding and subtracting whole numbers?

enVision STEM Project: Changing Environments
Do Research Forest fires destroy, but they also make room for new growth. Use the Internet or other sources to find information about forest fires. Describe the effect of forest fires on plant and animal populations.
Journal: Write a Report Include data with numbers for the population you researched. Also in your report:

• Choose a kind of animal or plant. Tell how a change in the environment can affect the number of animals or plants.
• Write and solve an addition and a subtraction problem using your data.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.

• Associative Property of Addition
• Commutative Property of Addition
• compatible numbers
• inverse operations

Question 1.
___ are easy to add or subtract mentally.
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Thus, Compatible numbers are easy to add or subtract mentally.

Question 2.
According to the _______, the grouping of addends can be changed, and the sum will remain the same.
Answer:
The commutative property of addition says that changing the order of addends does not change the sum.
So, According to the commutative property of addition, the grouping of addends can be changed, and the sum will remain the same.

Question 3.
Addition and subtraction are ___
Answer:
Inverse operations are pairs of mathematical manipulations in which one operation undoes the action of the other.
Thus Addition and subtraction are inverse operations.

Rounding

Round each number to the nearest ten.

Question 4.
57
Answer:
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Here 7 is greater than 5.
So, 57 round to the nearest ten is 60.

Question 5.
241
Answer:
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
So, 241 round to the nearest ten is 240.

Question 6.
495
Answer:
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Thus 495 round to the nearest ten is 500.

Round each number to the nearest hundred.

Question 7.
732
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 732 to the nearest hundred is 700.

Question 8.
81
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 81 to the nearest hundred is 100.

Question 9.
553
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 553 to the nearest hundred is 600.

Estimating Sums

Use compatible numbers to estimate each sum.

Question 10.
27 + 12
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Write 27 and 12 to the nearest ten.
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
27 to the nearest ten is 30.
12 to the nearest ten is 10.
30 + 10 = 40
Thus the estimated sum is 40.

Question 11.
133 + 102
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
133 to the nearest ten is 130.
102 to the nearest ten is 100.
130 + 100 = 230
Thus the estimated sum is 230.

Question 12.
504 + 345
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 504 to the nearest hundred is 500.
Thus the number 345 to the nearest hundred is 300.
500 + 300 = 800
Thus the estimated sum is 800.

Question 13.
52 + 870
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Thus the number 52 to the nearest ten is 50.
Thus the number 870 to the nearest hundred is 900.
900 + 50 = 950
Thus the estimated sum is 950.

Question 14.
293 + 278
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Thus the number 293 to the nearest hundred is 300.
Thus the number 278 to the nearest hundred is 300.
300 + 300 = 600
Thus the estimated sum is 600.

Question 15.
119 + 426
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Thus the number 119 to the nearest hundred is 100.
Thus the number 426 to the nearest hundred is 400.
100 + 400 = 500
Thus the estimated sum is 500.

Estimating Differences

Question 16.
Tony and Kim play a video game. Tony scores 512 points. Kim scores 768 points. About how many more points does Kim score than Tony? Which estimation method did you use?
Answer:
Given,
Tony and Kim play a video game. Tony scores 512 points. Kim scores 768 points.
768 – 512
Write the nearest hundred values for both the numbers to estimate the sum.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 512 to the nearest hundred is 500.
Thus the number 768 to the nearest hundred is 800.
800 – 500 = 300
Thus Kim scores nearly .00 points than Tony.

Question 17.
Which number sentence shows the most reasonable estimate for
A. 425 – 250 = 175
B. 500 – 200 = 300
C. 400 – 300 = 100
D. 470 – 230 = 240
Answer: 500 – 200 = 300

Pick a Project

PROJECT 9A

How do you know which is the tallest building?
Project: Research the Heights of Tall Buildings

PROJECT 9B
How can you record what you bought over time? Project: Create an Addition Skit

PROJECT 9C
How long before the space shuttle launches?
Project: Write a Report About Your Vacation

3-ACT MATH PREVIEW

Math Modeling
Fun Raiser

Before watching the video, think: When a school needs extra money for a field trip or a student club, it might hold a fundraiser to collect that money.
This check is SO BIG, we must have collected a ton of money!

Lesson 9.1 Use Partial Sums to Add

Activity

Solve & Share
There are 2 bins of oranges. One bin has 378 oranges. The other bin has 243 oranges. Find the sum of 378 + 243. Think about place value.

You can use structure. You can break apart the problem to show each of the addends in expanded form.

Look Back! Adam has 9 bags of oranges with 8 oranges in each. He also has a bin with 325 oranges. How many oranges does Adam have in all? Think about how you can use place value or other tools to help solve the problem. Explain your solution, what tool you used, and why.

Essential Question How Can You Break Apart Addition Problems to Solve?

Visual Learning Bridge

A.
Margot counted 243 manatees one year and 179 manatees the next. How many manatees did Margot count all together?

B.
You can estimate and then use place value to add the numbers.


The sum is about 400 manatees.

C.
One Way
Add each place value. Start with hundreds.

300, 110, and 12 are partial sums.
243 + 179 = 422 manatees

D.
Another Way
Add each place value. Start with ones.

When you add by place value, you add the hundreds, the tens, and the ones.

243 + 179 = 422 manatees
422 is close to the estimate of 400.
So, 422 is a reasonable sum.

Convince Me!
Critique Reasoning Lexi used partial sums to complete the problem. Critique Lexi’s reasoning. Is her work correct? Explain.

Guided Practices

Do You Understand?

Question 1.
Suppose you were adding 527 + 405. What numbers would you combine when adding the tens? Why?
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Add 3 to 527 = 530
530
410
940
Thus, It would be 3 because when you add it, it gets to be 932 and the tens place is 3.

Question 2.
Find the error. Show how to find the correct answer.

Answer:
First round the numbers to the nearest hundred.
237 to the nearest hundred is 200
285 to the nearest hundred is 300
200 + 300 = 500
So, the estimated answer is 500.

Do You Know How?

In 3, estimate the sum. Use place-value blocks or drawings and partial sums to add.

Question 3.

Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
365 to the nearest hundred is 400
422 to the nearest hundred is 400
400 + 400 = 800
So, the estimated answer is 800.

Independent Practice

Leveled Practice In 4-11, estimate each sum. Use place-value blocks or drawings and partial sums to add.

Question 4.

Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
356 to the nearest hundred is 400
123 to the nearest hundred is 100
400 + 100 = 500
So, the estimated answer is 500.

Question 5.

Answer:
550 + 423 = 973
973 is close to 1000.
So, the estimated sum is 1000.

Question 6.
185 + 613
Answer:
185 + 613 = 798
798 is close to 800.
So, the estimated sum is 800.

Question 7.
730 + 168
Answer:
730 + 168 = 898
898 is close to 900.
So, the estimated sum is 900.

Question 8.
546 + 143
Answer:
546 + 143 = 689
689 is close to 700.
So, the estimated sum is 700.

Question 9.
362 + 524
Answer:
362 + 524 = 886
886 is close to 900.
So, the estimated sum is 900.

Question 10.
644 + 101
Answer:
644 + 101 = 745
745 is close to 700.
So, the estimated sum is 700.

Question 11.
463 + 315
Answer:
463 + 315 = 778
778 is close to 800.
So, the estimated sum is 800.

Problem Solving

Question 12.
Model with Math John read a book with 377 pages. Jess read a book with 210 pages. How many pages did John and Jess read? Use place-value blocks and partial sums to solve. Draw a model to represent the problem.
Answer:
Given,
John read a book with 377 pages. Jess read a book with 210 pages.
377 + 210 = 587
587 is close to 600.
So, the estimated sum is 600.

Question 13.
Explain how the solids shown in Group A and Group B could have been sorted.

Answer:

Question 14.
Henry believes the sum of 275 + 313 is 598. Is Henry correct? Use place-value blocks or drawings and partial sums in your explanation.

Answer:
Given,
Henry believes the sum of 275 + 313 is 598.
The sum of 275 and 313 os 588.
Henry is not correct.

Question 15.
Higher Order Thinking A school cafeteria sold 255 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday. Did the cafeteria sell more lunches on Monday and Tuesday or on Tuesday and Wednesday? Use place value blocks or drawings to solve.
Answer:
Given,
A school cafeteria sold 255 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday.
225 + 140 = 365
140 + 226 = 366
Thus cafeteria sells more lunches on Tuesday and Wednesday.

Assessment Practice

Question 16.
Which shows breaking 622 + 247 apart by place value to find the sum?
A. 600 + 200; 22 + 40; 2 + 7
B. 600 + 300; 20 + 40; 2 + 7
C. 600 + 200; 20 + 40; 2 + 7
D. 600 + 200; 20 + 47; 2 + 7
Answer: A. 600 + 200; 22 + 40; 2 + 7

Question 17.
Break 331 + 516 apart by place value. Find the sum.
A. 848
B. 847
C. 748
D. 488
Answer:
331 + 516 = 847
Thus the correct answer is option B.

Lesson 9.2 Use Regrouping to Add

Activity

Solve & Share

Suppose a bus travels 276 miles on Monday and 248 miles on Tuesday. How many miles does the bus travel?

You can use appropriate tools, such as place-value blocks, to add larger numbers. What other strategies can you use to solve
this problem?

Look Back! On Wednesday, the bus gets stuck in traffic. It travels 8 miles each hour for 8 hours. The bus needs to travel 600 miles total from Monday to Wednesday to make it to its destination. Does the bus make it to its destination? Why would it be a good idea to estimate first before you solve this problem?

Visual Learning Bridge

Essential Question
How Can You Use Regrouping to Solve Addition Problems?

You know one way to record partial sums.

A.
Jason’s family drove from Ocala, Florida to Miami. They drove 139 miles in the morning and 187 miles in the afternoon. How far did Jason’s family drive? Find 139 + 187. ?

Estimate: 139 + 187 is about 100 + 200, or 300 miles.
Jason’s family drove 326 miles. 300 is close to 326, so the sum is reasonable.

B.
Here is another way. Write the partial sums.

Regroup the ones. 16 ones = 1 ten + 6 ones

Regroup the tens. 12 tens = 1 hundred + 2 tens

When you regroup, you name a whole number in a different way.

139 + 187 = 326
Jason’s family drove 326 miles.

Convince Me!
Model with Math Show how to use place-value blocks to find 128 +235 using regrouping.

Another Example!

Find 154 + 163.

You can find partial sums. Then you can regroup place values to find the final sum.

Regroup the tens.
1 hundred + 1 ten = 11 tens
154 + 163 = 317

Guided Practice

Do You Understand?

Question 1.
When you add 3-digit numbers, how do you know if you need to regroup?
Answer: When you add 3-digit numbers if the sum of the place value is greater than 9 then we can know we have to regroup the addend.

Question 2.
To add 546 + 327, would you need to regroup? Explain.
Answer:
546 + 327
7 + 6 = 13, yes we need to regroup
546 + 327 = 873

Do You Know How?

In 3 and 4, estimate by rounding. Then find each sum. Use place-value blocks or drawings to help.

Question 3.

Answer:

Question 4.

Answer:

Independent Practice

In 5-12, estimate and then find each sum.

Question 5.

Answer:
The estimated number of 136 is 100.
The estimated number of 252 is 300.
The sum of 100 and 300 is 400.

Question 6.

Answer:
The estimated number of 678 is 700.
The estimated number of 129 is 100.
The sum of 700 and 100 is 800.

Question 7.

Answer:
The estimated number of 564 is 600.
The estimated number of 283 is 300.
The sum of 600 and 300 is 900.

Question 8.

Answer:
The estimated number of 118 is 100.
The estimated number of 335 is 300.
The sum of 100 and 300 is 400.

Question 9.
172 + 534
Answer:
The estimated number of 172 is 200.
The estimated number of 534 is 500.
The sum of 200 and 500 is 700.

Question 10.
324 + 508
Answer:
The estimated number of 324 is 300.
The estimated number of 508 is 500.
The sum of 300 and 500 is 800.

Question 11.
582 + 230
Answer:
The estimated number of 582 is 600.
The estimated number of 230 is 200.
The sum of 600 and 200 is 800.

Question 12.
207 + 238
Answer:
The estimated number of 207 is 200.
The estimated number of 238 is 200.
The sum of 200 and 200 is 400.

Problem Solving

In 13 and 14, use the table at the right.

Question 13.
How many soup can labels did Grades 1 and 2 collect? Estimate by rounding to the nearest hundred. Then solve. Write an equation that represents the problem.

Answer:
Estimate: 400 + 300 = 700
385 + 294 = 679, grade 1 and 2 collected 679 labels.

Question 14.
Make Sense and Persevere Is your answer to Exercise 13 reasonable? Explain.
Answer: Yes, 679 is close to my estimate of 700, so 679 is a reasonable answer.

Question 15.
Number Sense The roller coaster Kingda Ka is 192 feet taller than the first Ferris wheel. Use the symbols < and > to compare the heights of the two rides in two different ways.

Answer: 264 feet < 456 feet; 456 feet > 264 feet

Question 16.
Higher Order Thinking Pete can run 178 yards in one minute. Sharon can run 119 more yards than Pete in one minute. How many yards can they both run in one minute?
Answer:
Given,
Pete can run 178 yards in one minute.
Sharon can run 119 more yards than Pete in one minute.
178 + 119 = 297 yards
178 + 297 = 475 yards

Question 17.
Abi practiced her flute for 215 minutes last week and 178 minutes this week. How many minutes has Abi practiced?
Answer:
Given,
Abi practiced her flute for 215 minutes last week and 178 minutes this week.
215 + 178 = 393
Thus Abi practiced 393 minutes.

Assessment Practice

Question 18.
What is 126 + 229?
A. 355
B. 345
C. 255
D. 245
Answer: 355
The sum of 126 and 229 is 355.
Thus the correct answer is option A.

Question 19.
What is the value of the unknown in 248 + = 521?
A. 248
B. 263
C. 273
D. 283
Answer: 273
Let the missing number be x.
248 + x = 521
x = 521 – 248
x = 273
Thus the correct answer is option C.

Lesson 9.3 Add 3 or More Numbers

Activity

Solve & Share

A pet store has 162 goldfish, 124 angelfish, and 6 bowls with 9 pufferfish in each. How many fish are there in all?

You can generalize. Use what you know about adding two numbers to add three numbers.

Look Back! How can you decide if your answer is reasonable?

Visual Learning Bridge

Essential Question
How Can You Add More Than Two Numbers?

A.
Different kinds of birds are for sale at a pet store. How many birds are for sale?
Find 137 + 155 + 18.
Round to the nearest ten to estimate: 140 + 160 + 20 = 320.

B.
One Way
Use partial sums.

In all, 310 birds are for sale.

C.
Another Way
Use column addition.

The answer is reasonable because 310 is close to the estimate of 320.

In all, 310 birds are for sale.