Go through the enVision Math Common Core Grade 5 Answer Key Topic 9 Apply Understanding of Division to Divide Fractions regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 9 Apply Understanding of Division to Divide Fractions

enVision STEM Project: Thermal Energy
Do Research Use the Internet or other sources to learn about thermal energy. Make a list of 3 ways you use thermal energy in your home and at school. Which use is most important to you? Why?
Journal: Write a Report Include what you found. Also in your report:
• Ask each member of your household 3 ways they use thermal energy. Organize your data in a table.
• Draw conclusions from your data. How does your household use thermal energy?
• Make up and solve problems with fraction division.

Review What You Know

A-Z Vocabulary

Choose the best term from the list at the right. Write it on the blank.

• common factor
• equivalent fractions
• estimate
• like denominators
• mixed number
• quotient

Question 1.
To find an approximate answer or solution is to ______
Answer:
To find an approximate answer or solution is to estimate

Question 2.
The fractions \(\frac{3}{4}\) and \(\frac{17}{4}\) are fractions with
Answer:
The fractions \(\frac{3}{4}\) and \(\frac{17}{4}\) are fractions with common factor.

Question 3.
The fractions that name the same amount are ______
Answer:
The fractions that name the same amount are equivalent fractions.

Question 4.
The answer to a division problem is the ______
Answer:
The answer to a division problem is the quotient.

Question 5.
A number that has a whole-number part and a fraction part is called a _____
Answer:
A number that has a whole-number part and a fraction part is called a mixed number.

Meaning of Fractions Each rectangle represents one whole. Write the shaded part of each rectangle as a fraction.

Question 6.

Answer:
The shaded part of each rectangle as a fraction is \(\frac{11}{7}\).

Explanation:
We can see that above rectangle shaded part is \(\frac{5}{7}\) and below rectangle shaded part is \(\frac{6}{7}\), so the total shaded part of each rectangle as a fraction is \(\frac{5}{7}\) + \(\frac{6}{7}\) which is \(\frac{11}{7}\).

Question 7.

Answer:
The shaded part of each rectangle as a fraction is \(\frac{4}{3}\).

Explanation:
We can see that above rectangle shaded part is \(\frac{2}{3}\) and below rectangle shaded part is \(\frac{2}{3}\), so the total shaded part of each rectangle as a fraction is \(\frac{2}{3}\) + \(\frac{2}{3}\) which is \(\frac{4}{3}\).

Fraction Computation
Find each sum, difference, or product.

Question 8.
\(\frac{2}{5}\) + \(\frac{1}{4}\)
Answer:
\(\frac{2}{5}\) + \(\frac{1}{4}\) = \(\frac{13}{20}\).

Explanation:
The addition of \(\frac{2}{5}\) + \(\frac{1}{4}\)
= \(\frac{8+5}{20}\)
= \(\frac{13}{20}\).

Question 9.
\(\frac{5}{6}\) – \(\frac{1}{4}\)
Answer:
\(\frac{5}{6}\) – \(\frac{1}{4}\) = \(\frac{7}{12}\).

Explanation:
The subtraction of \(\frac{5}{6}\) – \(\frac{1}{4}\)
= \(\frac{10-3}{12}\)
= \(\frac{7}{12}\).

Question 10.
2\(\frac{5}{8}\) + 7\(\frac{1}{4}\) is 9\(\frac{7}{8}\).
Answer:
The addition of 2\(\frac{5}{8}\) + 7\(\frac{1}{4}\) is

Explanation:
The addition of 2\(\frac{5}{8}\) + 7\(\frac{1}{4}\) is
= \(\frac{21}{8}\) + \(\frac{29}{4}\)
= \(\frac{21+58}{8}\)
= \(\frac{79}{8}\)
= 9\(\frac{7}{8}\).

Question 11.
14 – 3\(\frac{5}{8}\)
Answer:
The subtraction of 14 – 3\(\frac{5}{8}\) is 10\(\frac{3}{8}\).

Explanation:
The subtraction of 14 – 3\(\frac{5}{8}\) is
= 14 – \(\frac{29}{8}\)
= \(\frac{112-29}{8}\)
= \(\frac{83}{8}\)
= 10\(\frac{3}{8}\).

Question 12.
3\(\frac{2}{3}\) + 4\(\frac{1}{2}\)
Answer:
The addition of 3\(\frac{2}{3}\) + 4\(\frac{1}{2}\) is 8\(\frac{1}{6}\).

Explanation:
The addition of 3\(\frac{2}{3}\) + 4\(\frac{1}{2}\) is
= \(\frac{11}{3}\) + \(\frac{9}{2}\)
= \(\frac{22+27}{6}\)
= \(\frac{49}{6}\)
= 8\(\frac{1}{6}\).

Question 13.
\(\frac{3}{8}\) × 2
Answer:
The multiplication of \(\frac{3}{8}\) × 2 is \(\frac{3}{4}\).

Explanation:
The multiplication of \(\frac{3}{8}\) × 2 is
= \(\frac{3}{4}\).

Question 14.
\(\frac{1}{4}\) × \(\frac{3}{5}\)
Answer:
The multiplication of \(\frac{1}{4}\) × \(\frac{3}{5}\) is \(\frac{3}{20}\).

Explanation:
The multiplication of \(\frac{1}{4}\) × \(\frac{3}{5}\) is
\(\frac{3}{20}\).

Question 15.
8 × \(\frac{9}{10}\)
Answer:
The multiplication of 8 × \(\frac{9}{10}\) is 7\(\frac{1}{5}\).

Explanation:
The multiplication of 8 × \(\frac{9}{10}\) is
= \(\frac{36}{5}\)
= 7\(\frac{1}{5}\).

Question 16.
3\(\frac{1}{2}\) × 2\(\frac{3}{5}\)
Answer:
The multiplication of 3\(\frac{1}{2}\) × 2\(\frac{3}{5}\) is 9\(\frac{1}{10}\).

Explanation:
The multiplication of 3\(\frac{1}{2}\) × 2\(\frac{3}{5}\) is
= \(\frac{7}{2}\) × \(\frac{13}{5}\)
= \(\frac{91}{10}\)
= 9\(\frac{1}{10}\).

Pick a Project

PROJECT 9A
Will your prototype make you rich and famous?
Project: Build a FractionDivision Prototype

PROJECT 9B
Why do so many math problems use pizza?
Project: Write a Skit About Pizza

PROJECT 9C
Would you like to improve your memory?
Project: Create a Mnemonic Device

3-ACT MATH PREVIEW

Math Modeling

Video

Slime Time

Before watching the video, think:
Slime is so much fun it makes me giggle. And the best part about slime is you can make it yourself with simple ingredients, including school glue.

Lesson 9.1 Fractions and Division

Solve & Share
Four people want waffles for breakfast. There are 6 waffles left. How can 6 waffles be shared equally among 4 people? How much does each person get? Draw a picture and write a division expression to model the problem.

You can use a circle to represent each whole waffle.

Answer:
Each person will get 1\(\frac{1}{2}\) waffle.

Explanation:
Given that four people want waffles for breakfast and there are 6 waffles left. So the number of waffles did each people get is 6 ÷ 4 which is 1\(\frac{1}{2}\).

Look Back! Construct Arguments One of the waffles was burnt. Explain how they can share 5 waffles equally.

Visual Learning Bridge

Essential Question
How Are Fractions Related to Division?

A.
Tom, Joe, and Sam each made a clay pot in his favorite color. They were given a total of two rolls of clay. If they shared the clay equally, how much clay did each friend use?

Divide 2 by 3 to find what fraction of the clay each person used.

B.
One Way
Think about sharing 2 rolls of clay equally among 3 people. Partition each roll into 3 equal parts. Each part is of \(\frac{1}{3}\) one roll.

Each person colored one part from each roll of clay for a total of 2 parts. So, 2 ÷ 3 = 2 × \(\frac{1}{3}\) = \(\frac{2}{3}\). Each friend used \(\frac{2}{3}\) of a roll of clay.

C.
Another Way
Place the rolls end-to-end and divide the 2 rolls among 3 people. Each person gets \(\frac{1}{3}\) of 2 wholes. You can see this with shading on a number line.

S0, 2 ÷ 3 = 2 × \(\frac{1}{3}\) = \(\frac{2}{3}\). Each friend used \(\frac{2}{3}\) of a roll of clay.

Convince Me! Reasoning Amelia is sharing 4 slices of cheese with 5 friends. How much cheese will each person get? Explain how you decided.

Guided Practice

Do You Understand?

Question 1.
Explain how to write \(\frac{3}{10}\) as a division expression.
Answer:
The division expression is 3 ÷ 10.

Explanation:
Given the expression is \(\frac{3}{10}\), so to division expression will be 3 ÷ 10.

Question 2.
Explain how to write 2 ÷ 5 as a fraction.
Answer:
The expression as a fraction will be \(\frac{2}{5}\).

Explanation:
Given the expression is 2 ÷ 5, so the expression as a fraction will be \(\frac{2}{5}\).

Question 3.
Use the number line below to show 3 ÷ 4

Answer:
The number line for 3 ÷ 4 is

Do You Know How?

In 4 and 5, write a division expression for each fraction.

Question 4.
\(\frac{1}{9}\)
Answer:
The division expression will be 1 ÷ 9.

Explanation:
Given that the expression is \(\frac{1}{9}\), so the division expression will be 1 ÷ 9.

Question 5.
\(\frac{7}{8}\)
Answer:
The division expression will be 7 ÷ 8.

Explanation:
Given that the expression is \(\frac{7}{8}\), so the division expression will be 7 ÷ 8.

In 6 and 7, tell what fraction each person gets when they share equally.

Question 6.
Five friends share 8 apples.
Answer:
The fraction will be \(\frac{5}{8}\).

Explanation:
Given that five friends share 8 apples, so the fraction will be \(\frac{5}{8}\).

Question 7.
Two friends share 1 bagel.
Answer:
The fraction will be \(\frac{1}{2}\).

Explanation:
Given that two friends share 1 bagel, so the fraction will be \(\frac{1}{2}\).

Independent Practice

In 8-12, write a division expression for each fraction.

Question 8.
\(\frac{6}{7}\)
Answer:
The division expression is 6 ÷ 7.

Explanation:
Given that the expression is \(\frac{6}{7}\), so the division expression is 6 ÷ 7.

Question 9.
\(\frac{1}{4}\)
Answer:
The division expression is 1 ÷ 4.

Explanation:
Given that the expression is \(\frac{1}{4}\), so the division expression is 1 ÷ 4.

Question 10.
\(\frac{6}{11}\)
Answer:
The division expression is 6 ÷ 11.

Explanation:
Given that the expression is \(\frac{6}{11}\), so the division expression is 6 ÷ 11.

Question 11.
\(\frac{4}{9}\)
Answer:
The division expression is 4 ÷ 9.

Explanation:
Given that the expression is \(\frac{4}{9}\), so the division expression is 4 ÷ 9.

Question 12.
\(\frac{8}{12}\)
Answer:
The division expression is 8 ÷ 12.

Explanation:
Given that the expression is \(\frac{8}{12}\), so the division expression is 8 ÷ 12.

In 13-17, write each division expression as a fraction.

Question 13.
9 ÷ 11
Answer:
The expression as a fraction will be \(\frac{9}{11}\).

Explanation:
Given the expression is 9 ÷ 11, so the expression as a fraction will be \(\frac{9}{11}\).

Question 14.
1 ÷ 10
Answer:
The expression as a fraction will be \(\frac{1}{10}\).

Explanation:
Given the expression is 1 ÷ 10, so the expression as a fraction will be \(\frac{1}{10}\).

Question 15.
7 ÷ 13
Answer:
The expression as a fraction will be \(\frac{7}{13}\).

Explanation:
Given the expression is 7 ÷ 13, so the expression as a fraction will be \(\frac{7}{13}\).

Question 16.
11 ÷ 17
Answer:
The expression as a fraction will be \(\frac{11}{17}\).

Explanation:
Given the expression is 11 ÷ 17, so the expression as a fraction will be \(\frac{11}{17}\).

Question 17.
25 ÷ 75
Answer:
The expression as a fraction will be \(\frac{25}{75}\).

Explanation:
Given the expression is 25 ÷ 75, so the expression as a fraction will be \(\frac{25}{75}\).

In 18-21, tell what fraction each person gets when they share equally.

Question 18.
8 students share 6 breakfast bars.
Answer:
The fraction will be \(\frac{8}{6}\).

Explanation:
Given that 8 students share 6 breakfast bars, so the fraction will be \(\frac{8}{6}\).

Question 19.
6 soccer players share 5 oranges.
Answer:
The fraction will be \(\frac{6}{5}\).

Explanation:
Given that 6 soccer players share 5 oranges, so the fraction will be \(\frac{6}{5}\).

Question 20.
10 friends share 7 dollars.
Answer:
The fraction will be \(\frac{10}{7}\).

Explanation:
Given that 10 friends share 7 dollars, so the fraction will be \(\frac{10}{7}\).

Question 21.
8 friends share 8 muffins.
Answer:
The fraction will be \(\frac{8}{8}\).

Explanation:
Given that 8 friends share 8 muffins, so the fraction will be \(\frac{8}{8}\).

Problem Solving

Question 22.
Four friends are baking bread. They equally share 3 sticks of butter. Write an equation to find the fraction of a stick of butter that each friend uses.

Answer:
The equation to find the fraction of a stick of butter that each friend uses is \(\frac{4}{3}\).

Explanation:
Given that four friends are baking bread and they equally share 3 sticks of butter, so the equation to find the fraction of a stick of butter that each friend uses is \(\frac{4}{3}\).

Question 23.
A group of friends went to the movies. They shared 2 bags of popcorn equally. If each person got \(\frac{2}{3}\) of a bag of popcorn, how many people were in the group?
Answer:
The number of people in the group is 3 people.

Explanation:
Given that a group of friends went to the movies and they shared 2 bags of popcorn equally and each person got \(\frac{2}{3}\) of a bag of popcorn, so the number of people were in the group is 3 people.

Question 24.
Higher Order Thinking Missy says that \(\frac{5}{6}\) equals 6 ÷ 5. Is she correct? Why or why not?
Answer:
Missy is not correct.

Explanation:
Given that Missy says that \(\frac{5}{6}\) which is equal to 5 ÷ 6, so she is not correct.

Question 25.
Make Sense and Persevere
The table shows the food and drinks Tabitha bought for herself and 4 friends for her party. How much did Tabitha spend for each person? Show your work.

Answer:

Assessment Practice

Question 26.
Which equation is made true with the number 5?

Answer:
The equation is 3 ÷ 5.

Explanation:
The equation that made true with the number 5 is 3 ÷ 5.

Question 27.
Which equation is made true with the number 3?

Answer:
The equation is 1 ÷ 3 and 3 ÷ 8.

Explanation:
The equation that made true with the number 3 is 1 ÷ 3 and 3 ÷ 8.

Lesson 9.2 Fractions and Mixed Numbers as Quotients

Solve & Share
Jonah has an 8-pound bag of potting soil. He divides it evenly among 5 flowerpots. How much soil is in each pot? Show your answer as a fraction or mixed number. Solve this problem any way you choose.

You can write an equation or draw a picture to help find the answer.

Look Back! Be Precise Suppose one of the pots breaks, so Jonah has to divide the soil evenly among 4 pots. How much soil is in each pot then?

Visual Learning Bridge

Essential Question
How Can You Show a Quotient Using estion a Fraction or Mixed Number?

A.
Three friends are going hiking. They bought a tub of trail mix to share equally. How much will each friend get?

You can divide to share 4 pounds among 3 people: 4 ÷ 3.

B.
Divide each pound into 3 equal parts. Each part is 1 ÷ 3 or \(\frac{1}{3}\)
Each friend gets 1 pound plus \(\frac{1}{3}\) of a pound, or 1 + \(\frac{1}{3}\) = 1\(\frac{1}{3}\) pounds of trail mix in all.
So, 4 ÷ 3 = \(\frac{4}{3}\) = 1\(\frac{1}{3}\)

Convince Me! Construct Arguments Kate shares a 64-ounce bottle of apple cider with 5 friends. Each person’s serving will be the same number of ounces. Between what two whole number of ounces will each person’s serving be? Explain using division.

Guided Practice

Do You Understand?

Question 1.
How can you write \(\frac{10}{3}\) to as a division expression and as a mixed number?
Answer:
The division expression is 10 ÷ 3 and as a mixed number, it will be 3\(\frac{1}{3}\).

Explanation:
Given that the equation is \(\frac{10}{3}\), so the division expression is 10 ÷ 3 and as a mixed number it will be 3\(\frac{1}{3}\).

Question 2.
Suppose 3 friends want to share 16 posters equally. For this situation, why does the quotient 5 R1 make more sense than the quotient 5\(\frac{1}{3}\)?
Answer:
Here, each friend gets 5 posters and 1 1 is left over and \(\frac{1}{3}\) poster does not make sense.

Do You Know How?

Question 3.
Find 11 ÷ 10 and 10 ÷ 11. Write each quotient as a fraction or mixed number.
Answer:
The quotient is 1\(\frac{1}{10}\).

Explanation:
The quotient of 11 ÷ 10 is 1\(\frac{1}{10}\) and the fraction of 10 ÷ 11 is \(\frac{10}{11}\)

In 4 and 5, tell how much each person gets when they share equally.

Question 4.
2 friends share 3 apples.
Answer:
Each person will get \(\frac{3}{2}\) share.

Explanation:
Given that 2 friends share 3 apples, so each person will get \(\frac{3}{2}\) share.

Question 5.
3 students share 5 breakfast bars.
Answer:
Each student will get \(\frac{5}{3}\) breakfast bars.

Explanation:
Given that 3 students share 5 breakfast bars, so each student will get \(\frac{5}{3}\) breakfast bars.

Independent Practice

In 6-13, find each quotient. Write each answer as either a fraction or mixed number.

Question 6.
11 ÷ 6
Answer:
The quotient will be 1\(\frac{5}{6}\).

Explanation:
Given the division expression is 11 ÷ 6, so the quotient will be 1\(\frac{5}{6}\).

Question 7.
1 ÷ 5
Answer:
The quotient will be 0.2.

Explanation:
Given the division expression is 1 ÷ 5, so the quotient will be 0.2.

Question 8.
18 ÷ 4
Answer:
The fraction will be 4\(\frac{1}{2}\).

Explanation:
Given the division expression is 18 ÷ 4, so the fraction will be 4\(\frac{1}{2}\).

Question 9.
5 ÷ 9
Answer:
The quotient will be 0.56.

Explanation:
Given the division expression is 5 ÷ 9, so the quotient will be 0.56.

Question 10.
9 ÷ 8
Answer:
The fraction will be 1\(\frac{1}{8}\).

Explanation:
Given the division expression is 9 ÷ 8, so the fraction will be 1\(\frac{1}{8}\).

Question 11.
23 ÷ 10
Answer:
The fraction will be 2\(\frac{3}{10}\).

Explanation:
Given the division expression is 23 ÷ 10, so the fraction will be 2\(\frac{3}{10}\).

Question 12.
12 ÷ 17
Answer:
The quotient will be 0.70.

Explanation:
Given the division expression is 12 ÷ 17, so the quotient will be 0.70.

Question 13.
28 ÷ 20
Answer:
The fraction will be 1\(\frac{2}{5}\).

Explanation:
Given the division expression is 28 ÷ 20, so the fraction will be 1\(\frac{2}{5}\).

In 14-17, tell how much each person gets when they share equally.

Question 14.
2 girls share 7 yards of ribbon.
Answer:
Each girl will get \(\frac{7}{2}\).

Explanation:
Given that 2 girls share 7 yards of ribbon, so each girl will get \(\frac{7}{2}\).

Question 15.
4 friends share 7 bagels.
Answer:
Each friend will get \(\frac{7}{4}\).

Explanation:
Given that 4 friends share 7 bagels, so each friend will get \(\frac{7}{4}\).

Question 16.
4 cousins share 3 pies.
Answer:
Each cousin will get \(\frac{3}{4}\).

Explanation:
Given that 4 cousins share 3 pies, so each cousin will get \(\frac{3}{4}\).

Question 17.
8 soccer players share 12 oranges.
Answer:
Each player will get \(\frac{12}{8}\).

Explanation:
Given that 8 soccer players share 12 oranges, so each player will get \(\frac{12}{8}\).

Problem Solving

Question 18.
Daniella made gift bows from 8 yards of ribbon. The bows are all the same size. If she made 16 bows, how much ribbon did she use for each one? Give the answer as a fraction or mixed number.
Answer:
The ribbon did she uses is \(\frac{1}{2}\) yard.

Explanation:
Given that Daniella made gift bows from 8 yards of ribbon and the bows are all the same size and she made 16 bows. So the number of ribbons did she use for each one gets is 8 ÷ 16 which is \(\frac{1}{2}\) yard.

Question 19.
Be Precise Tammi has 4 pounds of gala apples and 3\(\frac{1}{2}\) pounds of red delicious apples. If she uses 1\(\frac{3}{4}\) pounds of gala apples in a recipe, how many pounds of apples does she have left?
Answer:
The number of pounds of apples does she have left is 5\(\frac{1}{4}\).

Explanation:
Given that Tammi has 4 pounds of gala apples and 3\(\frac{1}{2}\) pounds of red delicious apples and she uses 1\(\frac{3}{4}\) pounds of gala apples in a recipe, so the number of pounds of apples does she have left is 3\(\frac{1}{2}\) + 1\(\frac{3}{4}\) which is
= \(\frac{7}{2}\) + \(\frac{7}{4}\)
= \(\frac{14+7}{4}\)
= \(\frac{21}{4}\)
= 5\(\frac{1}{4}\).

Question 20.
Casey bought a 100-pound bag of dog food. He gave his dogs the same amount of dog food each week. The dog food lasted 8 weeks. How much dog food did Casey give his dogs each week? Give the answer as a fraction or mixed number.
Answer:
The number of pounds of food did Casey give his dogs each week is 12\(\frac{1}{2}\) pounds.

Explanation:
Given that Casey bought a 100-pound bag of dog food and he gave his dogs the same amount of dog food each week and the dog food lasted 8 weeks. So the number of pounds of food did Casey give his dogs each week is 100 ÷ 8 which is 12\(\frac{1}{2}\) pounds.

Question 21.
Higher Order Thinking Write a word problem that can be solved by dividing 6 by 5.
Answer:

Question 22.
The amount of fabric needed for an adult and a baby scarecrow costume is shown at the right. The amount of fabric for an adult scarecrow costume is how many times the amount of fabric for a baby scarecrow costume? Give the answer as a fraction or mixed number.

Answer:
The fraction will be 3\(\frac{1}{2}\).

Explanation:
Given that the amount of fabric needed for an adult 7 yards and the amount of fabric needed for baby is 2 yards. So the fraction will be \(\frac{7}{2}\) which is 3\(\frac{1}{2}\).

Assessment Practice

Question 23.
Jamal had 37 feet of decorative tape to share with 5 friends and himself. How much tape does each person get?
A. \(\frac{6}{37}\) feet
B. 6\(\frac{1}{6}\) feet
C. 6\(\frac{5}{6}\) feet
D. 6\(\frac{1}{37}\) feet
Answer:
6\(\frac{1}{6}\) feet.

Explanation:
Given that Jamal had 37 feet of decorative tape to share with 5 friends and himself, so how much tape does each person get is 37 ÷ 6 which is 6\(\frac{1}{6}\) feet.

Question 24.
Lindsay divides 40 by 9. Between what two whole numbers is her answer?
A. 2 and 3
B. 3 and 4
C. 4 and 5
D. 5 and 6
Answer:
4 and 5.

Explanation:
Given that Lindsay divides 40 by 9, so the whole numbers in her answer is 4 and 5.

Lesson 9.3 Use Multiplication to Divide

Activity

Solve&Share
A sandwich shop prepares large wraps and cuts them into fourths. Each fourth is one serving. William buys 5 whole wraps for a party. How many servings in all does he get? Solve this problem any way you choose.

How could fraction strips, bar diagrams, or other models help you visualize the problem?

Look Back! Model with Math Write an equation that represents the problem about the wraps.

Visual Learning Bridge

Essential Question How Is Dividing by a Fraction Related to Multiplication?

A.
If a bottle of liquid plant food contains 3 cups, how many plants will you be able to feed? Explain why your answer makes sense.

You need to find how many eighths are in 3 cups. 3 ÷ \(\frac{1}{8}\) = ?

B.
How many \(\frac{1}{8}\)s are in 3?

Use a model and multiplication to solve.
Since there are 8 eighths in each whole, there are 3 × 8 = 24 eighths in 3 wholes.
S0, 3 ÷ \(\frac{1}{8}\) = 24.
The plant food can feed 24 plants.

C.
Does the answer make sense?
Do 24 eighths equal 3?
Use multiplication to check.
24 × \(\frac{1}{8}\) = \(\frac{24}{8}\) = 3
Yes, 24 eighths equals 3, so the answer makes sense.

The inverse relationship between multiplication and division applies to fraction computation, too!

The division equation 3 ÷ \(\frac{1}{8}\) = 24 is true because the multiplication equation
24 × \(\frac{1}{8}\) = 3 is true.

Convince Me! Use Structure Use the same numbers in the multiplication equation 15 × \(\frac{1}{3}\) = 5 to write a division equation. Draw a diagram to show that your division equation makes sense.

Guided Practice

Do You Understand?

Question 1.
Explain how to use multiplication to find 4 ÷ \(\frac{1}{5}\).
Answer:
The multiplication is 4 × 5 = 20.

Explanation:
Here, we can use multiplication to the given expression 4 ÷ \(\frac{1}{5}\) as 4 × 5 which is 20.

Question 2.
Show how to use multiplication to check your answer to Exercise 1.
Answer:

Do You Know How?

Question 3.
Find 3 ÷ \(\frac{1}{10}\).
Answer:
3 ÷ \(\frac{1}{10}\) = 30.

Explanation:
Given the expression is 3 ÷ \(\frac{1}{10}\) which is 3 × 10 which is 30.

Question 4.
Draw a model to find 2 ÷ \(\frac{1}{6}\).
Answer:
2 ÷ \(\frac{1}{6}\) = 12.

Explanation:
Given the expression is 2 ÷ \(\frac{1}{6}\) which is 12.

Question 5.
Use a multiplication equation to check your answer to Exercise 4.
Answer:

Independent Practice

In 6-9, use the model to find each quotient. Use multiplication to check your answer.

Question 6.
3 ÷ \(\frac{1}{4}\)

Answer:
The multiplication will be 12.

Explanation:
Given the expression is 3 ÷ \(\frac{1}{4}\), so the multiplication will be 3 × 4 which is 12.

Question 7.
2 ÷ \(\frac{1}{12}\)

Answer:
The multiplication will be 24.

Explanation:
Given the expression is 2 ÷ \(\frac{1}{12}\), so the multiplication will be 2 × 12 which is 24.

Question 8.
4 ÷ \(\frac{1}{9}\)

Answer:
The multiplication will be 36.

Explanation:
Given the expression is 4 ÷ \(\frac{1}{9}\), so the multiplication will be 4 × 9 which is 36.

Question 9.
3 ÷ \(\frac{1}{6}\)

Answer:
The multiplication will be 18.

Explanation:
Given the expression is 3 ÷ \(\frac{1}{6}\), so the multiplication will be 3 × 6 which is 18.

In 10-12, draw a model to find each quotient. Use multiplication to check your answer.

Question 10.
5 ÷ \(\frac{1}{6}\)
Answer:
The multiplication will be 30.

Explanation:
Given the expression is 5 ÷ \(\frac{1}{6}\), so the multiplication will be 5 × 6 which is 30.

Question 11.
4÷ \(\frac{1}{8}\)
Answer:
The multiplication will be 32.

Explanation:
Given the expression is 4÷ \(\frac{1}{8}\), so the multiplication will be 4 × 8 which is 32.

Question 12.
3 ÷ \(\frac{1}{3}\)
Answer:
The multiplication will be 9.

Explanation:
Given the expression is 3 ÷ \(\frac{1}{3}\), so the multiplication will be 3 × 3 which is 9.

Problem Solving

Question 13.
Model with Math Write and solve a division equation to find the number of \(\frac{1}{3}\) pound hamburger patties that can be made from 4 pounds of ground beef.

Answer:
The number of patties will be 12 patties.

Explanation:
Given that there are \(\frac{1}{3}\) pound hamburger patties that can be made from 4 pounds of ground beef, so the number of patties will be 4 × 3 which is 12 patties.

Question 14.
Write and solve a word problem for the expression 8 ÷ \(\frac{1}{2}\).
Answer:
How many half-hour chess classes can a chess teacher give in 8 hours?

Explanation:
The number of classes will be 8 ÷ \(\frac{1}{2}\) which is 16 classes.

Question 15.
Use the numbers in the multiplication equation 28 × \(\frac{1}{7}\) = 4 to write a division equation involving division by a fraction.
Answer:
The division equation will be 4 ÷ \(\frac{1}{7}\) = 28.

Explanation:
Given the multiplication equation 28 × \(\frac{1}{7}\) = 4, so the division equation involving division by a fraction is 4 ÷ \(\frac{1}{7}\) = 28.

Question 16.
Number Sense Sally and Timothy have two different answers for 1,785 ÷ 35. Without dividing, how can you tell whose answer is wrong?
Sally: 1,785 ÷ 35 = 51
Timothy: 1,785 ÷ 35 = 501
Answer:
Timothy’s answer is wrong.

Explanation:
Given that Sally and Timothy have two different answers for 1,785 ÷ 35, here Timothy’s answer is wrong. Because when we multiply factors, the product with a certain number of place values and the product should have the sum of the number of place values. So without dividing, we can say as 35 has 2 digits and 51 has 2 digits, so 2 + 2 = 4, and 1785 has 4 digits.

Question 17.
Higher Order Thinking A restaurant charges $3.50 for a slice of pie that is one sixth of a pie and $3.00 for a slice that is one eighth of a pie. One day they baked 5 pies, all the same size. If they sell all the slices, would they make more money by slicing each pie into sixths or eighths? How much more? Explain.
Answer:
They make $15 more money by slicing each pie into sixths or eighths.

Explanation:
Given that a restaurant charges $3.50 for a slice of pie that is one-sixth of a pie and $3.00 for a slice that is one-eighth of a pie and they baked 5 pies all the same size. So if they sell all the slices, would they make more money by slicing each pie into sixths or eighths. So one-sixth of a pie will be 5 ÷ \(\frac{1}{6}\) which is 30 slices and they would make $3.50 × 30 which is $105. And for one-eighth of a pie 5 ÷ \(\frac{1}{8}\) which is 40 slices and they would make $3.00 × 40 which is $120. So $120 – $105 = $15.

Assessment Practice

Question 18.
Javier drew a model to determine how many fifths are in 6 wholes.

Part A
Describe Javier’s work by writing a division equation that includes a fraction.

Answer:
The division equation will be 6 ÷ \(\frac{1}{5}\) = 30.

Explanation:
Javier’s work by writing a division equation will be 6 ÷ \(\frac{1}{5}\) which will be 30.
Part B
Check your answer by using the numbers in your division equation to write a multiplication equation.
Answer:
The multiplication equation is 30 × \(\frac{1}{5}\) = 6.

Explanation:
The multiplication equation will be 30 × \(\frac{1}{5}\) which is 6.

Lesson 9.4 Divide Whole Numbers by Unit Fractions

Activity

Solve & Share
One ball of dough can be stretched into a circle to make a pizza. After the pizza is cooked, it is cut into 8 equal slices. How many slices of pizza can you make with 3 balls of dough? Solve this problem any way you choose.

You can use appropriate tools to help find the answer. Show your work!

Look Back! Into how many slices of pizza will each ball of dough be divided? What fraction of a whole pizza does 1 slice represent?

Visual Learning Bridge

Essential Question How Can You Divide by a Unit Fraction?

A.
Joyce is making sushi rolls. She needs \(\frac{1}{4}\) cup of rice for each sushi roll. How many sushi rolls can she make if she has 3 cups of rice?

\(\frac{1}{4}\) is a unit fraction. A unit fraction is a fraction that describes one part of the whole. So, it has a numerator of 1.

B.
One Way Use an area model to find how many \(\frac{1}{4}\)s are in 3.

There are four \(\frac{1}{4}\)s in 1 whole cup. So, there are twelve \(\frac{1}{4}\)s in three whole cups. So, Joyce can make 12 sushi rolls.
You can use multiplication to check your answer.
3 × 4 = 12

C.
Another Way Use a number line to find how many \(\frac{1}{4}\)s are in 3.

You can see that there are four \(\frac{1}{4}\)s in between each whole number.
There are four \(\frac{1}{4}\)s in 1 whole, eights in \(\frac{1}{4}\)s in 2 wholes, and twelve \(\frac{1}{4}\)s in 3 wholes.
So, 3 ÷ \(\frac{1}{4}\) = 12.
Joyce can make 12 sushi rolls.

Convince Me! Use Structure Use the diagram below to find 4 ÷ \(\frac{1}{3 }\).

Answer:
The multiplication equation will be 4 × 3 = 12.

Explanation:
Given that the expression is 4 ÷ \(\frac{1}{3 }\), so the multiplication equation will be 4 × 3 which is 12.

Guided Practice

Do You Understand?

Question 1.
In the example at the top of page 398, if Joyce had 4 cups of rice, how many rolls could she make?
Answer:
There will be 16 sushi rolls.

Explanation:
If Joyce had 4 cups of rice, then there will be 4 × 4 which will be 16 sushi rolls.

Question 2.
In the example at the top of page 398, how does the number line help to show that 3 ÷ \(\frac{1}{4}\) is equal to 3 × 4?
Answer:

Do You Know How?

In 3 and 4, use the picture below to find each quotient.

Question 3.
How many \(\frac{1}{3}\)s are in 3?
3 ÷ \(\frac{1}{3}\) = _____
Answer:
3 ÷ \(\frac{1}{3}\) = 3.

Explanation:
Here, we need to find \(\frac{1}{3}\)s in 3. So there will be 3 × 3 which is 9.

Question 4.
How many \(\frac{1}{3}\)s are in 6?
6 ÷ \(\frac{1}{3}\) = _____
Answer:
6 ÷ \(\frac{1}{3}\) = 18.

Explanation:
Here, we need to find \(\frac{1}{3}\)s in 6. So there will be 3 × 6 which is 18.

Independent Practice

Leveled Practice in 5 and 6, use the picture to find each quotient.

Question 5.
How many \(\frac{1}{6}\)s are in 1?
1 ÷ 6\(\frac{1}{3}\) = ___
Answer:

Question 6.
How many \(\frac{1}{6}\)s are in 5?
5 ÷ \(\frac{1}{6}\) = _____
Answer:

In 7-14, draw a picture or use a number line to find each quotient. Then use multiplication to check your answer.

Question 7.
4 ÷ \(\frac{1}{2}\)
Answer:
The multiplication equation will be 4 × 2 = 8.

Explanation:
Given that the expression is 4 ÷ \(\frac{1}{2}\), so the multiplication equation will be 4 × 2 which is 8.

Question 8.
2 ÷ \(\frac{1}{8}\)
Answer:
The multiplication equation will be 2 × 8 = 16.

Explanation:
Given that the expression is 2 ÷ \(\frac{1}{8}\), so the multiplication equation will be 2 × 8 which is 16.

Question 9.
2 ÷ \(\frac{1}{3}\)
Answer:
The multiplication equation will be 2 × 3 = 6.

Explanation:
Given that the expression is 2 ÷ \(\frac{1}{3}\), so the multiplication equation will be 2 × 3 which is 6.

Question 10.
6 ÷ \(\frac{1}{4}\)
Answer:
The multiplication equation will be 6 × 4 = 24.

Explanation:
Given that the expression is 2 ÷ \(\frac{1}{8}\), so the multiplication equation will be 2 × 8 which is 16.

Question 11.
8 ÷ \(\frac{1}{3}\)
Answer:
The multiplication equation will be 3 × 8 = 24.

Explanation:
Given that the expression is 8 ÷ \(\frac{1}{3}\), so the multiplication equation will be 3 × 8 which is 24.

Question 12.
3 ÷ \(\frac{1}{10}\)
Answer:
The multiplication equation will be 3 × 10 = 30.

Explanation:
Given that the expression is 3 ÷ \(\frac{1}{10}\), so the multiplication equation will be 3 × 10 which is 30.

Question 13.
9 ÷ \(\frac{1}{10}\)
Answer:
The multiplication equation will be 9 × 10 = 90.

Explanation:
Given that the expression is 9 ÷ \(\frac{1}{10}\), so the multiplication equation will be 9 × 10 which is 90.

Question 14.
15 ÷ \(\frac{1}{5}\)
Answer:
The multiplication equation will be 15 × 5 = 75.

Explanation:
Given that the expression is 15 ÷ \(\frac{1}{5}\), so the multiplication equation will be 15 × 5 which is 75.

Problem Solving

Question 15.
Dan has 4 cartons of juice. He pours \(\frac{1}{8}\) carton for each person on a camping trip. How many people can he serve? Draw a picture to help you answer the question.

Answer:
The number of people can he serve is 32 people.

Explanation:
Given that Dan has 4 cartons of juice and he pours \(\frac{1}{8}\) carton for each person on a camping trip, so the number of people can he serve is 4 ÷ \(\frac{1}{8}\) which is 4 × 8 = 32 people.

Question 16.
Higher Order Thinking Write a word problem that can be solved by dividing 10 by \(\frac{1}{3}\). Then answer the problem.
Answer:

Question 17.
Number Sense The Nile River is the longest river in the world. It is 4,160 miles long. You want to spend three weeks traveling the entire length of the river, traveling about the same number of miles each day. Estimate the number of miles you should travel each day.
Answer:
The number of miles you should travel each day is 198.09 miles per day.

Explanation:
Given that the Nile River is 4,160 miles long and if we are going to calculate the length for each day. And we need to multiply the number of weeks by the amount for each week is 3 × 7 which is 21 days. So to find the distance we should travel per day, divide the total distance by the number of days. So 4,160 ÷ 21 which is 198.09 miles per day.

Question 18.
Make Sense and Persevere
Maria used one bag of flour. She baked two loaves of bread. Then she used the remaining flour to make 48 muffins. How much flour was in the bag when Maria began?

Answer:

Assessment Practice

Question 19.
Deron is making light switch plates from pieces of wood. He starts with a board that is 18 feet long. How many light switch plates can he make?

A. 9 light switch plates
B. 24 light switch plates
C. 27 light switch plates
D. 54 light switch plates
Answer:

Lesson 9.5 Divide Unit Fractions by Non-Zero Whole Numbers

Activity

Solve & Share
Yesterday, the cooking club made a pan of lasagna. They left half of the lasagna for 4 members of the photography club to share equally. What fraction of the pan of lasagna did each photography club member get? Solve this problem any way you choose.

You can use appropriate tools to show how to divide what is left. Show your work!

Look Back! What equation can you write to model this problem?

Visual Learning Bridge

Essential Question How Can You Model Dividing a Unit Question Fraction by a Whole Number?

A.
Half of a pan of cornbread is left over. Ann, Beth, and Chuck are sharing the leftovers equally. What fraction of the original cornbread does each person get?

You can make a drawing to show \(\frac{1}{2}\) of the cornbread.

B.
One Way On an area model, divide \(\frac{1}{2}\) into 3 equal parts.

Each part contains \(\frac{1}{6}\) of the whole.
\(\frac{1}{2}\) ÷ 3 = \(\frac{1}{6}\)
Each person gets \(\frac{1}{6}\) of the cornbread.

C.
Another Way Use a number line. Shades \(\frac{1}{2}\) on the number line. Partition \(\frac{1}{2}\) into 3 equal parts.

Each part is \(\frac{1}{6}\).
\(\frac{1}{2}\) ÷ 3 = \(\frac{1}{6}\)
Each person gets \(\frac{1}{6}\) of the cornbread.

Convince Me! Reasoning in the example above, how is dividing by 3 the same as multiplying by \(\frac{1}{3}\)?

Guided Practice

Do You Understand?

Question 1.
In the example at the top of page 402, suppose that 4 people were sharing half of the cornbread equally. What fraction of the original cornbread would each person get? Draw a picture or use objects to help.
Answer:

Question 2.
When you divide a unit fraction by a non-zero whole number greater than 1, will the quotient be greater than or less than the unit fraction?
Answer:

Do You Know How?

In 3-6, find each quotient. Use the picture or objects to help.

Qestion 3.
\(\frac{1}{4}\) ÷ 2
Answer:
The quotient will be \(\frac{1}{8}\).

Explanation:
Given that the expression is \(\frac{1}{4}\) ÷ 2, so the quotient will be \(\frac{1}{8}\).

Question 4.
\(\frac{1}{4}\) ÷ 4
Answer:
The quotient will be \(\frac{1}{16}\).

Explanation:
Given that the expression is \(\frac{1}{4}\) ÷ 4, so the quotient will be \(\frac{1}{16}\).

Question 5.
\(\frac{1}{2}\) ÷ 2
Answer:
The quotient will be \(\frac{1}{4}\).

Explanation:
Given that the expression is \(\frac{1}{2}\) ÷ 2, so the quotient will be \(\frac{1}{4}\).

Question 6.
\(\frac{1}{2}\) ÷ 4
Answer:
The quotient will be \(\frac{1}{8}\).

Explanation:
Given that the expression is \(\frac{1}{2}\) ÷ 4, so the quotient will be \(\frac{1}{8}\).

Independent Practice

Leveled Practice In 7 and 8, find each quotient. Use a picture or objects to help.

Question 7.
\(\frac{1}{2}\) ÷ 5

Answer:
The quotient will be \(\frac{1}{10}\).

Explanation:
Given that the expression is \(\frac{1}{2}\) ÷ 5, so the quotient will be \(\frac{1}{10}\).

Question 8.
\(\frac{1}{5}\) ÷ 2

Answer:
The quotient will be \(\frac{1}{10}\).

Explanation:
Given that the expression is \(\frac{1}{5}\) ÷ 2, so the quotient will be \(\frac{1}{10}\).

Partitioning pictures or objects can help when dividing fractions by a whole number.

In 9-14, find each quotient.

Question 9.
\(\frac{1}{2}\) ÷ 7
Answer:
The quotient will be \(\frac{1}{14}\).

Explanation:
Given that the expression is \(\frac{1}{2}\) ÷ 7, so the quotient will be \(\frac{1}{14}\).

Question 10.
\(\frac{1}{4}\) ÷ 3
Answer:
The quotient will be \(\frac{1}{12}\).

Explanation:
Given that the expression is \(\frac{1}{4}\) ÷ 3, so the quotient will be \(\frac{1}{12}\).

Question 11.
\(\frac{1}{6}\) ÷ 2
Answer:
The quotient will be \(\frac{1}{10}\).

Explanation:
Given that the expression is \(\frac{1}{2}\) ÷ 5, so the quotient will be \(\frac{1}{10}\).

Question 12.
\(\frac{1}{3}\) ÷ 4
Answer:
The quotient will be \(\frac{1}{12}\).

Explanation:
Given that the expression is \(\frac{1}{3}\) ÷ 4, so the quotient will be \(\frac{1}{12}\).

Question 13.
\(\frac{1}{4}\) ÷ 5
Answer:
The quotient will be \(\frac{1}{20}\).

Explanation:
Given that the expression is \(\frac{1}{4}\) ÷ 5, so the quotient will be \(\frac{1}{20}\).

Question 14.
\(\frac{1}{5}\) ÷ 3
Answer:
The quotient will be \(\frac{1}{15}\).

Explanation:
Given that the expression is \(\frac{1}{5}\) ÷ 3, so the quotient will be \(\frac{1}{15}\).

Problem Solving

Question 15.
Vin, Corrie, Alexa, and Joe equally shared one fourth of a submarine sandwich. What fraction of the original sandwich did each friend get? Use the number line to help you find the answer.

Answer:
Each person gets is \(\frac{1}{4}\).

Explanation:
Given that Vin, Corrie, Alexa, and Joe equally shared one fourth of a submarine sandwich, so the fraction of the original sandwich did each friend get is, as the sandwich a whole is \(\frac{4}{4}\) and there is 4 people, so each person gets is \(\frac{1}{4}\).

Question 16.
Sue has \(\frac{1}{2}\) gallon of milk to share evenly among four people. How much milk, in gallons, should she give each person?
Answer:
Sue gave \(\frac{1}{8}\) gallons of milk.

Explanation:
Given that Sue has \(\frac{1}{2}\) gallon of milk to share evenly among four people, so she gave each person \(\frac{1}{2}\) ÷ 4 which is \(\frac{1}{8}\) gallons.

Question 17.
Critique Reasoning Taryn says that \(\frac{1}{4}\) of a cereal bar is larger than \(\frac{1}{3}\) of the cereal bar. Is she correct? Explain.
Answer:
Taryn is not correct.

Explanation:
Given that Taryn says that \(\frac{1}{4}\) of a cereal bar is larger than \(\frac{1}{3}\) of the cereal bar. Here, Taryn is not correct. As it’s \(\frac{1}{4}\) is getting smaller than \(\frac{1}{3}\).

Question 18.
Algebra On Saturday, Amir ran 1\(\frac{3}{4}\) miles, and Janie ran 2\(\frac{1}{2}\) miles. Who ran farther? How much farther? Write an equation to find d, the difference of the two distances.
Answer:
The difference of the two distances is \(\frac{3}{4}\).

Explanation:
Given that on Saturday, Amir ran 1\(\frac{3}{4}\) miles, and Janie ran 2\(\frac{1}{2}\) miles. And the equation to find d is
d = Janie – Amir
= 2\(\frac{1}{2}\) – 1\(\frac{3}{4}\)
= \(\frac{5}{2}\) – \(\frac{7}{4}\)
= \(\frac{10-7}{4}\)
= \(\frac{3}{4}\).

Question 19.
Higher Order Thinking Five friends equally shared half of one large pizza and \(\frac{1}{4}\) of another large pizza. What fraction of each pizza did each friend get? How do the two amounts compare to each other?
Answer:
Each friend gets \(\frac{1}{20}\) of pizza.

Explanation:
Given that five friends equally shared half of one large pizza and \(\frac{1}{4}\) of another large pizza, so the fraction of each pizza did each friend get is \(\frac{1}{4}\) ÷ 5 which is \(\frac{1}{20}\).

Assessment Practice

Question 20.
Jamie cut a rope into thirds. He used two of the pieces to make a swing. He used equal lengths of the leftover rope on four picture frames. What fraction of the original rope did he use for each picture frame?
A. \(\frac{1}{4}\)
B. \(\frac{1}{12}\)
C.\(\frac{1}{16}\)
D. \(\frac{3}{4}\)
Answer:
The fraction of the original rope did he use for each picture frame \(\frac{3}{4}\).

Explanation:
Given that Jamie cut a rope into thirds and he used two of the pieces to make a swing and he used equal lengths of the leftover rope on four picture frames. So the fraction of the original rope did he use for each picture frame \(\frac{3}{4}\).

Question 21.
One half of an apple pie is left for 5 family members to share equally. What fraction of the original pie will each member get?
A. \(\frac{1}{10}\)
B.\(\frac{1}{7}\)
C. \(\frac{1}{3}\)
D. \(\frac{2}{5}\)
Answer:
The fraction of the original pie will each member get is \(\frac{1}{10}\).

Explanation:
Given that One half of an apple pie is left for 5 family members to share equally. So the fraction of the original pie will each member get is \(\frac{1}{2}\) ÷ 5 which is \(\frac{1}{10}\).

Lesson 9.6 Divide Whole Numbers and Unit Fractions

Activity

Solve&Share
The Brown family is planting \(\frac{1}{3}\) of their garden with flowers, \(\frac{1}{3}\) with berries, and \(\frac{1}{3}\) with vegetables. The vegetable section has equal parts of carrots, onions, peppers, and tomatoes. What fraction of the garden is planted with carrots? Solve this problem any way you choose.

How can you show an equal share of each vegetable?

Look Back! Model with Math Write an equation that models this problem. Explain your reasoning.

Visual Learning Bridge

Essential Question How Can You Divide with Unit Fractions and Whole Numbers?

A.
A utility company is planning to install wind turbines on 4 square miles of land. Each turbine requires \(\frac{1}{6}\) square mile of land. How many turbines can be installed?

Model the problem with a picture or an equation to help you.

B.
One Way
Use an area model to show 4 square miles. Divide each square mile into 6 equal parts to represent \(\frac{1}{6}\) square mile.

There are 24 parts.
So, 24 wind turbines will fit on the land.

C.
Another Way
Use a number line to show 4 wholes.

There are 6\(\frac{1}{6}\)s in each whole.
So, there are 24\(\frac{1}{6}\)s in 4 wholes.
4 ÷ \(\frac{1}{6}\) = 24
24 wind turbines will fit on the land.

Convince Me! Reasoning Use an area model to find 2 ÷ \(\frac{1}{4}\). Then use multiplication to check your answer.

Another Example
Use a number line to find \(\frac{1}{4}\) ÷ 6.
If you partition \(\frac{1}{4}\) into 6 equal segments, how long is each segment?

\(\frac{1}{4}\) ÷ 6 = \(\frac{1}{24}\)
Check your answer using multiplication: \(\frac{1}{24}\) × 6 = \(\frac{1}{4}\).

Guided Practice

Do You Understand?

Question 1.
When you divide a whole number by a fraction less than 1, will the quotient be greater than or less than the whole number?
Answer:
The quotient will be less than 1.

Explanation:
The quotient will be less than 1. Because, if we take example a fraction which is less than 1 which is \(\frac{2}{3}\) and a whole number 4 which is greater than 1. So when we divide \(\frac{2}{3}\) with 4 which is \(\frac{2}{3}\) ÷ 4 on solving we will get \(\frac{1}{6}\) which is less than 1.

Question 2.
4 square miles of land is separated into sections that each have an area of \(\frac{1}{2}\) square mile. How many sections are there?

Answer:

Do You Know How?

In 3-6, find each quotient. 3. 2-1

Question 3.
2 ÷ \(\frac{1}{4}\)
Answer:
The quotient will be \(\frac{1}{8}\).

Explanation:
Given that the expression is \(\frac{1}{4}\) ÷ 2, so the quotient will be \(\frac{1}{8}\).

Question 4.
3 ÷ \(\frac{1}{4}\)
Answer:
The quotient will be \(\frac{1}{12}\).

Explanation:
Given that the expression is \(\frac{1}{4}\) ÷ 3, so the quotient will be \(\frac{1}{12}\).

Question 5.
\(\frac{1}{6}\) ÷ 2
Answer:
The quotient will be \(\frac{1}{12}\).

Explanation:
Given that the expression is \(\frac{1}{6}\) ÷ 2, so the quotient will be \(\frac{1}{12}\).

Question 6.
2 ÷ \(\frac{1}{3}\)
Answer:
The quotient will be \(\frac{1}{6}\).

Explanation:
Given that the expression is \(\frac{1}{3}\) ÷ 2, so the quotient will be \(\frac{1}{6}\).

Draw a number line or use a model to help you find the answers!

Independent Practice

Leveled Practice In 7-10, find each quotient. Use a model or number line to help.

Question 7.
5 ÷ \(\frac{1}{2}\)

Answer:
The quotient will be 10.

Explanation:
Given that the expression is 5 ÷ \(\frac{1}{2}\), so the quotient will be 10.

Question 8.
\(\frac{1}{2}\) ÷ 5

Answer:
The quotient will be \(\frac{1}{10}\).

Explanation:
Given that the expression is \(\frac{1}{2}\) ÷ 5, so the quotient will be \(\frac{1}{10}\).

Question 9.
6 ÷ \(\frac{1}{3}\)

Answer:
The quotient will be 18.

Explanation:
Given that the expression is 6 ÷ \(\frac{1}{3}\), so the quotient will be 18.

Question 10.
\(\frac{1}{3}\) ÷ 6

Answer:
The quotient will be \(\frac{1}{18}\).

Explanation:
Given that the expression is \(\frac{1}{3}\) ÷ 6, so the quotient will be \(\frac{1}{18}\).

Problem Solving

Question 11.
Keiko divided 5 cups of milk into \(\frac{1}{4}\)-cup portions. How many \(\frac{1}{4}\)-cup portions did Keiko have? Complete the picture to show your solution.

Answer:
The number of portions did Keiko have is \(\frac{1}{20}\).

Explanation:
Given that Keiko divided 5 cups of milk into \(\frac{1}{4}\)-cup portions. So the number of portions did Keiko have is \(\frac{1}{4}\) ÷ 5 which is \(\frac{1}{20}\).

Question 12.
Algebra Ms. Allen has \(\frac{1}{8}\) of a pan of brownies left to divide between 2 children. Draw a picture to find what fraction, f, of the original pan of brownies each child gets. Write an equation for f that models the solution.
Answer:
The fraction equation will be \(\frac{1}{8}\) ÷ 2 = \(\frac{1}{16}\).

Explanation:
Given that Ms. Allen has \(\frac{1}{8}\) of a pan of brownies left to divide between 2 children. So the fraction equation will be \(\frac{1}{8}\) ÷ 2 which is \(\frac{1}{16}\).

Question 13.
Make Sense and Persevere A regular polygon has a perimeter of 2 feet. If each side measures \(\frac{1}{3}\) foot, what is the name of the polygon?
Answer:

A regular polygon has equal side lengths and equal angle measures.

Answer:
The name of the polygon is Hexagon.

Explanation:
The name of the polygon is Hexagon. As \(\frac{1}{3}\) fits into two 6 times. That means there are 6 sides.

Question 14.
Higher Order Thinking Mr. Brent uses \(\frac{1}{4}\) cup of blue paint and \(\frac{1}{4}\) cup of yellow paint to make each batch of green paint. How many batches of green paint can he make with the amount of paint he has left? Explain how you found your answer.

Answer:
Mr. Brent makes 12 batches of green paint.

Explanation:
Given that Mr. Brent uses \(\frac{1}{4}\) cup of blue paint and \(\frac{1}{4}\) cup of yellow paint to make each batch of green paint. Here, every \(\frac{1}{2}\) cup yellow paint combined with \(\frac{3}{4}\) cup of blue paint would make 1 + \(\frac{1}{4}\) cup which is \(\frac{4+1}{4}\) which is \(\frac{5}{4}\). As we can make a total of 15 cups of green paint, so 15 ÷ 1.25 which is 12 batches of paint.

Assessment Practice

Question 15.
Jordan says that 6 ÷ \(\frac{1}{2}\) = 3. Is he correct? If not, justify your reasoning and give the correct quotient.
Answer:
Jordan is wrong.

Explanation:
Given that Jordan says that 6 ÷ \(\frac{1}{2}\) = 3, Jordan is not correct. Because 6+1 = 7 and 7 ÷ 2 which is 3.5. So Jordan is wrong.

Lesson 9.7 Solve Problems Using Division

Solve & Share
Organizers of an architectural tour need to set up information tables every \(\frac{1}{8}\) mile along the 6-mile tour, beginning \(\frac{1}{8}\) mile from the start of the tour. Each table needs 2 signs. How many signs do the organizers need? Solve this problem any way you choose.

Make Sense and Persevere What steps do you need to do to solve this problem? Show your work!

Look Back! How does the number line help you solve this problem?

Visual Learning Bridge

Essential Question How Can You Solve Division Home Problems with Unit Fractions?

A.
John plans to buy sheets of plywood like the ones shown to make boxes with lids. Each box is a cube that has \(\frac{1}{3}\)foot edges. How many sheets of plywood does John need in order to make 5 boxes with lids?

Remember, a cube has 6 identical faces.

B.
What do you know?
Six pieces of plywood are needed for each of the 5 boxes.
Boxes are \(\frac{1}{3}\)-foot cubes. Each sheet of plywood is \(\frac{1}{3}\) foot wide and 4 feet long.
What are you asked to find?
The number of sheets of plywood John needs to buy

C.
Write an equation to help answer each question.
1. How many pieces of plywood are needed boxes for 5 boxes with lids?

2. How many pieces can be cut from 1 sheet of plywood?
4 ÷ \(\frac{1}{3}\) = 12

3. How many sheets of plywood does John need for 5 boxes with lids? 30 ÷ 12 = 2 R6
John needs 3 sheets of plywood.

Convince Me! Reasoning Write a real-world problem that can be solved by first adding 24 and 36 and then dividing by \(\frac{1}{4}\). Find the solution to your problem and explain your answer.

Guided Practice

Do You Understand?

Question 1.
In the example on page 410, why were additional questions answered to help solve the problem?
Answer:

Question 2.
What equations were used to solve the example on page 410?
Answer:

Do You Know How?

Question 3.
Tamara needs tiles to make a border for her bathroom wall. The border will be 9 feet long and \(\frac{1}{3}\) foot wide. Each tile measures \(\frac{1}{3}\) foot by \(\frac{1}{3}\) foot. Each box of tiles contains 6 tiles. How many boxes of tiles does Tamara need? Write two equations that can be used to solve the problem.
Answer:
Tamara needs 5 boxes of tiles.

Explanation:
Given that each tile measures \(\frac{1}{3}\) foot by \(\frac{1}{3}\) foot and each box of tiles contains 6 tiles which is 6X × \(\frac{1}{3}\) × \(\frac{1}{3}\) = 9 × \(\frac{1}{3}\). Therefore X = 4.5. Since X is an integer, the smallest integer such that X = 5.

Independent Practice

Write the equations needed to solve each problem. Then solve.

Question 4.
Robert wants to use all the ingredients listed in the table at the right to make trail mix. How many \(\frac{1}{2}\)-pound packages can he make?

Equations: _______________
Answer: _______________
Answer:
Total number of pounds Robert can make is 8 pounds.

Explanation:
Robert makes a package of 2\(\frac{1}{2}\) + 4 + 1\(\frac{1}{2}\) which is \(\frac{5+8+3}{2}\) which is \(\frac{16}{2}\) = 8.

Question 5.
Rachel used \(\frac{2}{3}\) of a package of cornbread mix. She will use equal parts of the leftover mix to make 2 batches of cornbread. What fraction of the original package will she use for each batch?
Equations: _________
Answer: ____________
Answer:
The fraction of the original package will she use for each batch is \(\frac{1}{3}\).

Explanation:
Given that Rachel used \(\frac{2}{3}\) of a package of cornbread mix and she will use equal parts of the leftover mix to make 2 batches of cornbread. So the fraction of the original package will she use for each batch is \(\frac{2}{3}\) ÷ 2 which is \(\frac{1}{3}\).

Problem Solving

Question 6.
Make Sense and Persevere Sandra is making vegetable soup. If she makes 12 cups of soup, how many cups of onions does she need? Use the data table on the right. Write the equations needed to solve the problem. Then solve.

Answer:
The number of cups of onions does she need is \(\frac{1}{2}\) cups.

Explanation:
Given that Sandra is making vegetable soup and if she makes 12 cups of soup, so the number of cups of onions does she need is, as \(\frac{1}{8}\) cup of onions needed for 3 cups. So for 12 cups Sandra needed \(\frac{1}{8}\) × 4 which is \(\frac{1}{2}\) cups.

Question 7.
Emily needs to buy fabric to make curtain panels for her windows. Each panel will be 4 feet long and \(\frac{1}{2}\) foot wide. Each piece of fabric that she can buy is 4 feet long and 2 feet wide. How many panels can she make from 1 piece of fabric?
Answer:
The number of panels can she make from 1 piece of fabric is 8 .

Explanation:
Here, each panel is 4 ft long and \(\frac{1}{2}\) foot wide and the piece of fabric is 4 ft long and 2 ft wide. So she can fit 4 panels and calculate this area which is
4 × \(\frac{1}{2}\) = 2ft^2
4 × 2 = 8ft^2
So 4 × 2 = 8.

Question 8.
Algebra Barry buys a package of pasta for $2.39 and a jar of tomato sauce for $3.09. He uses a $0.75 coupon and a $0.50 coupon. What is the total cost of Barry’s purchase? Write an expression to show your work.
Answer:
The expression will be $5.48 – $1.25 = $4.23.

Explanation:
Given that Barry buys a package of pasta for $2.39 and a jar of tomato sauce for $3.09, so the total cost is $2.39 + $3.09 which is $5.48 and he uses a $0.75 coupon and a $0.50 coupon and the coupons is $0.75+$0.50 = $1.25. So the expression will be $5.48 – $1.25 which is $4.23.

Question 9.
Higher Order Thinking Mr. Moss had 4 gallons of paint. He painted 8 doors. How many benches can he paint with the paint that is left? Show your work.

Answer:
Mr. Moss can paint 6 benches.

Explanation:
Given that Mr. Moss had 4 gallons of paint and he painted 8 doors. So the number of benches can he paint with the paint that is left is
8 doors/2 = 4,
4 × \(\frac{1}{2}\) = 2 gallons.
He used 2 gallons remaining for the benches.
By dividing remaining paint by paint per bench, so 2 ÷ \(\frac{1}{3}\) on solving we will get 6.
So he can paint 6 benches.

Assessment Practice

Question 10.
Sophia uses \(\frac{1}{2}\) pound of white flour to make one loaf of bread and \(\frac{1}{4}\) pound of cake flour to make one cake. Which shows how many cakes and loaves of bread Sophia can make with the amount of flour that she has?

A. 12 cakes, 4 loaves of bread
B. 6 cakes, 8 loaves of bread
C. 8 cakes, 6 loaves of bread
D. 4 cakes, 12 loaves of bread
Answer:
Sophia can make 12 cakes, 4 loaves of bread.

Explanation:
Given that white flour used for one loaf of bread is \(\frac{1}{2}\) pounds and white flour available is 2 pounds. And cake flour used to make one cake is \(\frac{1}{4}\) pounds and cake flour available is 3 pounds. Now we will divide the available amount by amount used for one.
Number of loaves of bread is 2 × \(\frac{1}{2}\) = 2 × 2 which is 4.
So, the number of loaves of bread is 4.
Number of cakes is 3 × \(\frac{1}{4}\) = 3 × 4 = 12.
So Sophia can make 12 cakes, 4 loaves of bread.

Lesson 9.8 Repeated Reasoning

Activity

Solve & Share
What do you notice about the calculations below? Make a generalization about what you notice. Complete the remaining examples.

Thinking Habits
Be a good thinker! These questions can help you.
• Are any calculations repeated?
• Can I generalize from examples?
• What shortcuts do I notice?

Look Back! Generalize Test your general method by writing another pair of equations like Sue’s and Randy’s equations.

Visual Learning Bridge

Essential Question How Do You Use Repeated Reasoning When Dividing Whole Numbers and Unit Fractions?

A.
Ali partitioned a 4-foot board into \(\frac{1}{2}\)-foot pieces. She counted 8 pieces.
Then she partitioned a \(\frac{1}{2}\)-foot board into 4 equal pieces. Each piece was \(\frac{1}{8}\) of a foot.

Study the equations below. What generalizations can you make? Explain.

What do I need to do?
I need to understand the equations and make generalizations about them.

B.
How can I make a generalization from repeated reasoning?
I can
• look for things that repeat in a problem.
• test whether my generalization works for other numbers.

Here’s my thinking..

C.
I see that
4 ÷ 2 = 4 × 2 and \(\frac{1}{2}\) ÷ 4 = \(\frac{1}{2}\) × \(\frac{1}{4}\)
Check if the same relationship applies to other numbers.
10 ÷ \(\frac{1}{3}\) = 30 and 10 × 3 = 30
\(\frac{1}{3}\) ÷ 10 = 30 and \(\frac{1}{3}\) × \(\frac{1}{10}\) = \(\frac{1}{30}\)
Dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction.
Dividing a unit fraction by a whole number other than zero is the same as multiplying the unit fraction by a unit fraction with the whole number as the denominator.

Convince Me! Generalize Marcus made the following generalization: 12 ÷ \(\frac{1}{5}\) = \(\frac{1}{12}\) × \(\frac{1}{5}\). Is he correct? Explain.

Guided Practice

Generalize
Nathan has two 8-foot boards. He cuts one board into \(\frac{1}{4}\)-foot pieces. He cuts the other board into \(\frac{1}{2}\)-foot pieces.

Repeated reasoning can help you find a general method for solving problems that are same type.

Question 1.
Write and solve a division equation to find how many \(\frac{1}{4}\)-ft pieces can be cut from an 8-foot board. Explain your reasoning.
Answer:

Question 2.
Find how many \(\frac{1}{2}\)-ft pieces can be cut from the 8-foot board. Can you repeat the method you used in Exercise 1 to solve this problem? Explain.
Answer:

Independent Practice

Remember, the method for dividing a whole number by a unit fraction is different from the method for dividing a unit fraction by a whole number.

Generalize
A landscaper’s truck is filled with \(\frac{1}{2}\) ton of gravel. The gravel is shared equally among 3 projects.

Question 3.
Write and solve a division equation to find how much gravel each project will get. Explain your reasoning.
Answer:

Question 4.
Suppose another truck is filled with \(\frac{1}{2}\) ton of gravel. Find how much gravel each project will get if the \(\frac{1}{2}\) ton of gravel is shared equally among 8 projects. Can you repeat the method you used in Exercise 3 to solve this problem? Explain.
Answer:

Problem Solving

Performance Task

Pet Food
Pet Food Karl has a cat and a dog. He buys one bag of cat food and one bag of dog food. How many \(\frac{1}{4}\)-lb servings of cat food can he get from one bag? How many \(\frac{1}{2}\)-lb servings of dog food can he get from one bag?

Question 5.
Reasoning Karl thinks that he will be able to get more servings of dog food than cat food because the bag of dog food weighs more than the bag of cat food. Do you agree with his reasoning? Explain.
Answer:

Question 6.
Model with Math Write a division and a multiplication equation that Karl could use to find the number of servings of cat food in one bag.
Answer:

When you use repeated reasoning, you notice repetition in calculations.

Question 7.
Generalize What generalization can you make that relates the division equation to the multiplication equation you wrote in Exercise 6?
Answer:

Question 8.
Generalize Find how many servings of dog food are in one bag. Can you repeat the method you used in Exercise 6 to solve this problem? Explain.
Answer:

Topic 9 Fluency Practice

Activity

Follow the Path

Solve each problem. Follow problems with an answer of 3,456 to shade a path from START to FINISH. You can only move up, down, right, or left.

Topic 9 Vocabulary Review

Glossary

Understand Vocabulary

Write always, sometimes, or never.

Word List
• dividend
• divisor
• factor
• inverse operations
• product
• quotient
• unit fraction

Question 1.
A whole number divided by a fraction less than 1 is a mixed number. ____
Answer:
A whole number divided by a fraction less than 1 is a mixed number

Question 2.
The answer to a division problem is greater than the dividend. ___
Answer:
The answer to a division problem is greater than the dividend.

Question 3.
A fraction less than 1 divided by a whole number is a whole number. ____
Answer:

Question 4.
Dividing by \(\frac{1}{2}\) means you are finding how many halves are in the dividend. ____
Answer:

Question 5.
The dividend is the greatest number in a division problem. ____
Answer:

Question 6.
A whole number can be written as a fraction with 1 as the denominator. ____
Answer:

Draw a line from each number in Column A to the correct answer in Column B.

Answer:

Use Vocabulary in Writing

Question 11.
Explain how to use what you know about whole number division to check your work when you divide with fractions. Use at least three terms from the Word List in your explanation.
Answer:

Topic 9 Reteaching

Set A
pages 385-388, 389-392

You can represent the fraction \(\frac{3}{4}\) as division.

Think: \(\frac{1}{4}\) of 3 wholes.
So, \(\frac{3}{4}\) = 3 ÷ 4.

Remember that any fraction can be represented as division of the numerator by the denominator.

Write a division expression for each fraction.

Question 1.
\(\frac{7}{9}\)
Answer:
The division expression is 7 ÷ 9.

Explanation:
Given that the expression is \(\frac{7}{9}\) and the division expression is 7 ÷ 9.

Question 2.
\(\frac{11}{17}\)
Answer:
The division expression is 11 ÷ 17.

Explanation:
Given that the expression is \(\frac{11}{17}\) and the division expression is 11 ÷ 17.

Question 3.
\(\frac{10}{3}\)
Answer:
The division expression is 10 ÷ 3.

Explanation:
Given that the expression is \(\frac{10}{3}\) and the division expression is 10 ÷ 3.

Write each expression as a fraction or mixed number.

Question 4.
7 ÷ 12
Answer:
The fraction is \(\frac{7}{12}\).

Explanation:
Given that the division expression is 7 ÷ 12 and the fraction is \(\frac{7}{12}\).

Question 5.
13 ÷ 20
Answer:
The fraction is \(\frac{13}{20}\).

Explanation:
Given that the division expression is 7 ÷ 12 and the fraction is \(\frac{13}{20}\).

Question 6.
9 ÷ 5
Answer:
The fraction is 1\(\frac{4}{5}\).

Explanation:
Given that the division expression is 9 ÷ 5 and the fraction is \(\frac{9}{5}\) which is 1\(\frac{4}{5}\).

Question 7.
17 ÷ 7
Answer:
The fraction is 2\(\frac{3}{7}\).

Explanation:
Given that the division expression is 17 ÷ 7 and the fraction is \(\frac{9}{5}\) which is 2\(\frac{3}{7}\).

Set B
pages 393-396, 397-400

A 4-foot board is cut into pieces that are \(\frac{1}{2}\) foot in length. How many pieces are there?

There are 8 pieces.

Remember that you can use multiplication to check your answer.

Question 1.
A 12-foot-long playground is marked off into \(\frac{1}{5}\)-foot-long sections for a game. How many sections are there?
Answer:
The number of sections will be about 2.

Explanation:
Given that a 12-foot-long playground is marked off into \(\frac{1}{5}\)-foot-long sections for a game. So the number of sections are \(\frac{1}{5}\) ÷ 12 which is 2.4.

Question 2.
A 4-pound package of peanuts is divided into \(\frac{1}{4}\)-pound packages. How many \(\frac{1}{4}\)-pound packages are there?
Answer:

Set C
pages 401-404, 405-408

Find \(\frac{1}{2}\) ÷ 4.
Use a number line. Partition \(\frac{1}{2}\) into 4 equal parts.

Remember that you can use objects or a number line to help you divide.

Question 1.
\(\frac{1}{3}\) ÷ 2
Answer:

Question 2.
\(\frac{1}{7}\) ÷ 7
Answer:

Question 3.
\(\frac{1}{2}\) ÷ 8
Answer:

Question 4.
\(\frac{1}{8}\) ÷ 2
Answer:

Question 5.
7 ÷ \(\frac{1}{2}\)
Answer:

Question 6.
25 ÷ \(\frac{1}{6}\)
Answer:

Set D
pages 409-412

Helen has $97 in quarters and half dollars combined. She has $13 in quarters. How many half dollars does she have? How much does Helen have in half dollars?

$97 – $13 = $84
How many \(\frac{1}{2}\) dollars are in $84?

Helen has 168 half dollars.

Remember to read the problem carefully and make sure that you answer the right question and that your answer makes sense.

Question 1.
Ana participated in a charity walk. She raised $0.25 for each \(\frac{1}{2}\) mile that she walked. The first day, Āna walked 11 miles. The second day, she walked 14 miles. How much money did Ana raise?
Answer:

Question 2.
Mr. Holms used \(\frac{4}{5}\) of a carton of orange juice. He used equal amounts of the leftover juice for 2 servings. What fraction of the whole carton of juice did he use for each serving?
Answer:

Set E
pages 413-416

Think about these questions to help you use repeated reasoning when solving division problems.

Thinking Habits
• Are any calculations repeated?
• Can I generalize from examples?
• What shortcuts do I notice?

Remember that repeated reasoning can help you find a general method for solving problems that are the same type. Teresa has two 6-foot pieces of ribbon. One piece she cuts into \(\frac{1}{4}\)-foot pieces. The other piece she cuts into \(\frac{1}{2}\)-foot pieces.

Question 1.
How many \(\frac{1}{4}\)-foot pieces can she cut from one piece of ribbon? Explain.
Answer:

Question 2.
How many \(\frac{1}{2}\)-foot pieces can be cut from the 6-foot ribbon? Repeat the method you used in Exercise 1 to solve this problem.
Answer:

Topic 9 Assessment Practice

Question 1.
If the diameter of a tree trunk is growing \(\frac{1}{4}\) inch each year, how many years will it take for the diameter to grow 8 inches? Explain how you found your answer.
Answer:

Question 2.
Select all the equations that the number 4 will make true.
1 ÷ 4=?
5 ÷ ? = \(\frac{4}{5}\)
? ÷ = \(\frac{1}{2}\)
4 ÷ ? = 16
Answer:

Question 3.
Mrs. Webster wants to divide 6 pints of water into \(\frac{1}{3}\)-pint servings. How many servings are possible? Explain how you found your answer.
Answer:

Question 4.
How many \(\frac{1}{8}\)s are in 25? What multiplication equation can you use to check your answer?
Answer:

Question 5.
Raven is making pillows. She needs \(\frac{1}{5}\) yard of fabric for each pillow. If she has 6 yards of fabric, how many pillows can she make? Use the number line. Choose the equation that represents the problem.

Answer:

Question 6.
A farmer owns 24 acres of land. He plans to use 6 acres for an entrance into the farm and partition the remaining land into \(\frac{1}{3}\)-acre lots. How many \(\frac{1}{3}\)-acre lots will he have?
A. 6 lots
B. 54 lots
C. 18 lots
D. 72 lots
Answer:

Question 7.
One half of a cantaloupe was shared equally among 3 people. What fraction of the whole cantaloupe did each person get? Explain how you found your answer.
Answer:

Question 8.
Cecil and three friends ran a 15-mile relay race. Each friend ran an equal distance. Use an equation to find the distance each friend ran.
Answer:

Question 9.
Match each expression to its quotient.

Answer:

Question 10.
A. Select all the expressions that are equal to \(\frac{1}{6}\).
6 ÷ 1
1 ÷ 6
3 ÷ 18
\(\frac{1}{3}\) ÷ 2
2 ÷ \(\frac{1}{3}\)
B. How can you check your answer?
Answer:

Question 11.
Josie has a rug with an area of 18 square feet that is 6 feet long and 3 feet wide. She will put the rug on a floor that is covered in \(\frac{1}{3}\)-square-foot tiles. How many tiles will the rug cover? What equation can you use to check your answer?
Answer:

Question 12.
Ellen says that 1\(\frac{2}{5}\) equals 5 ÷ 7. Is she correct? Explain.
Answer:

Question 13.
Corey has a piece of fabric that is \(\frac{1}{4}\) yard long. He cuts the length of the fabric into 2 equal pieces. Write an expression for the length, in yards, of each piece of fabric and solve.
Answer:

Question 14.
Look at the equations below.

A. Write numbers in the boxes above to make each equation true.
B. What generalization can you make about the equations? Explain.
Answer:

Topic 9 Performance Task

Making Cloth Dolls
Julie and Erin are making cloth dolls for the craft fair. The figure below shows some of the materials they need for each doll.

Question 1.
The Julie and Erin’s Supplies table shows the amounts they have of some of the materials they need.
Part A
If Julie and Erin use the brown yarn they have to make 4 dolls, how much yarn can they use for each doll? Show your work.

Part B
How many dolls can Julie and Erin make with the amount of black velvet they have? Complete the model to represent the problem.


Part C
How many dolls can Julie and Erin make with the amount of white cloth they have? Write an equation to represent the problem. Use multiplication to check your answer.
Part D
The ribbon used for each doll is divided into 3 equal pieces. What is the length in yards of each piece? Complete the number line to solve.

Answer:

Question 2.
Julie and Erin have 6\(\frac{1}{3}\) yards of red checked cloth. After making dresses for 4 dolls, they use the remaining cloth to make bows for the dolls’ hair. They need 8 bows for 4 dolls.
Part A
How much cloth do Julie and Erin have for each bow? Explain.
Part B
Julie wrote the equations shown. What is the pattern in her equations? Explain how to use the pattern to find the quotient you found in Part A.

Answer:

Go through the enVision Math Common Core Grade 1 Answer Key Topic 8 Understand Place Value regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 8 Understand Place Value

enVision STEM Project: Daylight Throughout the Year
Find Out Talk to friends and relatives about why there is more daylight in summer than in winter.
Ask them to help you find information about the changes in daylight each season.

Journal: Make a Book Draw pictures of the tilting globe and the sun at different times of the year. In your book, also:

• Add labels to show summer and winter.
• Write a sentence to describe the pattern of the seasons in your own words.

Review What You Know

Vocabulary

Question 1.
Circle the tens digit.

Answer:

Explanation:
Given 2 digit number 48.
Two digit number have tens place and ones place.
4 is in tens place and 8 in ones place
4 is circled as tens digit.

Question 2.
Circle the ones digit.

Answer:

Explanation:
Given 2 digit number 76.
Two digit number have tens place and ones place.
7 is in tens place and 6 in ones place
6 is circled as ones digit.

Question 3.
Use the ten-frames to find the sum.
7 + 9 = ___

Answer:

Counting to 120

Question 4.
Write the number that comes next when counting forward by Is. Use a hundred chart to help you.
110, 111, 112, ____
Answer:
110, 111, 112, 113
Explanation:
Given
A sequence of  3 digit numbers
110, 111, 112, ____ and asked to find the 4th digit by counting forward by Is
3 digit number have hundreds place  tens place and ones place
Since counting forward by 1s
we add the 1 to the ones place of 3rd digit to get the 4th digit keeping the tens place and hundreds place constant.
112 + 001 = 113.
Missing number is 113.

Question 5.
Maria counts by 10s. She starts at 30. Write the missing numbers.
30, ___, ___
60, ___
Answer:
30, _40__, _50__
60, _70__
Explanation:
Maria counts by 10s
Given
30, ___, ___ and 2 number missing to find the missing number we add 1 to the tens place keeping ones place constant.
given
30 = 3 is tens digit and 0 ones digit.
Adding tens digit with 1
3 + 1 = 4, 4 + 1 = 5.
30, _40__,_50__
60 = 6 tens digit and 0 ones digit
60 + 10 = 70
60, _70__

Hundred Chart

Question 6.
Write the missing numbers in this part of the hundred chart.

Answer:

pick a Project

PROJECT 8A
What do you put on your hot dog?
Project: Act Out Serving Up Hot Dogs

Answer:
Topping on the Hot dog
1. Hot dog bun.
2. Veg- dog or Non- Veg dog
3. Onion
4. Jalapenos
5. Lattice
6. Herbs
7. Sauces.

PROJECT 8B
What is your favorite color?
Project: Make a Color Poster

PROJECT 8C
Can you eat a tiger?
Project: Play a Cracker Stack Game

PROJECT 8D
Which sea creatures have 10 legs?
Project: Make a Finger Painting

Answer:

Lesson 8.1 Make Numbers 11 to 19

Solve & Share

Use counters and ten-frames to show 12, then 15, and then 18. Draw your counters in the ten-frames below. Tell what is the same and different about each number you show.

Visual Learning Bridge

Answer:

Convince Me!
How could you use ten-frames to show 13 counters?
Answer:

Explanation:
one group of 10 ones = 1 ten
13 is made up of one group of 10 ones and 3 ones
13 is 1 ten and  3 ones.

Guided Practice

Use counters to make each number. Then write each number as I ten and some ones.

Question 1.
twelve
is 1 ten and ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
12 is made up of one group of 10 ones and 2 ones
12 = 10 + 2
12 is 1 ten and  2 ones.

Question 2.
fourteen
is 1 ten and ___ ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
14 is made up of one group of 10 ones and 4 ones
14 = 10 + 4
14 is 1 ten and  4 ones.

Question 3.
fifteen
is 1 ten and __ ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
15 is made up of one group of 10 ones and 5 ones
15 = 10 + 5
15 is 1 ten and  5 ones.

Independent Practice

Use counters to make each number. Then write the word or number.

Question 4.
sixteen
is ___ ten and 6 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
16 is made up of one group of 10 ones and 6 ones
16 = 10 + 6
16 is 1 ten and  6 ones.

Question 5.
____
is 1 ten and 8 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
18 is made up of one group of 10 ones and 8 ones
18 = 10 + 8
18 is 1 ten and  8 ones.

Question 6.
thirteen
is 1 ten and __ ones.
Answer:

is 1 ten and __ ones.
Explanation:
one group of 10 ones = 1 ten
13 is made up of one group of 10 ones and 3 ones
13 = 10 + 3
13 is 1 ten and 3 ones.

Question 7.
eleven
is ___ ten and 1 one.
Answer:

Explanation:
one group of 10 ones = 1 ten
11 is made up of one group of 10 ones and 1 ones
11 = 10 + 1
11 is 1 ten and  1 ones.

Question 8.
_____
is 1 and 7 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
17 is made up of one group of 10 ones and  7 ones
17 = 10 + 7
17 is 1 ten and  7 ones.

Question 9.
nineteen
is 1 ten and 9 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
19 is made up of one group of 10 ones and 9 ones
19 = 10 + 9
19 is 1 ten and  9 ones.

Question 10.
Vocabulary Circle the tens and ones that match the words shown.

Answer:

Explanation:
one group of 10 ones = 1 ten
12 is made up of one group of 10 ones and 2 ones
12 = 10 + 2
12 is 1 ten and 2  ones.
Explanation:
one group of 10 ones = 1 ten
15 is made up of one group of 10 ones and 5 ones
15 = 10 + 5
15 is 1 ten and  5 ones.

Problem Solving

Solve each problem below.

Question 11.
Use Tools Jill has 14 buttons and 2 boxes. She puts 10 buttons in one box. How many buttons does Jill put in the other box? Draw counters to solve. Write the numbers.
___ buttons
__ is ___ ten and __ ones.

Answer:

Question 12.
Higher Order Thinking Choose a number between 11 and 14. Draw a picture to show how to make the number with ten-frames. Write the number and the number word.

Answer:

Question 13.
Assessment Practice Match the groups or numbers on the left with the number word on the right.

Answer:

Lesson 8.2 Numbers Made with Tens

Solve & Share

How are 2 tens and 20 ones alike and different?
Use cubes to show your answer. Then draw your cubes.

Visual Learning Bridge

Answer:

Convince Me!
How many tens are in 90? How do you know?
Answer:

Explanation:
10 cubes make 1 ten.
To count the number of tens in 90
we count by 10’s as  10,20,30,40,50,60,70,80,90.
we count by tens as 1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens.
There are 90 cubes
90 is 9 tens and 0 ones.

Guided Practice

Use cubes. Count by 10s. Write the numbers.

Question 1

Answer:

Explanation:
10 cubes make 1 ten.
Here are 3 ten.
Count by 10’s to
10, 20, 30.
There are 30 cubes in all.
3 tens and 0 ones is 30.

Question 2.

___ tens and ___ ones is ____.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 5 ten.
Count by 10’s to
10, 20, 30, 40, 50.
There are 50 cubes in all.
5 tens and 0 ones is 50.

Independent Practice

Use cubes. Count by 10s. Draw the cubes. Write the numbers.

Question 3.

6 tens and 0 ones is ___.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 6 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60.
There are 60 cubes in all.
6 × 10 = 60.
6 tens and 0 ones is Sixty.

Question 4.

___ tens and ___ ones is 90.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 9 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70, 80, 90.
There are 90 cubes in all.
9 × 10 = 90.
9 tens and 0 ones is Ninety.

Question 5.

8 tens and 0 ones is ___.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 8 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70, 80.
There are 80 cubes in all.
8 × 10 = 80.
8 tens and 0 ones is Eighty.

Question 6.

__ tens and ___ ones is 70.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 7 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70.
There are 70 cubes in all.
7 × 10 = 70.
7 tens and 0 ones is Seventy

Question 7.
Number Sense Joey has 2 tens. He wants to trade the tens for ones. How many ones should Joey get?
____ ones

Answer:
Number of tens Joey has = 2 tens
Joey wants to trade tens for ones.
1 ten = 10 ones
So, 2 tens  = 2 × 10 = 20 ones.
Joel gets 20 ones foe 2 tens.

Problem Solving

Solve the problems below.

Question 8.
Reasoning There are 2 buses. 10 people are in each bus. How many people ride in the buses? Count by 10s. Draw a picture to solve.

Answer:

Question 9.
Reasoning George has 3 boxes of pens. 10 pens are in each box. How many pens does George have?
___ pens
Answer:

Question 10.
Higher Order Thinking Brian has a book. He reads 10 pages every day. Show how many pages Brian reads in 5 days. Use pictures, numbers, or words.

Answer:

Question 11.
Assessment Practice
Beth has 4 jars. Each jar has 10 bouncy balls in it. How many bouncy balls does Beth have in all?


Answer:
Number of Jars Beth has = 4
Number of bouncy balls in each jar = 10
Total number of bouncy balls in the 4  jars = 10 + 10 + 10 + 10 = 40
4 × 10 = 40.
C)40 is the answer.
There are 40 bouncy balls in the jars.

Lesson 8.3 Count with Groups of Tens and Ones

Solve & Share

Tara has 34 cubes. How many groups of 10 can she make with the cubes? Show your work in the space below.

Answer:

Visual Learning Bridge

Convince Me!
Why does 37 have 3 groups of 10 and not 4 groups of 10?
Answer:
37 = 10 + 10 + 10 + 7
= 3 tens and 7 ones
= 3 groups of 10 and 7 ones.
4 groups of 10 = 10 + 10 + 10 + 10  = 40
So, 37 has 3 groups of 10 and 7 ones.

Guided Practice
Circle groups of 10. Write the numbers.

Question 1.

Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 5 sets of 5 cubes and 2 cubes
out of 5 set of 5 cubes 4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 5 + 2 = 7 ones.
2 groups of 10’s and 7 ones = 27 .

Question 2.

Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 7 sets of 5 cubes and 9 cubes
out of 7 set of 5 cubes 6 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
3 group of  10’s are formed.
The left over cubes are ones  = 5 + 4 = 9 ones.
3 groups of 10’s and 9 ones = 39.

Independent Practice

Circle the groups of 10. Write the numbers.

Question 3.

___ groups of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 8 sets of 5 cubes and 3 cubes
8 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
4 group of  10’s are formed.
The left over cubes are ones  = 3 = 3 ones.
4 groups of 10’s and 3 ones = 43.

Question 4.

___ groups of 10 and __ ones is ____.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 7 sets of 5 cubes
out of 7 set of 5 cubes 6 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
3 group of  10’s are formed.
The left over cubes are ones  = 5 = 5 ones.
3 groups of 10’s and 5 ones = 35.

Question 5.

___ group of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 3 sets of 5 cubes and 1 cubes
out of 3 set of 5 cubes 2 sets of 5 cubes make a
5 + 5 = 10
1 group of  10’s are formed.
The left over cubes are ones  = 5 + 1 = 6 ones.
1 groups of 10’s and 6 ones = 16.

Question 6.

___ groups of 10 and ___ ones is ___.

Write the number of groups of 10 and the number of ones. Then write the total.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 9 sets of 5 cubes and 3 cubes
out of 9 set of 5 cubes 8 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
4 group of  10’s are formed.
The left over cubes are ones  = 5 +3 = 8 ones.
4 groups of 10’s and 8 ones = 48.

Question 7.

___ groups of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 5 sets of 5 cubes
out of 5 set of 5 cubes 4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 5  = 5 ones.
2 groups of 10’s and 5 ones = 25.

Question 8.

__ groups of 10 and ___ ones is __.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 4 sets of 5 cubes
4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 2  = 2 ones.
2 groups of 10’s and 2 ones = 22.

Problem Solving

Draw a picture and write the numbers to solve each Solving problem below.

Question 9.
Model A monkey has 32 bananas. 10 bananas are in each bunch.

How many bunches are there? ____
How many bananas are left over? ___
Answer:

Question 10.
Model The dogs have 21 bones. 10 bones are in each bowl.

How many bowls are there? ____
How many bones are left over? ____
Answer:

Question 11.
Higher Order Thinking
Amil writes a number. His number has 5 groups of 10. His number has less than 9 ones. What number could Amil have written? ____
Answer:
Number of groups of 10’s Amil number has = 5
10 + 10 + 10 + 10 + 10 = 50
Number of ones Amil number has = less than 9
less than 9 may be = 1,2, 3, 4, 5, 6, 7, 8.
The number may be
5 groups of 10’s and 1 ones = 51
5 groups of 10’s and 2 ones = 52
5 groups of 10’s and 3 ones = 53
5 groups of 10’s and 4 ones = 54
5 groups of 10’s and 5 ones = 55
5 groups of 10’s and 6 ones = 56
5 groups of 10’s and 7 ones = 57
5 groups of 10’s and 8 ones = 58.
Amil number may be 51, 52, 53, 54, 55, 56, 57, 58.

Question 12.
Assessment Practice
A store has 5 bunches of grapes and 3 left over. Each bunch has 10 grapes. How many grapes are there in all? Explain.
Answer:
Number of bunches of grapes in the store = 5
Number of grapes in each bunch = 10 grapes
Number of left over = 3
Number of grapes in 5 bunches = 10 + 10 + 10 + 10 + 10 = 50 grapes.
Total number of grapes = 50 grapes and 3 left over is 53 grapes.

Lesson 8.4 Tens and Ones

Solve & Share

Estimate how many cubes are in your bag. Then empty the bag in the space below. Without counting each cube, estimate how many cubes there are. Write each estimate.

Now count the cubes and write the total number of cubes.

Estimate 1: ___ cubes
Estimate 2: ___ cubes
Actual amount: ___ cubes
Answer:

Visual Learning Bridge

Convince Me!
How are these numbers alike? How are they different?

Answer:
46 and 64 are two digit numbers
Two digit number have tens and ones.
Both the number have tens and ones digits only.
They are different as the place values of the number are different.
46 has 4 in tens place and 6 in ones place
64 has 6 in tens place and 4 in ones place .

Guided Practice
Use cubes. Count the tens and ones. Then write the numbers.

Question 1.

Answer:

Explanation:
Given
3 sets of 10 cubes in tens place
5 + 3 = 8 cubes in ones place
30 + 8 = 38.
3 tens and 8 ones  is 38.
3 in  38 is the tens digit
8 in 38 is the ones digit.

Question 2.

Answer:

Explanation:
Given
4 sets of 10 cubes in tens place
1 cubes in ones place
40 + 1 = 41
4 tens and 1 ones  is 41.
4 in  41 is the tens digit
1 in 41 is the ones digit.

Independent Practice

Use cubes. Count the tens and ones. Then write the numbers.

Question 3.

___ Ten and ___ ones is ___.
Answer:

Explanation:
Given
1 sets of 10 cubes in tens place
5 + 4 = 9 cubes in ones place
10 + 9 = 19
1 ten and 9 ones  is 19.
1 in  19 is the tens digit
9 in 19 is the ones digit.

Question 4.

___ tens and ___ ones is ___.
Answer:

Explanation:
Given
2 sets of 10 cubes in tens place
3 cubes in ones place
20 + 3 = 23
2 tens and 3 ones  is 23.
2 in  23 is the tens digit
3 in 23 is the ones digit.

Question 5.

___ tens and ___ ones is ___.
Answer:

Explanation:
Given
4 sets of 10 cubes in tens place
5 + 3 = 8 cubes in ones place
40 + 8 = 48
4 tens and 8 ones  is 48.
4 in  48 is the tens digit
8 in 48 is the ones digit.

Solve the problem below any way you choose.

Question 6.
Number Sense Bill writes a number. It has the same number of tens and ones. What could Bill’s number be?
Answer:
The number Bill wrote has same number of tens and ones.
Bills number may be any of these numbers.
1 ten and 1 one is 11
2 tens and 2 ones is 22
3 tens and 3 ones is 33
4 tens and 4 ones is 44
5 tens and 5 ones is 55
6 tens and  6 ones is 66
7 tens and  7 ones is 77
8 tens and 8 ones is 88
9 tens and 9 ones is 99.
Bill number may be 11, 22, 33, 44, 55, 66, 77, 88, 99.

Problem Solving

Solve each problem below.

Answer:

Question 7.
Reasoning Luz has juice boxes at her party. There are 3 packages of 10 and 7 extra juice boxes.
How many juice boxes are there in all?
Write the number of tens and ones. Then write the total number of juice boxes.

Answer:

Question 8.
Higher Order Thinking Draw a picture to show a number greater than 25 and less than 75. Then write the number.

Answer:

Question 9.
Assessment Practice Kai brought 2 packages of 10 juice boxes and 5 extra juice boxes. How many juice boxes did Kai bring? Write the number of tens and ones. Then write the total number of juice boxes.

Answer:

Lesson 8.5 Continue with Tens and Ones

Solve & Share

Laylani has 28 buttons. Draw her buttons so that a friend can see that there are 28 buttons without counting them one by one.

Answer:

Visual Learning Bridge

Convince Me!
When you draw to model a number, which digit tells you how many lines to draw? Which digit tells you how many dots to draw?
Answer:
When we draw a model a number
Tens place digit tells us to draw the number of lines.
Ones place digit tells us to draw the number of dots.

Guided Practice

Write the numbers and draw a model to show each number. Count by tens and ones to check.

Question 1.

Answer:

Explanation:
Given number 17
17 is 1 ten and 7 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
17 is represented with 1 line and 7 dots.

Question 2.
29 is ___ tens and ___ ones.

Answer:

Explanation:
Given number 29
29 is 2 ten and 9 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
29 is represented with 2 line and 9 dots.

Independent Practice

Write the numbers and draw a model to show each number. Count by tens and ones to check.

Question 3.
There are ___ tens and ___ ones in 43.
Answer:

There are 4 tens and 3 ones.
Explanation:
Given number 43
43 is 4 ten and 3 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
43 is represented with 4 line and 3 dots.

Question 4.
There are ___ tens and ___ ones in 86.
Answer:

Explanation:
Given number 86
86 is 8 ten and 6 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
86 is represented with 8 line and 6 dots.

Question 5.
There are ___ ten and __ ones in 15.
Answer:

Explanation:
Given number 15
15 is 1 ten and 5 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
15 is represented with 1 line and 5 dots.

Question 6.
There are ___ tens and ___ ones in 37.
Answer:

Explanation:
Given number 37
37 is 3 ten and 7 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
37 is represented with 3 line and 7 dots.

Question 7.
There are ___ tens and ___ ones in 62.
Answer:

Explanation:
Given number 62
62 is 6 ten and 2 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
62 is represented with 6 line and 2 dots.

Question 8.
There are ___ tens and __ ones in 24.
Answer:

Explanation:
Given number 24
24 is 2 ten and 4 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
24 is represented with 2 line and 4 dots.

Problem Solving

Solve the problems below.

Question 9.
Model Kevin draws the model below to show a number. What number is Kevin showing?

Answer:

Question 10.
enVision® STEM Gina is collecting
data on the number of hours of daylight in the fall and winter. She records data for 68 days. Draw a model to show 68.
Answer:

Question 11.
Higher Order Thinking Peyton starts drawing a model for the number 48, but she is interrupted. Help her finish her model.

Answer:

Question 12.
Assessment Practice Which number is represented here?

Answer:
Given
2 lines and 3 dots
Line represent Tens
Dot represents Ones.
2 lines = 10 + 10 = 20
3 dots  = 3
The number which is represented is 20 + 3 = 23.
Answer is C)23.

Lesson 8.6 Different Names for the Same Number

Solve & Share

Use cubes. Show two different ways to make 28. Draw each way in the spaces below.

Visual Learning Bridge

Convince Me!
How could you break apart 24 using only I ten? Explain.
Answer:
24 is 2 tens and 4 left over
24 is 2 tens and 4 ones
breaking 24 using only 1 ten
Breaking other  ten to make 10 more ones
24 is 1 ten and 14 ones.

Guided Practice

Count the tens and ones. Write different Practice ways to show the number.

Question 1.
Write two ways to break apart 34.

Answer:

Explanation:
Given a model of number 34 in two different ways
34 is represented as
34 is 3 tens and 4 ones in 1st case.
In 2nd case
out of 3 tens. 1 ten is broken down to make 10 more ones.
34 is 2 tens and 14 ones.

Independent Practice

Count the tens and ones. Write different ways to show each number.

Question 2.
Write two ways to break apart 21.

21 is ___ ten and __ one.
Answer:

Explanation:
Given to break apart 21 in two way
Case 1.
21 is represented as
21 is 2 tens and 1 ones
21 = 20 + 1
In 2nd case
out of 2 tens. 1 ten is broken down to make 10 more ones.
21 is 1 tens and 11 ones.
21 = 10 + 11.

Question 3.
Draw models and write two ways to break apart 59.

59 is ___ tens and ___ ones.

59 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 59 in two way
Case 1.
59 is represented as
59 is 5 tens and 9 ones
59 = 50 + 9
In 2nd case
out of 5 tens. 1 ten is broken down to make 10 more ones.
59 is 4 tens and 19 ones.
59 = 40 + 19 .

Write each number in two different ways. Use cubes to help if needed.

Question 4.
Show two ways to break apart 44.
44 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 44 in two way
Case 1.
44 is represented as
44 is 4 tens and 4 ones
44 = 40 + 4
In 2nd case
out of 4 tens. 1 ten is broken down to make 10 more ones.
44 is 3 tens and 14 ones.
44 = 30 + 14.

Question 5.
Show two ways to break apart 25.
25 is __ tens and __ones.
25 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 25 in two way
Case 1.
25 is represented as
25 is 2 tens and 5 ones
25 = 20 + 5
In 2nd case
out of 2 tens. 1 ten is broken down to make 10 more ones.
25 is 1 tens and 15 ones.
25 = 10 + 15.

Problem Solving

Solve the problems below.

Question 6.
Explain Nate says 5 tens and 3 ones shows the same number as 3 tens and 13 ones. Do you agree? Explain.
Answer:

5 tens and 3 ones shows
50 + 3 = 53
3 tens and 13 ones shows
30 + 13 = 43
No, they both don’t show the same number.
To show the same number as
5 tens and 3 ones = 50 + 3 = 53
It should be 4 tens and 13 ones = 40 + 13 = 53 or
as given 3 tens and 13 ones add 10 more ones
3 tens and 23 ones = 30 + 23 = 53.

Question 7.
Number Sense Nancy shows a number as 4 tens and 16 ones. What number does she show?
Answer:
Nancy’s number shows 4 tens and 16 ones
4 tens and 16 ones = 40 + 16 = 56.
Nancy’s number is 56

Question 8.
What number is shown on the mat?

Answer:

Question 9.
Jeff picks 36 apples. He puts some of the apples in bags. Each bag holds 10 apples. Show two ways Jeff can put the apples in bags.

___ bags and __ apples left over
__ bags and __ apples left over
Answer:

Question 10.
Higher Order Thinking Meg breaks apart the number 80 three ways. What could be those ways?
___ tens and ___ ones
___ tens and ___ ones
___ tens and ___ ones
Answer:
Three ways Meg breaks apart the number 80 are
_80__ tens and _0__ ones
80 + 0 = 80
_70__ tens and _10__ ones
70 + 10 = 80
_60__ tens and _20__ ones
60 + 20 = 80.

Question 11.
Assessment Practice which is a way to break apart 38? Choose two that apply.
2 tens and 18 ones
2 tens and 8 ones
1 ten and 28 ones
8 tens and 3 ones
Answer:
The ways to break 38 are
3 tens and 8 ones
2 tens and 18 ones
1 ten and 28 ones
0 tens and 38 ones
In the above option given
2 tens and 18 ones is 38
1 ten and 28 ones is 38 make 38 other 2 options make
2 tens and 8 ones is 28
8 tens and 3 ones is 83.

Lesson 8.7 Look For and Use Structure

Solve & Share

Barry showed the number 42 with cubes. What are some of the ways he could have shown 42? Write the tens and ones to show the ways. Describe any patterns you see in the table.

Thinking Habits

Is there a pattern to the answers? How does the pattern help me? What do the answers have in common?

Visual Learning Bridge

Convince Me!
How can you help you. Talk to a partner about patterns use patterns to show all the ways to break apart a number into tens and ones?

Guided Practice

Make a list to solve. You can use cubes to help you. Talk to partner about patterns you see in your list.

Question 1.
Carly lists all the ways to 25 as tens and ones. What ways does she list?

Answer:

Explanation:
Here different way of 25 are represented
as you look at the ways you can notice a pattern
Ten decrease by 1 and Ones increase by 10.

Question 2.
Andy wants to show 31 as tens and ones. What are all the ways?

Answer:

Explanation:
Here different way of 31 are represented
as you look at the ways you can notice a pattern
Ten decrease by 1 and Ones increase by 10.

Independent Practice

Question 3.
Alma lists all the ways to show 46 as tens and ones. What ways does she list?

Answer:

Question 4.
Seth wants to show 33 as tens and ones. What are all the ways?

Answer:

Question 5.
Higher Order Thinking Dana says there are 4 ways to show 25 using tens and ones. Is she right? How do you know?

Answer:

Problem Solving

Performance Task

Bake Sale Rose brings 48 muffins to a bake sale. She only uses trays for groups of 10 muffins. Each plate holds only I muffin. How many trays and plates could Rose use to display the muffins?

Question 6.
Look For Patterns Fill in the table to show how many trays and plates Rose could use to display the muffins. Describe a pattern you see in the table.
Answer:

Question 7.
Reasoning Is there any way Rose can display her muffins using only trays? Explain how you know.
Answer:
No, Rose can not display her muffins using only trays.
Number of muffins Rose brought = 48
As she used trays for group of 10 muffins.
48 is 4 tens and 8 ones.
If she only uses trays then their will be 8 muffins left over. As she can only display 40 muffins in trays.

Topic 8 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 I and Partner 2 each point to a black number at the same time. Both partners add those numbers.

If the answer is on your color, you get a tally mark. Work until one partner gets twelve tally marks.

TOPIC 8 Vocabulary Review

Understand Vocabulary

Question 1.
Write the number word that is one more than fourteen.
Answer:
one more than fourteen is fifteen
1 + 14 = 15.

Question 2.
Write the number word that is one fewer than eighteen.
Answer:
Seventeen is one fewer than eighteen.
18 – 1 = 17.

Question 3.
Circle the cubes that make 2 tens.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 2 tens
2 sets of 5 cubes make 1 ten
So, to make 2 tens we need 4 sets of 5 cubes.
4 sets of 5 cubes make 2 tens.

Question 4.
Circle the cubes that make 1 ten and 5 ones.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 1 tens  and 5 ones
2 sets of 5 cubes make 1 ten
So, to make 1 tens we need 2 sets of 5 cubes.
2 sets of 5 cubes make 1 tens.
1 set of 5 cubes make 5 ones.

Question 5.
Circle the cubes that make 3 tens and 3 ones.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 3 tens  and 3 ones
2 sets of 5 cubes make 1 ten
So, to make 3 tens we need 6 sets of 5 cubes.
6 sets of 5 cubes make 3 tens.
3 cubes make 3 ones.

Use Vocabulary in Writing

Question 6.
Ben shows 33 as 3 tens and 3 ones. Show 33 a different way. Use tens and ones. Explain using a word from the Word List.
Answer:

33 is 2 tens and 13 ones
33 is 2 groups of 10 and 13 ones left overs.

TOPIC 8 Reteaching

Set A

You can group objects by 10 to count.

Answer:

Circle groups of 10. Write the numbers.

Question 1.

___ is ___ groups of 10 and __ ones left over.
Answer:

Explanation:
Given a set of 5 cubes.
There are 5 sets of 5 cubes.
To make groups of 10
2 sets of 5 cubes make 10
So, to make 10 we join 2 sets 5 cubes.
We get 2 groups of 10 and 5 more cubes left over.
2 tens and 5 ones is 25.

Question 2.

___ is ___ groups of 10 and __ ones left over.
Answer:

Set B

You can show a two-digit number as tens and ones.

Count the tens and ones. Then write the number.
Answer:

Explanation:
Given a two digit number.
Two digit number has Tens and Ones.
Here given 4 tens cubes in tens place and 3 one cubes is the table.
4 tens = 40
3 ones = 3
4 tens and 3 one is 43.

Question 3.

Answer:

Explanation:
Given a two digit number.
Two digit number has Tens and Ones.
Here given 5 tens cubes in tens place and 4 one cubes is the table.
5 tens = 50
4 ones = 4
5 tens and 4 one is 54.

Set C

You can draw a model to show tens and ones.

Answer:

Draw a model to show tens and ones.

Question 4.
There are __ tens and __ ones in 78.
Answer:

Explanation:
Given number 78
78 is 7 ten and 8 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
78 is represented with 7 line and 8 dots.

Set D

Thinking Habits
Look For and Use Structure

Is there a pattern to the answers? How does the pattern help me? What do the answers have in common?

Use patterns and make a list to solve.

Question 5.
Lupita wants to show all the ways to break apart 54 as tens and ones. What are all the ways?

Answer:

Topic 8 Assessment Practice

Question 1.
A. Which of these is a way to show 16?
A. 1 ten and 11 ones
B. 1 ten and 6 ones
C. 16 tens and 0 ones
D. 9 tens and 5 ones
Answer:

A. 1 ten and 11 ones is 10 + 11 = 21
B. 1 ten and 6 ones is 10 + 6 = 16
C. 16 tens and 0 ones is 160 + 0 = 160
D. 9 tens and 5 ones is 90 + 5 = 95
way to show 16 is B.

B. Which equation shows why your answer for A is correct?
A. 10+ 11 = 21
B 10+ 6 = 16
C 16 + 2 = 18
D 9 +5 = 14
Answer:

way to show 16
16 is 1 ten and 6 ones
16 is 0 tens and 16 ones.
16 = 10 + 6
So, B 10 + 6 = 16 is correct.

Question 2.
A. Write a way to show 42.
__ groups of ten and __ ones.
Answer:

42 is 4 groups of 10 and 2 ones.

B. Write another way to show 42.
___ groups of ten and ___ ones
Answer:
42 is 3 groups of ten and 12 ones.

Question 3.

___ Tens and ___ Ones is ___.
Answer:

Question 4.
Write two ways to show 1 1.
Answer:

Ways to show 11
11 is 1 ten and 1 one
11 is 0 tens and 11 ones.
These are the ways to show 11.

Question 5.
A. What number does 5 groups of ten represent?
Answer:

5 groups of ten represents
10 + 10+ 10+10+10 = 50.
5 groups of 10 represents 50.
B. What is another way to write 5 groups of ten?
___ groups of ten and ___ ones
Answer:

Another way to represent 5 group of ten
5 group of ten  is 50
50 is 4 tens and 10 ones
4 groups of 10 and 10 ones is 50.

Question 6.
A. Which of these is another way to show 4 groups of ten and 9 ones?
A 3 tens and 19 ones
B 5 tens and 0 ones
C 3 tens and 9 ones
D 5 tens and 8 ones
Answer:
A 3 tens and 19 ones is 30 + 19 = 49
B 5 tens and 0 ones is 50 + 0 = 50
C 3 tens and 9 ones is 30 + 9 = 39
D 5 tens and 8 ones is  50 + 8 = 58
Way to show 4 groups of tens and 9 ones is
4 groups of tens and 9 ones = 40 + 9 = 49.
A. 3 tens and 19 ones. is another way to represent 4 groups of tens and 9 ones.

Question 7.
Nicole found 2 ways to make 41. Complete the list to show all of the ways. Then draw a model to show one of the ways.

Answer:

TOPIC 8 Performance Task

Snack Time

Manuel’s class has a snack every day.

Question 1.
On Monday, Manuel and Ryan share 19 crackers. 10 crackers are in one bag. How many crackers are in the other bag?
Explain your answer. Use pictures, numbers, or words. Draw counters to solve. Write the word and numbers.

Answer:

Explanation:
one group of 10 ones = 1 ten
19 is made up of one group of 10 ones and  9 ones
19 = 10 + 9
19 is 1 ten and  9 ones.

Question 2.
On Tuesday, Manuel’s class has 3 packages of juice boxes. There are 10 juice boxes in each package.
How many juice boxes does his class have?
___ juice boxes
Explain your answer. Use pictures, numbers, and words.
Answer:

Explanation:
Given
3 packages of juice boxes
1 package has 10 juice boxes
3 packages of 10 juice boxes each
10 + 10 + 10 = 30
3 tens and 0 ones  is 30.
3 in  30 is the tens digit
0 in 30 is the ones digit.

Question 3.
On Wednesday, Manuel’s class has 28 bottles of water.
Manuel starts drawing a model for the bottles. Use lines and dots to finish his drawing.

Explain what the drawing shows.
Answer:

Explanation:
Given number 28
28 is 2 ten and 8 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
Manuel drew 1 line and 3 dots
To complete the 28 number model
we need to draw more 1 line and 5 dots.
2 line – 1 line = 1 line
8 dots – 3 dots = 5 dots.
28 is represented with 2 line and 8 dots.

Question 4.
On Thursday, Manuel’s class had 34 packages of raisins. How many ways could the packages of raisins be grouped as tens and ones? Make a list to show all of the ways.

Answer:

Question 5.
On Friday, Manuel’s class had 26 bags of grapes. Manuel said that there are 2 ways to group the 26 bags as tens and ones. Do you agree? Circle Yes or No. Explain your answer. Use numbers, pictures, or words.
Answer:

Go through the enVision Math Common Core Grade 2 Answer Key Topic 15 Graphs and Data regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 15 Graphs and Data

Essential Question:
How can line plots, bar graphs, and picture graphs be used to show data and answer questions?

enVision STEM Project: Comparing Objects and Data
Find Out Work with a partner. Compare two backpacks. Which one holds more? Which one has more parts? Which one is easier to put on? Think of other ways to compare.
Journal: Make a Book Show what you learn in a book. In your book, also:

• Tell one good thing and one bad thing about each backpack.
• Draw line plots, picture graphs, and bar graphs to show and compare data.

Review What You Know

Vocabulary
Question 1.
Circle the number that has a 6 in the tens place.

Answer:
6 in the ten’s place is 160. so circle the 169.

Question 2.
Circle the tally marks that show 6.

Answer: tally marks that show 6 is is a doll.

Question 3.
Circle the difference.
22 – 9 = 13
34 + 61 = 95
Answer:
From the given 22 – 9 = 13 is the difference. So circle the difference.

Comparing Numbers
Question 4.
A zoo has 405 snakes. It has 375 monkeys. Compare the number of snakes to the number of monkeys.
Write > or <.
405 375
Answer:
Given that,
Zoo has 405 snakes and 357 monkeys.
405 > 375

Interpret Data

Question 5.

Who sold the most picnic tickets?
Answer:
Given that,
Picnic tickets sold by Jean = 16
Picnic tickets sold by Paulo = 18
Picnic tickets sold by Fatima = 12
Therefore Paulo sold the most picnic tickets.

Addition and Subtraction

Question 6.
Byron scores 24 points in a game. Ava scores 16 points in the same game. How many more points does Byron score than Ανα?
________ more points
Answer:
Given that,
Byron scores in a game = 24 points
Ava scores in a game = 16 points
Byron scores than Ava = 24 – 16 = 8
Byron scores 8 points more than Ava.

Pick a Project

PROJECT 15A
What types of flowers grow in your neighborhood?
Project: Graph Data About Flowers

PROJECT 15B
How many birds do you see every day?
Project: Create a Bird-Watching Poster

PROJECT 15C
Why should you plan a Florida vacation?
Project: Make a Florida Travel Brochure

3-ACT MATH PREVIEW

Before watching the video, think: How do you know what size clothing you should wear? Is there a way you can find out without trying the clothes on?

I can … model with math to solve a problem that involves making graphs to study data.

Lesson 15.1 Line Plots

Solve & Share
Find four objects that are each shorter than 9 inches. Measure the length of each object to the nearest inch. Record the measurements in the table. Then plot the data on the number line. Which object is longest? Which is shortest?
I can … measure the lengths of objects, then make a line plot to organize the data.

Visual Learning Bridge

Convince Me! Measure the length of your pencil to the nearest inch. Record your measurement on the line plot above. How does it change the data?

Guided Practice

Use a ruler to measure each object in inches. Record each length in the table. Then make a line plot. Show each length on the line plot.
Question 1.

Answer: 3 inches long.

Question 2.

Answer:

Independent Practice

Use a ruler to measure each object in inches. Record each + Practice length in the table. Show each length on the line plot.
Question 3.
The paintbrush is ________ inches long.

Answer: the paintbrush is 7 inches long.

Question 4.
The chalk is _______ inches long.

Answer: the chalk is 3 inches long.

Question 5.
The straw is ________ inches long.

Answer: the straw is 8 inches long.

Question 6.
The feather is ________ inches long.

Answer:
The feather is 6 inches long.

Question 7.

Answer:

Problem Solving

Solve each problem. Use the line plot.
Question 8.
Be Precise Sophia measured the lengths of her colored pencils and made a table. Use the data to make a line plot.

Answer:

Question 9.
What is the length of the shortest pencil? Explain.
Answer:
Blue pencil is the shortest length in pencils.

Question 10.
Higher Order Thinking What are the lengths of the two pencils have a total length of 16 inches? Explain.
Answer:
Given that,
The length of the green pencil = 7 inches
The length of the yellow pencil = 9 inches
Adding of green pencil and yellow pencil = 16 inches

Question 11.
Assessment Practice Measure the length of the purple pencil in inches. Write the length below. Record your measurement on the line plot above in Item 8.

_________ inches
Answer: the length of the purple pencil is 4 inches long.

Lesson 15.2 More Line Plots

Solve & Share
Measure the length of your shoe to the nearest inch. Then use your data and data from your class to make a line plot. Tell one thing you learn from the data.

I can … measure the lengths of objects, then make a line plot to organize the data.

Visual Learning Bridge

Convince Me! In the example above, how many students measured their height? Tell how you know.

Guided Practice

Use the table to make a line plot. Then use the line plot to answer each question.
Question 1.

Question 2.
What is the most common feather length? _______ xm
Answer:
6 cm

Question 3.
Why does the number line use the numbers 4 through 9?
Answer:

Independent Practice

Collect data and use the data to complete the line plot. Then use the line plot to solve the problems.

Question 4.
Measure the length of your pencil in centimeters. Collect pencil-length data from your classmates. Make a line plot with the data.
Title: __________

Label: ________
Answer: length of the pencil date from classmates is 4, 6, 7, 8.

Question 5.

What is the length of the longest pencil?
Answer: The length of the longest pencil is 8 inches.

Question 6.
What is the sum of the lengths of the shortest and longest pencils?
Answer:
Given that;
The length of the shortest pencil is 4 inches
length of the longest pencil is 8 inches
The sum of the longest and shortest pencil is 8 + 4 = 12.

Question 7.
What is the difference in lengths between the shortest and longest pencils?
Answer:
Given that;
The length of the shortest pencil is 4 inches.
The length of the longest pencil is 8
The difference between the shortest and longest pencil is 8 – 4 = 4.

Question 8.
What is the most common pencil length?
Answer: The most common pencil length is 6 inches.

Question 9.
Vocabulary Use these words to complete the sentences.
longest
line plot
order
A ________ can help you see the data in __________.
A line plot can show the lengths of the shortest and _________ objects.
Answer:
A line plot can help you see the data in order.
A line plot can show the lengths of the shortest and longest objects.

Problem Solving

Model Use the data in the table to complete the line plot. Then use the line plot to solve the problems.
Question 10.

Answer:

Question 11.
Higher Order Thinking Measure the length of one of your crayons in centimeters, 5 different times. Make a line plot of the data on a separate sheet of paper. Did you get the same measurement each time? Explain.
Answer:

Question 12.
Assessment Practice Measure the length of the blue crayon to the nearest centimeter. Write the length below.

_______________
Then record your measurement on the line plot above that you made in Item 10.
Answer:

Lesson 15.3 Bar Graphs

Solve & Share
The graph shows the number of birthdays in each season for a class. Use the graph to write the number of birthdays in the table. How many more birthdays are celebrated during spring, fall, and winter than during summer? Be ready to explain how you know.
I can … draw bar graphs and use them to solve problems.

Visual Learning Bridge

Convince Me! Which activity did the most students choose? Explain how you know.

Guided Practice

Use the table to complete the bar graph. Then use the bar graph to solve the problems.

Question 1.
How many students chose cat? ________
Answer:
4 students choose a cat.

Question 2.
How many students chose bird or dog? _______
Answer:
6 students choose a dog.
2 students choose a bird.

Independent Practice

Use the bar graph to solve the problems.

Question 3.
How many students write after school?
Answer:
8 students write after school.

Question 4.
How many fewer students draw than write after school?
________ fewer students
Answer:
Students draw after school = 3
Students write after school = 8
Fewer students draw than write after school = 8 – 3 = 5

Question 5.
Which activity do the fewest students do after school?
Answer:
The fewest students do after school is writing activity.

Question 6.
How many students read or draw after school?
Answer:
Students read after school = 5
Students write after school = 8
Students read and write after school = 13

Question 7.
Which activity do the most students do after school?
Answer:
Most students do school in play activities.

Question 8.
How many more students play than read after school?
__________ more students
Answer:
Students play activity after the school = 11
Students read activity after the school = 5
Students play than read after school = 11 – 5 = 6 students

Question 9.
Higher Order Thinking How would the graph be different if 2 students changed their after-school activity from play to read?
Answer:

Problem Solving

Solve the problems below.
Question 10.
Model Wanda goes to the farm. She buys 8 pears, 5 oranges, 2 apples, and 9 peaches.
Use this data to make a bar graph.

Answer:

Question 11.
Higher Order Thinking Look at the graph you made in Item 10. How would the graph change if Wanda returns 3 of the pears that she buys?
Answer:

Question 12.
Assessment Practice Look at the bar graph you made in Item 10. Which are correct? Choose all that apply.
☐ Wanda buys the same number of pears and peaches.
☐ Wanda buys 3 more oranges than apples.
☐ Wanda buys 24 pieces of fruit in all.
☐ Wanda buys 3 fewer oranges than pears.
Answer:

Lesson 15.4 Picture Graphs

Solve & Share
The picture graph shows the favorite subjects of a class. Draw a smiley face on the graph to show your favorite subject. Then interview two classmates and add their data. How many students responded to the survey? Which subject do most students like best? How many students like math or science best?
I can … draw picture graphs and use them to solve problems.

Visual Learning Bridge

Convince Me! How are the tally chart and the picture graph for the favorite ball games of Ms. Green’s class alike?

Guided Practice

Use the tally chart to complete the picture graph. Then use the picture graph to solve the problems.

Question 1.
How many students like blue or red best? _______
Answer:
11

Question 2.
Which color is the favorite of most students? ________
Answer:
The blue color is the favorite of most students.

Independent Practice

Use the tally chart to complete the picture graph. Then use the picture graph to solve the problems.
Question 3.

Answer:

Question 4.
How many students like fall best?
Answer:
6 students like fall best.

Question 5.
Which season do exactly 4 students like best?
Answer:
Spring season do exactly 4 students like best.

Question 6.
Which season do the fewest students like?
Answer:
Winter season do the fewest students like.

Question 7.
How many fewer students voted for winter than for summer?
Answer:
Students voted for winter is 2
Students voted for summer is 10
Fewer students voted for winter than summer is 10 – 2 = 8.

Question 8.
How many more students voted for summer than for spring and winter combined?
__________ more students
Answer:
Students voted for summer is 10
Students voted for spring  is 4
Students voted for winter is 2
Students voted for winter and spring combined is 4 + 2 = 6
Students voted for summer more than winter and spring is 10 – 6 = 4

Question 9.

How many students like the season with the most votes?
Answer:
Students like the season with the most votes are the summer season.

Question 10.
Higher Order Thinking Look at the picture graph above. How would the graph change if 2 students changed their votes from summer to fall?
Answer:

Problem Solving

Use the tally chart to complete the picture graph. Use the picture graph to solve the problems.
Question 11.
Model Bob made a tally chart to show the trees in a park.

Answer:

Question 12.
en Vision® STEM Birch, oak, maple, and pine trees are common in North America. Which type of tree is most common in the park?
Answer:

Question 13.
Higher Order Thinking How many birch and maple trees are there in all?
Answer:
Birch trees in the park = 3
Maple tree in the park = 4
Birch and maple trees in all are 7.

Question 14.
Assessment Practice Draw a picture graph to show the data in the table.

Answer:

Lesson 15.5 Draw Conclusions from Graphs

Solve & Share
7 students voted for Turtle as their favorite pond animal. 10 students voted for Frog. 4 students voted for Fish. Make a picture graph to show the data. Write two things you notice about the data.
I can .. draw conclusions from graphs.

1. __________________
2. __________________

Visual Learning Bridge

Convince Me! Look at the graph above. How many tickets did Kim and Neil sell in all? How do you know?

Guided Practice

Use the bar graph to solve the problems.

Question 1.
How many pennies does Jake have? ________
Answer:
Jake has 5 pennies.

Question 2.
Jake spends 3 of his quarters. How many does he have left?
Answer:
Total quarters at Jake = 7
Jake spends 3 of his quarters
He have left = 7 – 3 = 4

Independent Practice

Use the bar graph to solve the problems.

Question 3.
How many absences were there in all on Tuesday and Thursday?
Answer:
Total students absences in Tuesday = 2
Total students absences in Thursday = 4
Total students absences in Tuesday and Thursday = 2 + 4 = 6 students.

Question 4.
Were fewer students absent on Monday or Friday? How many fewer?
Answer:
Total students absent on Monday = 5
Total students absent on Friday = 6
1 Fewer student is absent on Monday

Question 5.

Three of the students absent on Friday were boys. How many girls were absent on Friday?
Answer:
Given that,
Total students absent on Friday = 6
From 6 students 3 are boys = 6 – 3 = 3
3 girls are absent on Friday.

Question 6.
On which two days were the same number of students absent?
Answer:
No two days were the same number of students absent.

Question 7.
Were more students absent on Wednesday or Thursday? How many more?
Answer:
Given that,
Total number of students absent on Wednesday = 5
Total number of students absent on Thursday = 4
More students are absent on Wednesday than Thursday
1 student is more absent on Wednesday.

Question 8.
Higher Order Thinking The graph shows the number of absences last week. This week, there are 19 absences. Compare the number of absences this week to the number of absences last week.
Answer:

Problem Solving

Use the bar graph to solve each problem.

Question 9.
Make Sense Complete each sentence.
The farm has ________ Cows and ________ horses.
The farm has ________ goats and ________ sheep.
Answer:
The farm has 5 cows and 3 horses
The farm has 8 goats and 2 sheeps

Question 10.
The sheep and goats are kept in the same pen. How many farm animals are in that pen?
Answer:
Given that,
Sheep and goats are kept in the same pen.
Total number of sheep = 2
Total number of goats = 8
Total number of farm animals are in that pen = 8 + 2 = 10

Question 11.
Suppose 3 new baby goats are born. Then how many goats will the farmer have?
Answer:
Total number of goats = 8
3 new baby goats are born
Total number of goats at the farmer = 8 + 3 = 11 goats

Question 12.
How many fewer horses than cows are on the farm?
_________ fewer horses
Answer:
Total number of horses = 3
Total number of cows = 5
2 fewer horses than cows are on the farm.

Question 13.
Write the order of animals on the farm from the greatest number to the least number.
Answer:
Number of goats = 8
Number of cows = 5
Number of horses = 3
Number of sheep = 2

Question 14.

Higher Order Thinking Do you think the bars on a bar graph should all be the same color? Explain.
Answer:
No, the bars on a bar graph have different colours because to show the difference between the given data.

Question 15.
Assessment Practice The farmer wants to buy some sheep. He wants to have as many sheep as cows. How many more sheep should the farmer buy?
_________ more sheep
Answer:

Lesson 15.6 Problem Solving

Reasoning
Solve & Share

Make a picture graph to show how many connecting cubes, counters, and ones cubes you have. Then write and solve a problem about your data.
I can … reason about data in bar graphs and picture graphs to write and solve problems.

Each = 1 math tool

Thinking Habits What do the symbols mean? How are the numbers in the problem related?

Visual Learning Bridge

Convince Me! Use reasoning to write your own problem about the data in the graph. Then solve it.

Guided Practice

Use the bar graph to write and solve problems.

Question 1.

Answer:

Question 2.
_____________
_____________
________ _________ = ________
Answer:

Independent Practice

Use the bar graph to write and solve problems.

Question 3.
_____________
_____________
________ _________ = ________
_____________
_____________
Answer:

Question 4.
_____________
_____________
________ _________ = ________
_____________
_____________
Answer:

Problem Solving

Performance Task
Vacation Time! The picture graph shows votes for favorite vacation spots. Each student voted only once. Which vacation spot has the same number of votes as two other vacation spots combined?

Question 5.
Explain Solve the problem above and explain your reasoning.
Answer:

Question 6.
Make Sense How many students voted in all? Tell how you know.
Answer:

Question 7.
Reasoning Write your own problem about the data in the graph. Then solve it.
_____________
_____________
________ _________ = ________
_____________
_____________
Answer:

Topic 15 Fluency Practice

Find a Match
Find a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.
I can … add and subtract within 100.

Clues
A. The difference is less than 16.
B. The sum equals 43 + 25.
F The sum equals 75.
C. The difference equals 75 – 46.
D. The sum equals 53 + 20.
E. The difference equals 96 – 19.
G. The sum is between 60 and 65.
H. The difference is between 25 and 28.

Topic 15 Vocabulary Review

Understand Vocabulary

Label each data display. Write line plot, bar graph, or picture graph.
Word List
• bar graph
• data
• line plot
• picture graph
• symbol

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Use Vocabulary in Writing
Question 4.
Look at the graph in Item 2. Use words to tell how to find which ball game is the most popular. Use terms from the Word List.
Answer:

Topic 15 Reteaching

Set A

Line plots show and organize data. Use an inch ruler. Measure the length of the toy car. Then record the measurement in the table.

Place a dot over the number that shows the length of each toy.

Complete the table and show the data on a line plot.
Question 1.
Use an inch ruler. Measure the length of the pencil. Then record the measurement in the table.

Answer:

Question 2.
Make a line plot to show each length in the table.

Answer:

Set B

You can make a bar graph to show the data in a table.
Students voted for their favorite nut. The table shows the number of votes.

Color one space for each vote in the bar graph. Then use the graph to solve the problem.

How many students voted?
16

Use the table to complete the bar graph. Then solve each problem.
Question 3.

Answer:

Question 4.
How many more students voted for vanilla than banana? ________
Answer:
Given that,
Students voted for vanilla = 7
Students voted for banana = 6
Students voted for vanilla than banana is 1.

Question 5.
How many fewer students voted for lemon than vanilla? _________
Answer:
Given that,
Students voted for lemon = 3
Students voted for vanilla = 7
Fewer students voted for lemon than Vanilla is 7 – 3 = 4
4 students voted for lemon than Vanilla.

Set C

A picture graph uses pictures or symbols to show data.
The tally chart shows votes for favorite sea animals.

Which sea animal has the fewest votes?

Use the tally chart to complete the picture graph. Then solve each problem.
Question 6.

Answer:

Question 7.
How many votes did seagull get?
Answer:
10 votes did seagull get.

Question 8.
Which bird had the fewest votes?
Answer:
Blue Jay bird had the fewest votes.

Set D

Thinking Habits
Reasoning
What do the symbols mean?
How are the numbers in the problem related? How can I write a word problem using the information that is given? How do the numbers in my problem relate to each other? How can I use a word problem to show what an equation means?

Use the picture graph to solve each problem. Each student voted once.

Question 9.
How many fewer students chose ice fishing than snowboarding?
Answer:
given that;
students who chose ice fishing is 4
students who chose snowboarding is 10
students chose ice fishing than snowboarding is 10 – 4 = 6

Question 10.
Write and solve your own problem about the data.
______________
______________
____ ______ = _________
______________
Answer:

Topic 15 Assessment Practice

Question 1.
Pam has 5 pennies, 2 nickels, 8 dimes, and 9 quarters. Show this data in the bar graph below. Draw the bars.

Answer:

Question 2.
Use the bar graph you made above. Pam spends 5 of her dimes to buy an apple. Now how many dimes does Pam have left?
A. 13
B. 5
C. 3
D. 0
Answer:

Question 3.
Is each sentence about the picture graph correct? Choose Yes or No.

Answer:

Question 4.
How many more tickets did Kendra sell than Leon?

A. 5
B. 6
C. 11
D. 17
Answer:
5 more tickets did kendra band concert

Question 5
Complete the table and the line plot.
A. Use a centimeter ruler. Measure the length of the crayon to the nearest centimeter. Write the length in the table below.

Answer:

B. Use the data in the table to complete the line plot.

What is the difference in length between the shortest and longest crayon?
Answer:
The shortest length of the crayon is 4
The longest length of the crayon is 8
The difference between the shortest and longest crayon is 8 – 4 = 4.

Question 6.
Scott is making a picture graph from the data in the tally chart.
How many symbols should he draw in the bottom row?

A. 3
B. 4
C. 5
D. 6
Answer:

Question 7.
Mary gets new stamps every month. The bar graph shows the number of stamps she collects each month.

Which statements are true? Choose all that apply.
☐ Mary collects I more stamp in May than she does in April.
☐ Mary collects 2 fewer stamps in June than she does in July.
☐ Mary collects a total of |stamps in May and June.
☐ Mary collects one additional stamp each month from May to July.
☐ Mary collects the most stamps in June.
Answer:
the true statements are
Mary collects I more stamp in May than she does in April.
Mary collects one additional stamp each month from May to July.
Mary collects one additional stamp each month from May to July.

Question 8.
Use the tally chart to complete the picture graph. Then use the picture graph to solve the problems.

How many students voted for Lily? _________
Which flower is the least favorite? _________
Answer:
8 students voted for Lily.
Daisy is the least favorite flower.

Question 9.
Use the line plot and the numbers on the cards to complete each sentence.

3 pencils are ________ inches long.
The longest pencil is ________ inches long.
The shortest pencil is ________ inches long.
The difference between the shortest and longest pencil is _________ inches.
Answer:3 pencils are 1 inch long.
The longest pencil is 3 inches long.
The shortest pencil is 1 inch long.
The difference between the shortest and longest pencil is 2 inches

Topic 15 Performance Task

School Surveys Some students asked their classmates different questions.
George asked his classmates to vote for their favorite lunch. This table shows the results.

Question 1.
Use the table to complete the bar graph.

Answer:

Question 2.
Use the Favorite Lunch table to complete the picture graph.

Answer:

Question 3.
Use the graphs you made to answer these questions.
How many students chose salad as their favorite lunch? _________
How many fewer students chose taco than hamburger? __________ fewer students
How would the bar graph change if two more students chose taco?
Answer:

Question 4.
Write and solve a math story about the Favorite Lunch graphs you made.
Part A
Use the bar graph or the picture graph about favorite lunches to write a math story problem. The problem should include addition or subtraction.
Answer:

Part B
Solve your math story problem. Explain how you solved the problem.
Answer:

Question 5.
Gina asked her classmates to measure the length of their favorite storybook in inches. She recorded their measurements in this table.

Part A
Use the table to make a line plot.
Answer:

Part B What is the difference in length between the longest and shortest books?
________ inches
Answer:
Given that,
The length of the longest pencil is 12 inches
The length of the shortest book is 7 inches
The difference between longest book and shortest book = 12 – 7 = 5 inches

Go through the enVision Math Common Core Grade 1 Answer Key Topic 9 Compare Two-Digit Numbers regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 9 Compare Two-Digit Numbers

enVision STEM Project: Light and Objects

Find Out Talk to friends and relatives about light. Discuss how light changes when it shines on different kinds of objects.

Journal: Make a Book Show what you found out. In your book, also:

• Draw pictures showing light shining on objects that are see-through and not see-through.
• Make up and solve number stories about shining light on different objects.

Review What You Know

Vocabulary

Question 1.
Circle the group of cubes that has more.

Answer:

Explanation :
The orange cubes are 3
The Green cubes are 5
3 < 5 . so Green cubes are circled .

Question 2.
Circle the group of cubes that has less.

Answer:

Explanation :
The orange cubes are 3
The Green cubes are 5
3 < 5 . so orange cubes are circled .

Question 3.
How many tens are in the number?
50
___ tens
Answer:
50 = 5 tens
Explanation :
counting

Number Lines

Question 4.
Use the number line to count by 10s. Write the missing numbers.

Answer:

Explanation :
Count on Tens 10, 20, 30 and 40 .

Question 5.
Pat sees 5 bugs. Erin sees 6 bugs. How many bugs did they see in all?
Use the number line to count.

___ bags
Answer:
Number of bugs seen by Pat = 5 bugs
Number of bugs seen by Erin = 6 bugs
Total Number of bugs = 5 + 6 = 11 bugs  .

Hundred Chart

Question 6.
Use the part of the hundred chart to count.

Answer:
18, 19 , 20, 21, 22
Explanation:
Count by ones from 18 to 22 .

Pick a Project

PROJECT 9A

How hot can it get?
Project: Create a Temperature Drawing

Answer :

The climate is too hot as the camel cannot take the weight of the person so, walking in the Sand .

PROJECT 9B
Where did they all come from?
Project: Make a Shorebird Comparison Model

Answer :
Instructions used to make a Shoe bird

PROJECT 9C
How was that made?
Project: Make a Sponge Stamp Picture

Answer :

Explanation :
Take the sponge .
Cut the sponge into required shape like star, Moon , Heart and aetc into different shapes .
Then later , Put the required shape sponge in water colors or ink .
Then Press the sponge imprint on the paper . then required drawing can be made with the required shape .

Math Modeling

Digit Flip

3-ACT MATH PREVIEW
Before watching the video, think: Have you ever played a card game? What were some of the rules? How did someone win the game?

Lesson 9.1 1 More, 1 Less; 10 More, 10 Less

Solve & Share

Sarah has 12 marbles. Chris has one more marble than Sarah. Lucia has 10 more marbles than Sarah. How many marbles does Chris have? How many marbles does Lucia have? Show how you know.

Answer :
Number of Marbles with Sarah = 12
Number of Marbles with Chris = one more marble than Sarah = 12 + 1 = 13
Number of Marbles with Lucia = ten more marble than Sarah = 12 + 10 = 23

Visual Learning Bridge

Convince Me!
How can you find 10 more than a number? Explain.
Answer :
To find 10 more than a number, add 1 to the digit at the tens place.

Guided Practice

Use place-value blocks to show each number and to help you complete each sentence.

Question 1.

Answer:
1 more than 45 is 46
1 less than 45 is 44
10 more than 45 is 55
10 less than 45 is 35

Question 2.

1 more than 17 is ___
1 less than 17 is ___
10 more than 17 is ___
10 less than 17 is ___
Answer:
1 more than 17 is 18
1 less than 17 is 16
10 more than 17 is 27
10 less than 17 is 7

Independent Practice

Use place-value blocks to show each number and to help you
complete each sentence.

Question 3.

1 more than 11 is ___
1 less than 11 is ___
10 more than 11 is ___
10 less than 11 is ___
Answer:
1 more than 11 is 12
1 less than 11 is 10
10 more than 11 is 21
10 less than 11 is 1

Question 4.

1 more than 40 is ___
1 less than 40 is ___
10 more than 40 is __
10 less than 40 is ___
Answer:
1 more than 40 is 41
1 less than 40 is 39
10 more than 40 is 50
10 less than 40 is 30

Question 5.

1 more than 81 is ___
1 less than 81 is ___
10 more than 81 is ___
10 less than 81 is ___
Answer:
1 more than 81 is 82
1 less than 81 is 80
10 more than 81 is 91
10 less than 81 is 71

Question 6.

1 more than 19 is ___
1 less than 19 is ____
10 more than 19 is ___
10 less than 19 is ___
Answer:
1 more than 19 is 20
1 less than 19 is 18
10 more than 19 is 29
10 less than 19 is 9

Question 7.

1 more than 65 is ___
1 less than 65 is ___
10 more than 65 is ___
10 less than 65 is ___
Answer:
1 more than 65 is 66
1 less than 65 is 64
10 more than 65 is 75
10 less than 65 is 55

Question 8.

1 more than 43 is ___
1 less than 43 is ___
10 more than 43 is ___
10 less than 43 is ___
Answer:
1 more than 43 is 44
1 less than 43 is 42
10 more than 43 is 53
10 less than 43 is 33

Question 9.
Higher Order Thinking Circle the picture that shows 10 more than 24. Explain how you know.

Answer:

Explanation :
To find 10 more than a number, add 1 to the digit at the tens place.
24 + 10 = 34 .

Problem Solving
Solve each problem below.

Question 10.
Generalize Sheila wants to write instructions to tell her friend how to find 10 more than any number. What instructions should Sheila write?
Answer:
Instructions are :
To find 10 more than a number, add 1 to the digit at the tens place.
When we add 10 the ones always stay the same.

Question 11.
Number Sense Fill in the missing numbers. Use place-value blocks to help you.

Answer:

Question 12.
Higher Order Thinking Write and solve a riddle for a number greater than 40 and less than 60. Use “I more than” and “I less than” or “10 more than” and “10 less than” as clues.
Clues: __________
_______________
_______________
My number is ____.
Answer:
My number is 44

Question 13.
Assessment Practice Match each number with its description.

Answer:

Lesson 9.2 Find Numbers on a Hundred Chart

Solve & Share

How can you use a hundred chart to help you find I more than 36? What about I less, 10 more, and 10 less than 36? Write the numbers.

1 more than 36 is ___.
10 more than 36 is ___
1 less than 36 is ___
10 less than 36 is ____
Answer :
1 more than 36 is 37
10 more than 36 is 46
1 less than 36 is 35
10 less than 36 is 26 .
Explanation :
1 more than 36 means the next number to its right as per hundred chart .
10 more than 36 means the number below 36 as per hundred chart .
1 less than 36 means before number to its left as per hundred chart .
10 less than 36 means the Number above 36 as per hundred chart .

Visual Learning Bridge

Convince Me!
How could you use a hundred chart to find what number is 10 more than 86? What number is that?
Answer :

Explanation :
1 more than 86 means the next number to its right as per hundred chart .
10 more than 86 means the number below 86 as per hundred chart .
1 less than 86 means before number to its left as per hundred chart .
10 less than 86 means the Number above 86 as per hundred chart .

Guided Practice
Complete the part of the hundred chart. Practice Use place-value blocks if needed.

Question 1.

Answer:

Explanation :
1 more than 33 means the next number to its right as per hundred chart .
10 more than 33 means the number below 33 as per hundred chart .
1 less than 33 means before number to its left as per hundred chart .
10 less than 33 means the Number above 33 as per hundred chart .

Question 2.

Answer:

Explanation :
1 more than 46 means the next number to its right as per hundred chart .
10 more than 46 means the number below 46 as per hundred chart .
1 less than 46 means before number to its left as per hundred chart .
10 less than 46 means the Number above 46 as per hundred chart .

Independent Practice

Use a hundred chart to complete each sentence. Use place-value blocks if needed.

Question 3.
1 more than 37 is ___.
1 less than 37 is ____.
10 more than 37 is ___.
10 less than 37 is ____.
Answer:
1 more than 37 is 38.
1 less than 37 is  36.
10 more than 37 is 47.
10 less than 37 is 27

Explanation :
1 more than 37 means the next number to its right as per hundred chart .
10 more than 37 means the number below 37 as per hundred chart .
1 less than 37 means before number to its left as per hundred chart .
10 less than 37 means the Number above 37 as per hundred chart .

Question 4.
1 more than 22 is ___.
1 less than 22 is ___.
10 more than 22 is ___.
10 less than 22 is ___.
Answer:
1 more than 22 is 23.
1 less than 22 is 21.
10 more than 22 is 32.
10 less than 22 is 12

Explanation :
1 more than 22 means the next number to its right as per hundred chart .
10 more than 22 means the number below 22 as per hundred chart .
1 less than 22 means before number to its left as per hundred chart .
10 less than 22 means the Number above 33 as per hundred chart .

Question 5.
1 more than 54 is ___
1 less than 54 is ____
10 more than 54 is ___
10 less than 54 is ___
Answer:
1 more than 54 is 55
1 less than 54 is 53
10 more than 54 is 64
10 less than 54 is 44

Explanation :
1 more than 54 means the next number to its right as per hundred chart .
10 more than 54 means the number below 54 as per hundred chart .
1 less than 54 means before number to its left as per hundred chart .
10 less than 54 means the Number above 33 as per hundred chart .

Question 6.
1 more than 78 is ___.
1 less than 78 is ___.
10 more than 78 is ___.
10 less than 78 is ___.
Answer:
1 more than 78 is 79.
1 less than 78 is . 77
10 more than 78 is  88.
10 less than 78 is 68

Explanation :
1 more than 78 means the next number to its right as per hundred chart .
10 more than 78 means the number below 78 as per hundred chart .
1 less than 78 means before number to its left as per hundred chart .
10 less than 78 means the Number above 78 as per hundred chart .

Question 7.
1 more than 82 is ___
1 less than 82 is ____
10 more than 82 is ___.
10 less than 82 is ___.
Answer:
1 more than 82 is 83
1 less than 82 is 81
10 more than 82 is 92.
10 less than 82 is 72

Explanation :
1 more than 82 means the next number to its right as per hundred chart .
10 more than 82 means the number below 82 as per hundred chart .
1 less than 82 means before number to its left as per hundred chart .
10 less than 82 means the Number above 82 as per hundred chart .

Question 8.
1 more than 16 is ___
1 less than 16 is ___
10 more than 16 is ___
10 less than 16 is ___
Answer :
1 more than 16 is 17
1 less than 16 is 15
10 more than 16 is 26
10 less than 16 is 6

Explanation :
1 more than 16 means the next number to its right as per hundred chart .
10 more than 16 means the number below 16 as per hundred chart .
1 less than 16 means before number to its left as per hundred chart .
10 less than 16 means the Number above 16 as per hundred chart .

Algebra Use a hundred chart to find each student’s number.

Question 9.
Alex’s number is 27. Kendra’s number is 1 less than Alex’s number. Devon’s number is 10 more than Kendra’s number. Finish the equations to find each friend’s number.

Answer:

Explanation :
Alex Number = 27
Kendra’s number is 1 less than Alex’s number = 27 -1 = 26
Devon’s number is 10 more than Kendra’s number =  26 + 10 = 36

Problem Solving

Solve the problems below.

Question 10.
Look for Patterns Use the clues to find the missing number of marbles in each bag. Write the number. Ben has more than 54 marbles.
Anna has 10 more marbles than Ben.
Todd has a number that is 1 less than the number Anna has.

Answer:
Ben has more than 54 marbles. so, take 55 marbles .
Number of Marbles with Anna =10 more marbles than Ben = 10 + 55 = 65 Marbles .
Number of Marbles with Todd = has a number that is 1 less than the number Anna has = 65 – 1 = 64 marbles

Question 11.
Higher Order Thinking Write a clue a partner could use to find how many marbles are in a bag. Then use the clue to tell how many marbles are in the bag.

Answer:

Number of marbles in the bag = 10 less than 60 = 60 – 10 = 50 .

Question 12.
Assessment Practice

Which are true? Choose two.
10 more than 23 is 32.
1 more than 23 is 24.
10 less than 23 is 13.
1 less than 23 is 20.
Answer:
Option
Explanation :
10 more than 23 = 10 + 23 = 33 Option 1 is wrong .
1 more than 23 = 1 + 23 = 24 . Option 2 is right .
10 less than 23 = 23 – 10 = 13 Option 3 is right .
1 less than 23 = 23 – 1 = 22 Option 4 is right .