## enVision Math Common Core 5th Grade Answers Key Topic 2 Use Models and Strategies to Add and Subtract Decimals

**Use Models and Strategies to Add and Subtract Decimals**

**Essential Questions:** How can sums and differences of decimals be estimated? What are some common procedures for adding and subtracting decimals? How can sums and differences be found mentally?

**enVision STEM Project: Producers and Consumers**

**Do Research** Use the Internet or other sources to find information about producers and consumers.

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

- What do producers need to survive? What do consumers need to survive?
- Give at least three examples of both producers and consumers.
- Write and solve decimal addition and subtraction problems for the amounts of food the consumers need.

**Review What You Know**

**Vocabulary**

Choose the best term from the box. Write it on the blank.

• addend

• inverse operations

• round

• difference

• equivalent

• sum

Question 1.

The ___ is the result of subtracting one number from another.

Answer:

The difference is the result of subtracting one number from another.

Explanation:

In the above-given question,

given that,

the difference is the result of subtracting one number from another.

for example:

5 – 2 = 3.

3 is the difference.

Question 2.

Two numbers or expressions that have the same value are ___.

Answer:

The two numbers or expressions that have the same value are equivalent.

Explanation:

In the above-given question,

given that,

the two numbers or expressions that have the same value are equivalent.

for example:

2 + 3 = 5.

the two have the same value.

Question 3.

The answer to an addition problem is the ___.

Answer:

The answer to an addition problem is the sum.

Explanation:

In the above-given question,

given that,

the answer to an addition problem is the sum.

for example:

5 + 3 = 8.

8 is the sum.

Question 4.

One way to estimate an answer is to ___ the numbers and then do the calculation.

Answer:

One way to estimate an answer is to inverse the numbers and then do the calculation.

Explanation:

In the above-given question,

given that,

One way to estimate an answer is to inverse the numbers and then do the calculation.

5 + 6 = 11.

11 – 6 = 5.

11 – 5 = 6.

**Round Decimals**

Round each number to the nearest tenth.

Question 5.

74.362

Answer:

The number equal to the nearest tenth = 74.4.

Explanation:

In the above-given that,

given that,

to round a number to the nearest tenth,

look at the next place value to the right(the hundredths).

if it’s 4 or less, just remove all the digits to the right.

if it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.

74.362 in this the hundredths place is greater than 5.

so add 1 to the tenths place.

3 + 1 = 4.

the number equal to the nearest tenth = 74.4.

Question 6.

28.45

Answer:

The number equal to the nearest tenth = 28.5.

Explanation:

In the above-given that,

given that,

to round a number to the nearest tenth,

look at the next place value to the right(the hundredths).

if it’s 4 or less, just remove all the digits to the right.

if it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.

28.45 in this the hundredths place is greater than 5.

so add 1 to the tenths place.

4 + 1 = 5.

the number equal to the nearest tenth = 28.5.

Question 7.

13.09

Answer:

The number equal to the nearest tenth = 13.1.

Explanation:

In the above-given that,

given that,

to round a number to the nearest tenth,

look at the next place value to the right(the hundredths).

if it’s 4 or less, just remove all the digits to the right.

if it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.

13.09 in this the hundredths place is greater than 5.

so add 1 to the tenths place.

0 + 1 = 1.

the number equal to the nearest tenth = 13.1.

Round each number to the nearest hundredth.

Question 8.

43.017

Answer:

The number equal to the nearest hundredth = 43.02.

Explanation:

In the above-given that,

given that,

to round a number to the nearest hundredth,

look at the next place value to the right(the thousands).

if it’s 4 or less, just remove all the digits to the right.

if it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.

43.017 in this the thousands place is greater than 5.

so add 1 to the hundredths place.

1 + 1 = 2.

the number equal to the nearest hundredths = 43.02.

Question 9.

186.555

Answer:

The number equal to the nearest hundredth = 186.56.

Explanation:

In the above-given that,

given that,

to round a number to the nearest hundredth,

look at the next place value to the right(the thousands).

if it’s 4 or less, just remove all the digits to the right.

if it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.

186.555 in this the thousands place is greater than 5.

so add 1 to the hundredths place.

5 + 1 = 6.

the number equal to the nearest hundredths = 186.56.

Question 10.

222.222

Answer:

The number equal to the nearest hundredth = 222.20.

Explanation:

In the above-given that,

given that,

to round a number to the nearest hundredth,

look at the next place value to the right(the thousands).

if it’s 4 or less, just remove all the digits to the right.

if it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.

222.222 in this the thousands place is less than 5.

so do not add 1 to the hundredths place.

222.20

the number equal to the nearest hundredths = 222.20.

Round each number to the underlined digit.

Question 11.

8__4__.59

Answer:

The number round to the underlined digit is = 85.

Explanation:

In the above-given question,

given that,

the number is 84.59.

the underlined digit is 4.

4 + 1 = 5.

so the number round to the underlined digit = 85.

Question 12.

2.9__4__8

Answer:

The number round to the underlined digit is = 2.95.

Explanation:

In the above-given question,

given that,

the number is 2.948.

the underlined digit is 4.

4 + 1 = 5.

so the number round to the underlined digit = 2.95.

Question 13.

30.1__2__5

Answer:

The number round to the underlined digit is = 30.13.

Explanation:

In the above-given question,

given that,

the number is 30.125.

the underlined digit is 2.

2 + 1 = 3.

so the number round to the underlined digit = 30.13

**Addition and Subtraction of Whole Numbers**

Find each sum or difference.

Question 14.

9,536 + 495

Answer:

9536 + 495 = 10031.

Explanation:

In the above-given question,

given that,

the numbers are 9536 and 495.

add the two numbers.

9536 + 495 = 10031.

Question 15.

612 – 357

Answer:

612 – 357 = 255.

Explanation:

In the above-given question,

given that,

the numbers are 612 and 357.

subtract the two numbers.

612 – 357 = 255.

Question 16.

5,052 – 761

Answer:

5052 – 761 = 4291.

Explanation:

In the above-given question,

given that,

the numbers are 5052 and 761.

subtract the two numbers.

5052 – 761 = 4291.

Question 17.

Vivica sees that a printer costs $679 and a computer costs $1,358. What is the total cost of the printer and the computer?

Answer:

The total cost of the printer and the computer = $2037.

Explanation:

In the above-given question,

given that,

Vivica sees that a printer costs $679.

computer costs $1,358.

$679 + $1,358 = $2037.

so the total cost of the printer and the computer = $2037.

Question 18.

The Pecos River is 926 miles long, and the Brazos River is 1,280 miles long. How many miles longer is the Brazos River than the Pecos River?

A. 2,206 miles

B. 1,206 miles

C. 364 miles

D. 354 miles

Answer:

Option D is correct.

Explanation:

In the above-given question,

given that,

The Pecos River is 926 miles long, and the Brazos River is 1,280 miles long.

1280 – 926 = 354.

the longer is the Brazos River than the Pecos River is 354 miles.

so option D is correct.

**Pick a Project**

**PROJECT 2A**

How big are alligators and crocodiles?

Project: Compare the Sizes of Reptiles

Answer:

The crocodile weight is 410 – 520 kg approximately.

Explanation:

In the above-given question,

given that,

the water animals are crocodiles and alligators.

the size of the reptiles is very tiny.

so the crocodile weight is 410 – 520 kg approximately.

**PROJECT 2B**

How much should a theme park ticket cost?

Project: Make a Brochure for a Theme Park

Answer:

The cost of the ticket is $37 approximately.

Explanation:

In the above-given question,

given that,

the theme park is located in the united states of America.

so the cost of the ticket is $37 approximately.

**PROJECT 2C**

How much and how healthy is your meal in a restaurant?

Project: Plan Your Meal

**PROJECT 2D**

How far was your trip?

Project: Make a Travel Journal

Answer:

The travel trip is Vizag.

Explanation:

In the above-given question,

given that,

my travel trip is Vizag.

the distance from Hyderabad to Vizag is around 650 km.

so my travel trip is Vizag.

### Lesson 2.1 Mental Math

**Activity**

**Solve & Share**

Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software? Use mental math to solve.

You can use reasoning to help you. What do you know about adding three numbers that will make it easier to solve this problem?

Answer:

The total cost of the software is $49.59.

Explanation:

In the above-given question,

given that,

Three pieces of software cost $20.75, $10.59, and $18.25.

20.75 + 10.59 + 18.25 = 49.59.

so the total cost of the software is $49.59.

**Look Back!** Which two numbers above were easy to add in your head? Why?

**Visual Learning Bridge**

**Essential Question**

How Can You Use Mental Math to Add?

**A.**

Properties of addition can help you find the total cost of these three items.

The Commutative Property and Associative Property make it easy to add $11.45 + $3.39 + $9.55.

The Associative Property lets you change the grouping of addends.

($11.45 + $3.39) + $9.55 = $11.45 + ($3.39 + $9.55)

The Commutative Property lets you add two decimals in any order.

**B.**

Use the Commutative Property to change the order.

$11.45 + ($3.39 + $9.55) = $11.45 + ($9.55 + $3.39)

Use the Associative Property to change the grouping.

$11.45 + ($9.55 + $3.39) = ($11.45 + $9.55) + $3.39

**C.**

Add $11.45 and $9.55 first because they are easy to compute mentally.

$11.45 + $9.55 = $21

$21 + $3.39 = $24.39

The three items cost a total of $24.39.

Compatible numbers are numbers that are easy to compute mentally.

**Convince Me!** Reasoning Use mental math to find the sum. Explain your thinking. Jim earns $22.50, $14.75, and $8.50 on three different days. How much did he earn in all?

Answer:

The much did he earn in all = $45.75.

Explanation:

In the above-given question,

given that,

Jim earns $22.50, $14.75, and $8.50 on three different days.

we can find the answer in three ways.

$22.50 + $14.75 = 37.25.

$37.25 + $8.50 = $45.75.

so the much did he earn in all = $45.75.

**Another Example**

With compensation, adjust one or both numbers to make the calculation easier. Then adjust the difference or sum to get the final answer.

Use compensation to subtract.

Find 4.25 – 0.08 mentally.

4.25 – 0.10 = 4.15

4.25 – 0.08 = 4.17

Use compensation to add.

Find $3.47 + $4.35 mentally.

$3.47 + $4.35 = $7.82

**Guided Practice**

**Do You Understand?**

Question 1.

Show how to use compensation to add $3.18 and $6.50.

Answer:

$3.18 + $6.50 = $9.68.

Explanation:

In the above-given question,

given that,

the two numbers are 3.20 and 6.50.

$3.20 + $6.50 = $9.70.

we have to take 0.02 from $9.70.

$9.70 – 0.02 = $9.68.

so $3.18 + $6.50 = $9.68.

Question 2.

Use properties to rewrite the expression to be easier to solve. Explain. (13 + 4.63) + 7.4

Answer:

We can use two expressions that are associative and commutative properties.

Explanation:

In the above-given question,

given that,

the two properties are associative and commutative.

13 + 4.63 = 17.63.

17.63 + 7.4 = 25.03.

4.63 + 7.4 = 12.03.

12.03 + 13 = 25.03.

so we can use two expressions that are associative and commutative properties.

**Do You Know How?**

In 3-6, use mental math to add or subtract.

Question 3.

12 + 3.04 + 8.28

Answer:

12 + 3.04 + 8.28 = 23.32.

Explanation:

In the above-given question,

given that,

use mental math to add.

12 + 3.04 = 15.04.

15.04 + 8.28 = 23.32.

Question 4.

6.97 + 4.15

Answer:

6.97 + 4.15 = 11.12.

Explanation:

In the above-given question,

given that,

use mental math to add.

6.97 + 4.15 = 11.12.

Question 5.

9.04 – 6.98

Answer:

9.04 – 6.98 = 2.06.

Explanation:

In the above-given question,

given that,

use mental math to subtract.

9.04 – 6.98 = 2.06.

Question 6.

4.02 +0.19 + 16.48

Answer:

4.02 + 0.19 + 16.48 = 20.69.

Explanation:

In the above-given question,

given that,

use mental math to add.

4.02 + 0.19 = 4.21.

4.21 + 16.48 = 20.69.

**Independent Practice**

Leveled Practice In 7-12, use mental math to add or subtract.

Question 7.

7.1 + 5.4 + 2.9 =

___ + 5.4 =

_______

Answer:

7.1 + 5.4 + 2.9 = 15.4.

Explanation:

In the above-given question,

given that,

use mental math to add.

7.1 + 5.4 = 12.5.

12.5 + 2.9 = 15.4.

Question 8.

373.4 – 152.9 =

373.4 – __ = 220.4

___ + 0.1 = ___

Answer:

373.4 – 152.9 = 220.5.

Explanation:

In the above-given question,

given that,

use mental math to subtract.

373.4 – 152.9 = 220.5.

373.4 – 152.8 = 220.4.

220.4 + 0.1 = 220.5.

Question 9.

$18.25 + $7.99 + $4.75

Answer:

$18.25 + $7.99 + $4.75 = $30.99.

Explanation:

In the above-given question,

given that,

use mental math to add.

18.25 + 7.99 = 26.24.

26.24 + 4.75 = 30.99.

Question 10.

1.05 + 3 + 4.28 +0.95

Answer:

1.05 + 3 + 4.28 + 0.95 = 6.31.

Explanation:

In the above-given question,

given that,

use mental math to add.

1.05 + 3 = 1.08.

4.28 + 0.95 = 5.23.

5.23 + 1.08 = 6.31.

Question 11.

2,504 + 140 + 160

Answer:

2504 + 140 + 160 = 2804.

Explanation:

In the above-given question,

given that,

use mental math to add.

2504 + 140 = 2644.

2644 + 160 = 2804.

Question 12.

35.7 – 14.8

Answer:

35.7 – 14.8 =20.9.

Explanation:

In the above-given question,

given that,

the two numbers are 35.7 and 14.8.

use mental math to subtract.

35.7 – 14.8 = 20.9.

**Problem Solving**

Question 13.

Joanne bought three books that cost $3.95, $4.99, and $6.05. How much did she spend in all? Use compensation and mental math to find the sum.

Answer:

The total she spends in all = 14.09.

Explanation:

In the above-given question,

given that,

Joanne bought three books that cost $3.95, $4.99, and $6.05.

$3.95 + $4.100 = 8.05.

8.05 – 0.01 = 8.04.

8.04 + 6.05 = 14.09.

so the total she spends in all = 14.09.

Question 14.

**Construct Arguments** Use compensation to find each difference mentally. Explain how you found each difference.

A. 67.9 – 29.9

B. 456 – 198

Answer:

A. 67.9 – 29.9 = 38.

B. 456 – 198 = 258.

Explanation:

In the above-given question,

given that,

67.9 + 0.01 = 68.0.

68.0 – 0.01 = 67.9.

67.9 – 29.9 = 38.

456 – 200 = 256.

256 + 2 = 258.

Question 15.

**Number Sense** The table shows how many points Eduardo scored during each game. Use mental math to find how many points he scored in the first three games.

Answer:

The number of points Eduardo scored in the first three games = 99.

Explanation:

In the above-given question,

given that,

The table shows how many points Eduardo scored during each game.

in the first game, he scored 54 points.

in the second game, he scored 19 points.

in the third game, he scored 26 points.

54 + 19 + 26 = 99.

so the number of points Eduardo scored in the first three games = 99.

Question 16.

On three different days at her job, Sue earned $27, $33, and $49. She needs to earn $100 to buy a desk for her computer. If she buys the desk, how much money will she have left over?

Answer:

The money will she have leftover = 9.

Explanation:

In the above-given question,

given that,

On three different days at her job.

Sue earned $27, $33, and $49.

She needs to earn $100 to buy a desk for her computer.

$27 + $33 + $49 = 109.

109 – 100 = 9.

so the money will she have leftover = 9.

Question 17.

A shelf can hold 50 DVDs. Jill has 27 DVDs. She plans to buy 5 new ones. Each DVD costs $9. After she buys the new ones, how many more DVDs can the shelf hold?

Answer:

The number of DVDs can the shelf hold = 32.

Explanation:

In the above-given question,

given that,

A shelf can hold 50 DVDs. Jill has 27 DVDs.

She plans to buy 5 new ones.

Each DVD costs $9.

27 + 5 = 32.

so the number of DVDs can the shelf hold = 32.

Question 18.

When finding the difference of two numbers mentally, can you use the Commutative Property? Explain.

Answer:

No, we cannot use the commutative property.

Explanation:

In the above-given question,

given that,

the difference between the two numbers we cannot use the commutative property.

for example:

the two numbers are 5 and 3.

5 – 3 = 2.

so the difference is 2.

Question 19.

**Higher Order Thinking** Daria bought a skein of alpaca yarn for $47.50, a skein of angora yarn for $32.14, a skein of wool yarn for $16.50, and a pair of knitting needles for $3.86. How much did she spend in all? Describe how you calculated your answer.

Answer:

The more did she spend in all = $100.

Explanation:

In the above-given question,

given that,

Daria bought a skein of alpaca yarn for $47.50, a skein of angora yarn for $32.14.

a skein of wool yarn for $16.50, and a pair of knitting needles for $3.86.

47.50 + 32.14 + 16.50 + 3.86.

47.50 + 32.14 = 79.64.

16.50 + 3.86 = 20.36.

79.64 + 20.36 =

so the more did she spend in all = $100.

**Assessment Practice**

Question 20.

Mrs. Healer’s class took a field trip to a park 12.3 miles away. Mr. Dean’s class drove 4.9 miles to the public library. How much farther did Mrs. Healer’s class travel than Mr. Dean’s class? Explain how you used mental math to determine the difference.

Answer:

The much farther did Mrs. Healer’s class travel than Mr. Dean’s class = 7.4.

Explanation:

In the above-given question,

given that,

Mrs. Healer’s class took a field trip to a park 12.3 miles away.

Mr. Dean’s class drove 4.9 miles to the public library.

12.3 – 4.9 = 7.4.

so much farther did Mrs. Healer’s class travel than Mr.Dean’s class = 7.4.

### Lesson 2.2 Estimate Sums and Differences of Decimals

**Activity**

**Solve & Share**

An amusement park has two roller coasters. One is 628 feet long, and the other is 485 feet long. If you ride both roller coasters, about how many feet will you travel in all? Use estimation to solve.

You can use reasoning to decide what you are asked to find. Is the problem looking for an exact answer? How can you tell?

**Look Back!** About how much longer is the one coaster than the other? Show your work.

Answer:

The number of feet will you travel in all = 143 feet.

Explanation:

In the above-given question,

given that,

An amusement park has two roller coasters.

One is 628 feet long, and the other is 485 feet long.

628 – 485 = 143.

so the number of feet will you travel in all = 143 feet.

**Visual Learning Bridge**

**Essential Question** How Can You Estimate Sums?

**A.**

Students are collecting dog food to give to an animal shelter. Estimate how many pounds were collected in Weeks 3 and 4.

There is more than one way to find an estimate.

**B. One Way**

Round each addend to the nearest hundred.

237.5 + 345.1 is about 500.

The students collected about 500 pounds of dog food in Weeks 3 and 4.

**C.**

**Another Way**

Substitute compatible numbers.

Compatible numbers are easy to add!

237.5 + 345.1 is about 600.

The students collected about 600 pounds of dog food in Weeks 3 and 4.

**Convince Me!** Critique Reasoning Tomás said, “We did great in Week 4! We collected just about twice as many pounds as in Week 1!”

Use estimation to decide if he is right. Explain your thinking.

**Another Example**

You can estimate differences.

Estimate 22.84 – 13.97.

**One Way**

Round each number to the nearest whole number.

22.84 – 13.97 is about 9.

**Another Way**

Substitute compatible numbers.

22.84 – 13.97 is about 10.

**Guided Practice**

**Do You Understand?**

Question 1.

In the example above, which estimate is closer to the actual difference? How can you tell without subtracting?

Answer:

22.84 is near to the 23.

Explanation:

In the above-given question,

given that,

for example:

22.84 we can write it as 23.

22.84 we can write it as 25.

so 23 is near to 22.84.

Question 2.

In the example on the previous page, students collected more pounds of dog food in Week 4 than in Week 3. Estimate about how many more.

Answer:

The many more they have collected = 100 pounds.

Explanation:

In the above-given question,

given that,

the two numbers are 237.5 and 345.1.

250 + 350 = 600.

so the many more they have collected = 100 pounds.

**Do You Know How?**

In 3-10, estimate each sum or difference.

Question 3.

49 + 22.88

Answer:

49 + 23 = 72.

Explanation:

In the above-given question,

given that,

the two numbers are 49 and 23.

add the two numbers.

49 + 23 = 72.

Question 4.

86.9 – 18

Answer:

86.9 – 18 = 68.9

Explanation:

In the above-given question,

given that,

the two numbers are 86.9 and 18.

subtract the two numbers.

86.9 – 18 = 68.9.

Question 5.

179 + 277.1

Answer:

179 + 277.1 = 456.1

Explanation:

In the above-given question,

given that,

the two numbers are 179 and 277.1.

add the two numbers.

179 + 277.1 = 456.1.

Question 6.

23.2 – 9.71

Answer:

23.2 – 9.71 =13.49

Explanation:

In the above-given question,

given that,

the two numbers are 23.2 and 9.71.

subtract the two numbers.

23.2 – 9.71 = 13.49.

Question 7.

23.8 – 4.7

Answer:

23.8 – 4.7 = 19.1.

Explanation:

In the above-given question,

given that,

the two numbers are 23.8 and 4.7.

subtract the two numbers.

23.8 – 4.7 = 19.1.

Question 8.

87.2 + 3.9

Answer:

87.2 + 3.9 = 91.1.

Explanation:

In the above-given question,

given that,

the two numbers are 87.2 and 3.9.

add the two numbers.

87.2 – 3.9 = 91.1.

Question 9.

38.9 – 21.4

Answer:

38.9 – 21.4 = 17.5.

Explanation:

In the above-given question,

given that,

the two numbers are 38.9 and 21.4.

subtract the two numbers.

38.9 – 21.4 = 17.5.

Question 10.

576 +94.6

Answer:

576 + 94.6 = 670.6.

Explanation:

In the above-given question,

given that,

the two numbers are 576 and 94.6.

add the two numbers.

576 + 94.6 = 670.6.

**Independent Practice**

In 11-18, estimate each sum or difference.

Question 11.

79.1 + 32.4

Answer:

79.1 + 32.4 = 111.5.

Explanation:

In the above-given question,

given that,

the two numbers are 79.1 and 32.4.

add the two numbers.

79.1 + 32.4 = 111.5.

Question 12.

788.9 – 572

Answer:

788.9 – 572 = 216.9.

Explanation:

In the above-given question,

given that,

the two numbers are 788.9 and 572.

subtract the two numbers.

788.9 – 572 = 216.9.

Question 13.

837 + 488.12

Answer:

837 + 488.12 = 1325.12

Explanation:

In the above-given question,

given that,

the two numbers are 837 and 488.12.

add the two numbers.

837 + 488.12 = 1325.12.

Question 14.

418.5 – 23.7

Answer:

418.5 – 23.7 = 394.8.

Explanation:

In the above-given question,

given that,

the two numbers are 418.5 and 23.7.

subtract the two numbers.

418.5 – 23.7 = 394.8.

Question 15.

2.9 + 3.9

Answer:

2.9 + 3.9 = 6.8.

Explanation:

In the above-given question,

given that,

the two numbers are 2.9 and 3.9.

add the two numbers.

2.9 – 3.9 = 6.8.

Question 16.

$12.99 – $3.95

Answer:

$12.99 – $3.95 = 9.04.

Explanation:

In the above-given question,

given that,

the two numbers are 12.99 and 3.95.

subtract the two numbers.

12.99 – 3.95 = 9.04.

Question 17.

8.1 + 3.7 + 7.9.

Answer:

8.1 + 3.7 + 7.9 = 19.7.

Explanation:

In the above-given question,

given that,

the three numbers are 8.1, 3.7, and 7.9.

add the three numbers.

8.1 + 3.7 = 11.8.

7.9 + 11.8 = 19.7.

Question 18.

3.8 + 4.1 + 3.3

Answer:

3.8 + 4.1 + 3.3 = 11.2.

Explanation:

In the above-given question,

given that,

the three numbers are 3.8, 4.1, and 3.3.

add the three numbers.

3.8 + 4.1 = 7.9.

3.3 + 7.9 = 11.2.

**Problem Solving**

Question 19.

**Construct Arguments** The cost of one DVD is $16.98, and the cost of another DVD is $9.29. Ed estimated the cost of the two DVDs to be about $27. Is his estimate higher or lower than the actual cost? Explain.

Answer:

The estimate is equal.

Explanation:

In the above-given question,

given that,

The cost of one DVD is $16.98, and the cost of another DVD is $9.29.

Ed estimated the cost of the two DVDs to be about $27.

16.98 + 9.29 = 26.27.

the estimate is equal to the actual cost.

Question 20.

**Higher Order Thinking** A teacher is organizing a field trip. Each bus can seat up to 46 people. Is it better to estimate a greater or lesser number than the actual number of people going on the field trip? Why?

Answer:

The estimation is lesser than the actual number of people going on the field trip.

Explanation:

In the above-given question,

given that,

A teacher is organizing a field trip.

Each bus can seat up to 46 people.

the estimate a lesser number than the actual number of people going on the field trip.

Question 21.

The size and shape of Golden Gate Park are often compared to the size and shape of Central Park. About how many more acres does Golden Gate Park cover than Central Park?

Answer:

The number of acres does Golden Gate Park covers than central park = 174 acres.

Explanation:

In the above-given question,

given that,

The size and shape of Golden Gate Park are often compared to the size and shape of the central park.

the central park in New York City has an area of 843 acres.

Golden Gate Park in San Francisco, California, has an area of 1,017 acres.

1017 – 843 = 174.

so the number of acres does Golden Gate Park covers than central park = 174.

**Assessment Practice**

Question 22.

Three rock samples have masses of 74.05 grams, 9.72 grams, and 45.49 grams. A scientist estimates the total mass of the samples by rounding each mass to the nearest whole number. Which lists the numbers he will add?

A. 75, 10, and 46

B. 74.1, 9.7, and 45.5

C. 74, 10, and 45

D. 75, 10, and 50

Answer:

Option A is the correct answer.

Explanation:

In the above-given question,

given that,

Three rock samples have masses of 74.05 grams, 9.72 grams, and 45.49 grams.

A scientist estimates the total mass of the samples by rounding each mass to the nearest whole number.

74.05 = 75.

9.72 = 10.

45.49 = 46.

so option A is the correct answer.

Question 23.

Umberto buys a game for $7.89 and some batteries for $5.49. He pays with a $20 bill. Which is the best estimate of how much change he should get?

A. $5.00

B. $7.00

C. $13.00

D. $17.00

Answer:

The better estimate of change he should get = $7.00.

Explanation:

In the above-given question,

given that,

Umberto buys a game for $7.89 and some batteries for $5.49.

He pays with a $20 bill.

7.89 + 5.49 = 13.38.

20 – 13.38 = 6.62.

so option B is correct.

### Lesson 2.3 Use Models to Add and Subtract Decimals

**Solve & Share**

Gloria rode her bicycle 0.75 mile in the morning and 1.40 miles in the afternoon. How many miles did Gloria ride in all? Solve this problem any way you choose.

You can use tools, such as place-value blocks, to help determine how many miles Gloria rode.

Answer:

The number of miles did Gloria ride in all = 2.15.

Explanation:

In the above-given question,

given that,

Gloria rode her bicycle 0.75 miles in the morning and 1.40 miles in the afternoon.

0.75 + 1.40 = 2.15.

so the number of miles did Gloria ride in all = 2.15.

**Look Back!** **Make Sense and Persevere** How can you check that your answer is reasonable?

**Visual Learning Bridge**

**Essential Question**

How Can You Use Models to Add Decimals?

**A.**

Use the table at the right to find the total monthly cost of using the dishwasher and the DVD player.

Place-value blocks can be used to add decimals.

Use compatible numbers to estimate. $0.85 + $0.40 is about $0.80 + $0.40, so the sum is about $1.20.

**B.**

Use place-value blocks to model $0.85 + $0.40.

**C.**

Combine the blocks. Regroup when you can.

The monthly cost of using the dishwasher and DVD player is $1.25.

**Convince Me!** Critique Reasoning For the example above, Jesse said, “The total monthly cost of using the ceiling light and the dishwasher was $0.74.” Is Jesse correct? Explain.

Answer:

No, Jesse was not correct.

Explanation:

In the above-given question,

given that,

the total monthly cost of using the ceiling light and the dishwasher was $0.74.

the total monthly cost of using the ceiling light = $0.89.

the total monthly cost of using the dishwasher = $0.85.

0.89 + 0.85 = 1.74.

so Jesse was not correct.

**Another Example**

You can subtract decimals with place-value blocks. Find 1.57 – 0.89.

**Step 1**

Show 1.57 with place-value blocks.

**Step 2**

To subtract 0.89, regroup the blocks and remove 8 tenths and 9 hundredths. The blocks remaining are the difference.

**Guided Practice**

**Do You Understand?**

Question 1.

Explain how to use place-value blocks to find the difference between the monthly cost of using the DVD player and the dishwasher. Then find the difference.

Answer:

The difference between the DVD player and the dishwasher = $0.45.

Explanation:

In the above-given question,

given that,

the cost of a DVD player is $0.40.

the cost of the dishwasher is $0.85.

0.85-0.40 = 0.45.

so the difference between DVD player and the dishwasher = $0.45.

**Do You Know How?**

In 2-7, use place-value blocks to add or subtract.

Question 2.

1.22 +0.34

Answer:

1.22 + 0.34 = 1.56.

Explanation:

In the above-given question,

given that,

the two numbers are 1.22 and 0.34.

add the two numbers.

1.22 + 0.34 = 1.56.

Question 3.

0.63 +0.41

Answer:

0.63 + 0.41 = 1.04.

Explanation:

In the above-given question,

given that,

the two numbers are 0.63 and 0.41.

add the two numbers.

0.63 + 0.41 = 1.04.

Question 4.

2.73 – 0.94

Answer:

2.73 – 0.94 = 1.99.

Explanation:

In the above-given question,

given that,

the two numbers are 2.73 and 0.94.

subtract the two numbers.

2.73 – 0.94 = 1.99.

Question 5.

$1.38 – $0.73

Answer:

$1.38 – $0.73 = $0.65.

Explanation:

In the above-given question,

given that,

the two numbers are 1.38 and 0.73.

subtract the two numbers.

1.38 – 0.73 = $0.65.

Question 6.

0.47 – 0.21

Answer:

0.47 – 0.21 = 0.26.

Explanation:

In the above-given question,

given that,

the two numbers are 0.47 and 0.21.

subtract the two numbers.

0.47 – 0.21 = 0.26.

Question 7.

2.02 + 0.8

Answer:

2.02 + 0.8 = 2.82.

Explanation:

In the above-given question,

given that,

the two numbers are 2.02 and 0.8.

add the two numbers.

2.02 + 0.8 = 2.82.

**Independent Practice**

In 8-11, add or subtract. Use place-value blocks to help.

Question 8.

0.1 + 0.73

Answer:

0.1 + 0.73 = 0.83.

Explanation:

In the above-given question,

given that,

the two numbers are 0.1 and 0.73.

add the two numbers.

0.1 + 0.73 = 0.83.

Question 9.

$1.33 – $0.35

Answer:

$1.33 – $0.35 = 0.98.

Explanation:

In the above-given question,

given that,

the two numbers are 1.33 and 0.35.

subtract the two numbers.

1.33 – 0.35 = $0.98.

Question 10.

$0.37 + $0.47

Answer:

$0.37 + $0.47 = $0.84.

Explanation:

In the above-given question,

given that,

the two numbers are $0.37 and 0.47.

add the two numbers.

0.37 + 0.47 = 0.84.

Question 11.

1.11 +0.89

Answer:

1.11 + 0.89 = 2.00.

Explanation:

In the above-given question,

given that,

the two numbers are 1.11 and 0.89.

add the two numbers.

1.11 + 0.89 = 2.

**Problem Solving**

Question 12.

Construct Arguments How is adding 4.56 + 2.31 similar to adding $2.31 + $4.56?

Answer:

4.56 + 2.31 is equal to 2.31 + 4.56.

Explanation:

In the above-given question,

given that,

the two numbers are 4.56 and 2.31.

add the two numbers.

2.31 + 4.56 = 6.87.

Question 13.

Write an expression that is represented by the model below.

Answer:

The number is 1.45.

Explanation:

In the above-given question,

given that,

there is one hundred blocks.

1.

there are 4 tens blocks.

0.4.

there are 5 ones blocks.

1 + 0.4 + 0.05 = 1.45.

Question 14.

Without adding the decimals, tell if the sum of 0.46 + 0.25 is less than or greater than 1? Explain.

Answer:

The sum is greater than 1.

Explanation:

In the above-given question,

given that,

0.46 + 0.25 = 0.71.

46 + 25 = 71.

71 is greater than 1.

so the sum is greater than 1.

Question 15.

**Number Sense** Estimate to decide if the sum of 314 + 175 is more or less than 600.

Answer:

The sum is less than 600.

Explanation:

In the above-given question,

given that,

the two numbers are 314 + 175 = 489.

489 is less than 600.

so the sum is less than 600.

Question 16.

**Higher Order Thinking** Do you think the difference of 1.4 – 0.95 is less than or greater than 1? Explain.

Answer:

The difference of 1.4 and 0.95 = 0.45.

Explanation:

In the above-given question,

given that,

the two numbers are 1.4 and 0.95 = 489.

0.45 is less than 1.

so the difference is less than 1.

Question 17.

**Vocabulary** Estimate 53.8 – 27.6. Circle the compatible numbers to substitute.

54 – 28 53 – 28 55 – 27 55 – 25

Answer:

The numbers are 54 – 28 = 26.

Explanation:

In the above-given question,

given that,

the numbers are 53.8 and 27.6.

the numbers are 54-28, 53-28, 55-27, and 55-26.

53.8 is equal to 54.

27.6 is equal to 28.

54 – 28 = 26.

Question 18.

**Algebra** Write an expression that can be used to find the perimeter of the pool shown to the right. Remember, perimeter is the distance around a figure.

Answer:

The perimeter of the figure = 1250 sq m.

Explanation:

In the above-given question,

given that,

the length and breadth of the rectangle.

l = 50 m.

b = 25 m.

area = l x b.

area of the rectangle = l x b.

50 x 25 = 1250.

so the perimeter of the figure = 1250 sq m.

**Assessment Practice**

Question 19.

Each set of place-value blocks below represents a decimal.

**Part A**

What is the sum of the decimals?

**Part B**

Explain how you found your answer.

Answer:

0.3 + 0.01 = 0.31.

0.7 + 0.05 = 0.75.

Explanation:

In the above-given question,

given that,

there are 3 tens blocks.

there are 2 one’s blocks.

0.3 + 0.01 = 0.31.

there are 7 tens blocks.

there are 5 ones blocks.

0.7 + 0.05 = 0.75.

## Lesson 2.4 Use Strategies to Add Decimals

**Activity**

**Solve & Share**

Mr. Davidson has two sacks of potatoes. The first sack weighs 11.39 pounds. The second sack weighs 14.27 pounds. How many pounds of potatoes does Mr. Davidson have in all? Solve this problem any way you choose.

You can generalize what you know about whole number addition to decimal addition

**Look Back!** How is adding decimals similar to adding whole numbers?

Answer:

The number of pounds of potatoes does Mr. Davidson has in all = 25.66.

Explanation:

In the above-given question,

given that,

Mr. Davidson has two sacks of potatoes.

The first sack weighs 11.39 pounds.

The second sack weighs 14.27 pounds.

11.39 + 14.27 = 25.66.

so the number of pounds of potatoes does Mr. Davidson has in all = 25.66.

**Visual Learning Bridge**

**Essential Question** How Can You Add Decimals?

**A.**

A swim team participated in a relay race. The swimmers’ times for each leg of the race were recorded in a table. What was the combined time for Caleb and Bradley’s legs of the relay race?

You can find 21.39 + 21.59, but estimate first: 21 + 22 = 43.

**B.**

**Step 1**

Just like with whole numbers, line up the addends by place value. The decimal points will also line up.

**C.
Step 2**

Use what you know about partial sums to add the hundredths, tenths, ones, and tens.

The combined time for Caleb and Bradley was 42.98 seconds. The sum is close to the estimate.

Adding decimals is just like adding whole numbers!

**Convince Me!** **Critique Reasoning** André said the last two legs of the race took 3,938 seconds. What mistake did he make?

**Another Example**

Carson ran 7.81 miles last week. He ran 14 miles this week. How many miles did he run in the two weeks?

Use properties and a number line to find the sum.

7.81 + 14 = 14 + 7.81 (Commutative Property)

= 14 + (7 + 0.81)

= (14 + 7) + 0.81 (Associative Property)

= 21 + 0.81

= 21.81

Carson ran 21.81 miles in all.

A number line can help you visualize adding decimals.

**Guided Practice**

**Do You Know How?**

Question 1.

How is adding 21.39 + 21.59 like adding 2,139 + 2,159?

Answer:

The sum is the same.

Explanation:

In the above-given question,

given that,

the two numbers are 21.39 and 21.59.

add two numbers.

21.39 + 21.59 = 42.98.

2139 + 2159 = 4298.

so both are the same.

**Do You Understand?**

In 2-5, use place value and properties to find each sum.

Question 2.

0.82 + 4.21

Answer:

0.82 + 4.21 = 5.03.

Explanation:

In the above-given question,

given that,

the two numbers are 0.82 and 4.21.

add the two numbers.

0.82 + (4 + 0.21).

(0.82 + 0.21) + 4.

1.03 + 4.

5.03.

Question 3.

9.1 + 7.21

Answer:

9.1 + 7.21 = 16.31.

Explanation:

In the above-given question,

given that,

the two numbers are 9.1 and 7.21.

add the two numbers.

9.1 + (7 + 0.21).

(9.1 + 0.21) + 7.

9.31 + 7.

16.31.

Question 4.

0.26 + 8.3

Answer:

0.26 + 8.3 = 8.56.

Explanation:

In the above-given question,

given that,

the two numbers are 0.26 and 8.3.

add the two numbers.

0.26 + (8 + 0.3).

(0.26 + 0.3) + 8.

0.56 + 8.

8.56.

Question 5.

4.98 + 3.02

Answer:

4.98 + 3.02 = 8.00.

Explanation:

In the above-given question,

given that,

the two numbers are 4.98 and 3.02.

add the two numbers.

4.98 + (3 + 0.2).

(4.98 + 0.2) + 3.

5 + 3.

8.

**Independent Practice**

You can estimate first to be sure your answers are reasonable.

**Leveled Practice** In 6-12, use place value and properties of operations to find each sum.

Question 6.

Answer:

1.03 + 0.36 = 1.39.

Explanation:

In the above-given question,

given that,

the two numbers are 1.03 and 0.36.

add the two numbers.

0.36 + (1 + 0.3).

(0.36 + 0.3) + 1.

0.96 + 1.

1.03 + 0.36 = 1.39.

Question 7.

Answer:

6.9 + 2.8 = 9.7.

Explanation:

In the above-given question,

given that,

the two numbers are 6.9 and 2.8.

add the two numbers.

6.9 + (2 + 0.8).

(6.9 + 0.8) + 2.

7.7 + 2.

6.9 + 2.8 = 9.7

Question 8.

Answer:

45.08 + 2.01 = 47.09.

Explanation:

In the above-given question,

given that,

the two numbers are 45.08 and 2.01.

add the two numbers.

45.08 + (2 + 0.1).

(45.08 + 0.1) + 2.

45.09 + 2.

45.08 + 2.01 = 47.09.

Question 9.

Answer:

2.00 + 0.78 = 2.78.

Explanation:

In the above-given question,

given that,

the two numbers are 2.00 and 0.78.

add the two numbers.

0.78 + (1 + 1.0).

(0.78 + 1.0) + 1.

1.78 + 1.

2.00 + 0.78 = 2.78.

Question 10.

$271.90 + $34.22

Answer:

$271.90 + $34.22 = $316.12.

Explanation:

In the above-given question,

given that,

the two numbers are $271.90 and $34.22.

add the two numbers.

271.90 + (34 + 0.22).

(271.90 + 0.22) + 34.

272.12 + 34.

$271.90 + $34.22 = $316.12.

Question 11.

7.2 + 3.96 + 8.8

Answer:

7.2 + 3.96 + 8.8 = 19.96.

Explanation:

In the above-given question,

given that,

the two numbers are 7.2, 88, and 3.96.

add the three numbers.

7.2 + (88 + 3.96).

(7.2 + 3.96) + 88.

1.16 + 88.

7.2 + 3.96 + 8.8 = 19.96.

Question 12.

16.62 + 4 + 2.38

Answer:

16.62 + 4 + 2.38 = 23.

Explanation:

In the above-given question,

given that,

the two numbers are 16.62,4 and 2.38.

add the two numbers.

16.62 + (4 + 2.38).

(16.62 + 4) + 2.38.

16.66 + 2.38.

16.62 + 4 + 2.38 = 23.

**Problem Solving**

Question 13.

A farmer sold 53.2 pounds of carrots and 29.4 pounds of asparagus to a restaurant. How many pounds of these two vegetables did the restaurant buy?

Answer:

The number of pounds of these two vegetables did the restaurant buy = 82.6.

Explanation:

In the above-given question,

given that,

A farmer sold 53.2 pounds of carrots and 29.4 pounds of asparagus to a restaurant.

the two numbers are 53.2 and 29.4.

53.2 + 29.4 = 82.6.

so the number of pounds of these two vegetables did the restaurant buy = 82.6.

For 14 and 15, use the table.

Question 14.

**enVision® STEM** Which two cities have the greatest combined rainfall for a typical year?

Answer:

The two cities have the greatest combined rainfall for a typical year =

Explanation:

In the above-given question,

given that,

the cities that have the rainfall are:

Macon 45 inches.

Boise 12.19 inches.

Caribou 37.44 inches.

Springfield 44.97 inches.

the two cities that have the greater rainfall are Caribou and Springfield.

Question 15.

**Number Sense** Which location had less than 45 inches of rain but more than 40 inches of rain?

Answer:

The location that had less than 45 inches of rain but more than 40 inches of rain = Springfield, MO.

Explanation:

In the above-given question,

given that,

the cities that have the rainfall are:

Macon 45 inches.

Boise 12.19 inches.

Caribou 37.44 inches.

Springfield 44.97 inches.

44.97 < 45.

44.97 > 40.

so the location that had less than 45 inches of rain but more than 40 inches of rain = Springfield, MO.

Question 16.

**Higher Order Thinking** Tim earned $16 babysitting and $17.50 mowing a lawn. He paid $8.50 for a movie and bought a small popcorn for $1.95. Write an expression to show how much money he has left.

Answer:

The expression to show how much money he has left = $43.95.

Explanation:

In the above-given question,

given that,

Tim earned $16 babysitting and $17.50 mowing a lawn.

He paid $8.50 for a movie and bought a small popcorn for $1.95.

$16 + $17.50 + $8.50 + $1.95.

$16 + $17.50 = 33.5.

$8.50 + $1.95 = 10.45.

$33.5 + 10.45 = $43.95.

Question 17.

**Critique Reasoning** Juan adds 3.8 + 4.6 and gets a sum of 84. Is his answer correct? Tell how you know.

Answer:

No, he was not correct.

Explanation:

In the above-given question,

given that,

Juan adds 3.8 + 4.6 and gets a sum of 84.

3.8 + 4.6 = 8.4.

the sum is the same but the values are not the same.

so he was not correct.

**Assessment Practice**

Question 18.

Choose all expressions that are equal to 12.9.

0.02 + 12 + 0.88

0.06 + 12.03

11.9 + 1

6.2 + 3.4 + 2.3

3.01 + 2.01 + 7.7

Answer:

Options A and B are correct.

Explanation:

In the above-given question,

given that,

the expressions are 0.02 + 12 + 0.88.

0.02 + 12 = 12.02.

12.02 + 0.88 = 12.90.

11.9 + 1 = 12.9.

so the options A and B are correct.

Question 19.

Choose all expressions that are equal to 16.02.

16 + 0.02

3.42 + 8 + 4.6

16.01 + 1

12.06 + 3.14

7.36 +8.66

Answer:

Options A and B are correct.

Explanation:

In the above-given question,

given that,

the expressions are 16 + 0.02.

16.02.

3.42 + 8 + 4.6 = 16.02.

so options A and B are correct.

### Lesson 2.5 Use Strategies to Subtract Decimals

**Solve & Share**

Ms. Garcia is an electrician and has a length of wire that is 32.7 meters long. She has another length of wire that is 15.33 meters long. How much longer is one wire than the other? Solve this problem any way you choose.

You can use what you know about whole number subtraction to subtract decimals.

Answer:

The longer is one wire than the other = 17.37 meters.

Explanation:

In the above-given question,

given that,

Ms. Garcia is an electrician and has a length of wire that is 32.7 meters long.

She has another length of wire that is 15.33 meters long.

15.33 + 32.7 = 48.03.

32.7 – 15.33 = 17.37.

so the longer is one wire than the other = 17.37 meters.

**Look Back!** Use Structure How can you use the relationship between addition and subtraction to check your work above?

**Visual Learning Bridge**

**Essential Question**

How Can You Subtract Decimals?

**A.**

What is the difference in the wingspans of the two butterflies?

Estimate before you find the exact answer.

6 – 4 = 2

**B.**

You can use a number line to subtract.

**C.**

Here’s one way to subtract using partial differences.

Find 5.92 – 4.37

5.92 – 4.37 = 1.55

**Convince Me!** Be Precise in the solution above, what strategies can you use to subtract the 7 hundredths?

**Guided Practice**

**Do You Understand?**

Question 1.

How can you use addition to check that 1.55 cm is the difference in the wingspans of the two butterflies?

Answer:

The answers are 3.00 and 1.45.

Explanation:

In the above-given question,

given that,

the two numbers are 3.00 and 1.45.

3.00 – 1.45 = 1.55.

so the difference is 1.55.

the answers are 3.00 and 1.45.

Question 2.

Maria rewrote 45.59 – 7.9 as 45.59 – 7.90. Did she change the value of 7.9 by placing the zero after 7.9? Why or why not?

Answer:

Yes, she changed the value of 7.9 by placing the zero.

Explanation:

In the above-given question,

given that,

Maria rewrote 45.59 – 7.9 as 45.59 – 7.90.

45.59 – 7.9 = 37.69.

yes, she changed the value of 7.9 by placing the zer0.

**Do You Know How?**

In 3-10, subtract the decimals.

Question 3.

16.82 – 5.21

Answer:

16.82 – 5.21 = 11.61.

Explanation:

In the above-given question,

given that

the two numbers are 16.82 and 5.21.

subtract the numbers.

16.82 – 5.21 = 11.61.

Question 4.

7.21 – 6.1

Answer:

7.21 – 6.1 = 1.1.

Explanation:

In the above-given question,

given that

the two numbers are 7.21 and 6.1.

subtract the numbers.

7.21 – 6.1 = 1.1.

Question 5.

23.06 – 8.24

Answer:

23.06 – 8.24 = 14.82

Explanation:

In the above-given question,

given that

the two numbers are 23.06 and 8.24.

subtract the numbers.

23.06 – 8.24 = 14.82.

Question 6.

$4.08 – $2.12

Answer:

$4.08 – $2.12 = $1.96.

Explanation:

In the above-given question,

given that

the two numbers are $4.08 and $2.12.

subtract the numbers.

$4.08 – $2.12 = $1.96.

Question 7.

56.8 – 2.76

Answer:

56.8 – 2.76 = 54.04.

Explanation:

In the above-given question,

given that

the two numbers are 56.8 and 2.76.

subtract the numbers.

56.8 – 2.76 = 54.04.

Question 8.

$43.80 – $16.00

Answer:

$43.80 – $16.00 = $27.8.

Explanation:

In the above-given question,

given that

the two numbers are $43.80 and $16.00.

subtract the numbers.

$43.80 – $16.00 = $27.8.

Question 9.

22.4 – 10.7

Answer:

22.4 – 10.7 = 11.7.

Explanation:

In the above-given question,

given that

the two numbers are 22.4 and 10.7.

subtract the numbers.

22.4 – 10.7 = 11.7.

Question 10.

$36.40 – $21.16

Answer:

$36.40 – $21.16 = $15.24.

Explanation:

In the above-given question,

given that

the two numbers are $36.40 and $21.16.

subtract the numbers.

$36.40 – $21.16 = $15.24.

**Independent Practice**

**Leveled Practice** In 11-26, find the difference.

Question 11.

7.8 – 4.9

Answer:

7.8 – 4.9 = 2.9.

Explanation:

In the above-given question,

given that

the two numbers are 7.8 and 4.9.

subtract the numbers.

7.8 – 4.9 = 2.9.

Question 12.

$20.60 – $14.35

Answer:

$20.60 – $14.35 = $6.25.

Explanation:

In the above-given question,

given that

the two numbers are $20.60 and $14.35.

subtract the numbers.

$20.60 – $14.35 = $6.25.

Question 13.

43.90 – 7.52

Answer:

43.90 – 7.52 = 36.38.

Explanation:

In the above-given question,

given that

the two numbers are 43.90 and 7.52.

subtract the numbers.

43.90 – 7.52 = 36.38.

Question 14.

65.90 – 28.38

Answer:

65.90 – 28.38 = 37.52.

Explanation:

In the above-given question,

given that

the two numbers are 65.90 and 28.38.

subtract the numbers.

65.90 – 28.38 = 37.52.

Question 15.

15.03 – 4.12

Answer:

15.03 – 4.12 = 10.91.

Explanation:

In the above-given question,

given that

the two numbers are 15.03 and 4.12.

subtract the numbers.

15.03 – 4.12 = 10.91.

Question 16.

13.9 – 3.8

Answer:

13.9 – 3.8 = 10.1.

Explanation:

In the above-given question,

given that

the two numbers are 13.9 and 3.8.

subtract the numbers.

13.9 – 3.8 = 10.1.

Question 17.

65.18 – 12.05

Answer:

65.18 – 12.05 = 53.13.

Explanation:

In the above-given question,

given that

the two numbers are 65.18 and 12.05.

subtract the numbers.

65.18 – 12.05 = 53.13.

Question 18.

$52.02 – $0.83

Answer:

$52.02 – $0.83 = $51.19.

Explanation:

In the above-given question,

given that

the two numbers are $52.02 and $0.83.

subtract the numbers.

$52.02 – $0.83 = $51.19.

Question 19.

7.09 – 3.65

Answer:

7.09 – 3.65 = 3.44.

Explanation:

In the above-given question,

given that

the two numbers are 7.09 and 3.65.

subtract the numbers.

7.09 – 3.65 = 3.44.

Question 20.

34.49 – 12.61

Answer:

34.49 – 12.61 = 21.88

Explanation:

In the above-given question,

given that

the two numbers are 34.49 and 12.61.

subtract the numbers.

34.49 – 12.61 = 21.88.

Question 21.

85.22 – 43.5

Answer:

85.22 – 43.5 = 41.72.

Explanation:

In the above-given question,

given that

the two numbers are 85.22 and 43.5.

subtract the numbers.

85.22 – 43.5 = 41.72.

Question 22.

$10.05 – $4.50

Answer:

$10.05 – $4.50 = $5.55.

Explanation:

In the above-given question,

given that

the two numbers are $10.05 and $4.50.

subtract the numbers.

$10.05 – $4.50 = $5.55.

Question 23.

5.27 – 3.4

Answer:

5.27 – 3.4 = 1.87.

Explanation:

In the above-given question,

given that

the two numbers are 5.27 and 3.4.

subtract the numbers.

5.27 – 3.4 = 1.87

Question 24.

23.6 – 8.27

Answer:

23.6 – 8.27 = 15.33.

Explanation:

In the above-given question,

given that

the two numbers are 23.6 and 8.27.

subtract the numbers.

23.6 – 8.27 = 15.33.

Question 25.

8.04 – 0.3

Answer:

8.04 – 0.3 = 7.74.

Explanation:

In the above-given question,

given that

the two numbers are 8.04 and 0.3.

subtract the numbers.

8.04 – 0.3 = 7.74.

Question 26.

$21.37 – $10.95

Answer:

$21.37 – $10.95 = $10.42.

Explanation:

In the above-given question,

given that

the two numbers are $21.37 and $10.95.

subtract the numbers.

$21.37 – $10.95 = $10.42.

**Problem Solving**

Question 27.

**Algebra** The Pyramid of Khafre measured 143.5 meters high. The Pyramid of Menkaure measured 65.5 meters high. Write and solve an equation to find d, the difference in the heights of these two pyramids.

Answer:

The difference in the heights of these two pyramids = 143.5.

Explanation:

In the above-given question,

given that,

The Pyramid of Khafre measured 143.5 meters high.

The Pyramid of Menkaure measured 65.5 meters high.

143.5 – 65.5 = 78.

78 + 65.5 = 143.5.

so the difference in the heights of these two pyramids = 143.5.

Question 28.

**Higher Order Thinking** Jonah bought a 1.5-liter bottle of seltzer. He used 0.8 liter of seltzer in some punch. Which is greater, the amount he used or the amount he has left? Explain how you decided

Answer:

The amount he used is greater.

Explanation:

In the above-given question,

given that,

Johan bought a 1.5-liter bottle of seltzer.

He used 0.8 liters of seltzer in some punch.

1.5 – 0.8 = 0.7.

the amount he used is greater.

Question 29.

Sue subtracted 2.9 from 20.9 and got 1.8. Explain why this is not reasonable.

Answer:

2.9 – 20.9 = 18.

Explanation:

In the above-given question,

given that,

Sue subtracted 2.9 from 20.9 and got 1.8.

2.9 and 2.9 is the difference and got 1.8.

2.9 – 20.9 = 18.

so this is not reasonable.

Question 30.

**Make Sense and Persevere** Abe had $156.43 in his bank account at the beginning of the month. He made the two withdrawals shown in his check register. How much money does he have left in his bank account? He must have at least $100 in his account by the end of the month or he will be charged a fee. How much money does he need to deposit to avoid being charged a fee?

Answer:

The money does he need to deposit to avoid being charged a fee = $60.59.

Explanation:

In the above-given question,

given that,

Abe had $156.43 in his bank account at the beginning of the month.

He made the two withdrawals shown in his check register.

$156.43 + $17.85 = $174.28.

100 – 39.41 = 60.59.

so the money does he need to deposit to avoid being charged a fee = $60.59.

**Assessment Practice**

Question 31.

Circle all of the subtraction problems with a difference of 1.65.

27.30 – 16.65

11.23 – 9.58

40.4 – 23.9

12.68 – 2.03

21.74 – 20.09

Answer:

The subtraction problems with a difference of 1.65 is second and fifth expression.

Explanation:

In the above-given question,

given that,

27.30 – 16.65 = 10.65.

11.23 – 9.58 = 1.65.

40.4 – 23.9 = 16.5.

12.68 – 2.03 = 10.65.

21.74 – 20.09 = 1.65.

Lesson 2.6 Model with Math

**Activity**

**Problem Solving**

**Solve & Share**

At a baseball game, Sheena bought a sandwich for $6.95 and two pretzels for $2.75 each. She paid with a $20 bill. How much change did she receive? Solve this problem any way you choose. Use bar diagrams to help.

Answer:

The change did she receive = $10.3.

Explanation:

In the above-given question,

given that,

At a baseball game, Sheena bought a sandwich for $6.95 and two pretzels for $2.75 each.

She paid with a $20 bill.

$6.95 + $2.75 = $9.7.

$20 – $9.7 = $10.3.

so the change did she recieve = $10.3.

**Thinking Habits**

Be a good thinker!

• These questions can help you. How can I use math I know to help solve the problem?

• How can I use pictures, objects, or an equation to represent the problem?

• How can I use numbers, words, and symbols to solve the problem?

**Look Back!** **Model with Math** What other way can you represent this problem situation?

**Visual Learning Bridge**

**Essential Question** How Can You Represent a Problem with Bar Diagrams?

**A.**

Monica wants to buy all of the art supplies shown on this sign. She has a coupon for $5.50 off the cost of her purchases. What will Monica’s total cost be after the discount?

**Model with math** means you apply math you have learned to solve problems.

What do I need to do to solve the problem?

I need to find Monica’s cost for the art supplies.

Here’s my thinking

**B.**

**How can I model with math?**

**I can**

• use the math I know to help solve the problem.

• find and answer any hidden questions.

• use bar diagrams and equations to represent and solve this problem.

**C.**

I will use bar diagrams to represent this situation.

$59.95 + $24.95 + $9.75 + $13.50 = $108.15

The total cost before the discount is $108.15.

$108.15 – $5.50 = $102.65

Monica’s cost after the discount is $102.65.

**Convince Me! Model with Math** How could you decide if your answer makes sense?

**Guided Practice**

**Model with Math** Nate has $30.50. He wants to buy his dog a sweater that costs $15, a toy that costs $3.79, and a leash that costs $14.79. How much more money does he need?

Answer:

The more money does he need = $3.08.

Explanation:

In the above-given question,

given that,

Nate has $30.50.

He wants to buy his dog a sweater that costs $15.

a toy that costs $3.79, and a leash that costs $14.79.

$15 + $3.79 + $14.79 = 33.58.

33.58 – 30.50 = 3.08.

so the more money does he need = $3.08.

When you model with math you use the math you already know to solve new problems!

Question 1.

What do you need to find before you can solve the problem?

Answer:

The more money does he need = $3.08.

Explanation:

In the above-given question,

given that,

Nate has $30.50.

He wants to buy his dog a sweater that costs $15.

a toy that costs $3.79, and a leash that costs $14.79.

$15 + $3.79 + $14.79 = 33.58.

33.58 – 30.50 = 3.08.

so the more money does he need = $3.08.

Question 2.

Draw bar diagrams to represent the problem and then solve the problem. Show the equations you used to solve the problem.

Answer:

The more money does he need = $3.08.

Explanation:

In the above-given question,

given that,

Nate has $30.50.

He wants to buy his dog a sweater that costs $15.

a toy that costs $3.79, and a leash that costs $14.79.

$15 + $3.79 + $14.79 = 33.58.

33.58 – 30.50 = 3.08.

so the more money does he need = $3.08.

**Independent Practice**

**Model with Math**

Luz Maria has $15. She buys a ticket to a movie and a smoothie. How much money does she have left?

Question 3.

What do you need to find before you can solve the problem?

Answer:

The money does she have left = 412.35.

Explanation:

In the above-given question,

given that,

Luz Maria has $15.

She buys a ticket to a movie and a smoothie.

$9.50 + $2.85 = $12.35.

so the money does she have left = $12.35.

Question 4.

Draw two bar diagrams to represent the problem.

Answer:

The money does she have left = 412.35.

Explanation:

In the above-given question,

given that,

Luz Maria has $15.

She buys a ticket to a movie and a smoothie.

$9.50 + $2.85 = $12.35.

so the money does she have left = $12.35.

Question 5.

What is the solution to the problem? Show the equations you used to solve the problem.

Answer:

The money does she have left = 412.35.

Explanation:

In the above-given question,

given that,

Luz Maria has $15.

She buys a ticket to a movie and a smoothie.

$9.50 + $2.85 = $12.35.

so the money does she have left = $12.35.

**Problem Solving**

**Performance Task**

**School Trip**

Audrey is saving for a school trip. She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals. The table shows how much money she and her sister, Kelsey, have saved over a 4-month period. How much more money does Audrey need for the trip?

Question 6.

**Make Sense and Persevere** What are you trying to find?

Answer:

The more money does Audrey needs for the trip = $143.

Explanation:

In the above-given question,

given that,

Audrey is saving for a school trip.

She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals.

$68 + $31.50 + $158 + $74.75 = 332.25.

180 + 215 + 80 = 475.

475 – 332 = 143.

so the more money does Audrey needs for the trip = $143.

Question 7.

**Construct Arguments** Should you multiply Audrey’s savings for September by 4 since there are 4 months? Explain.

Answer:

No, we cannot multiply by 4.

Explanation:

In the above-given question,

given that,

Audrey’s savings for September is $68.

$68 x 4 = $272.

so we cannot multiply by 4.

You can model with math by using what you know about adding and subtracting whole numbers to add and

subtract decimals.

Question 8.

**Model with Math** Draw bar diagrams to represent the total cost of Audrey’s trip and the total she has saved. Then find the total cost and total savings.

Answer:

The total cost of Audrey’s trip is 332.25.

Explanation:

In the above-given question,

given that,

The total she has saved = 332.25.

the total cost of Audrey’s trip = 332.25.

Question 9.

**Model with Math** Write and solve an equation to determine how much more money Audrey needs for the trip.

Answer:

The more money Audrey needs for the trip = 475.

Explanation:

In the above-given question,

given that,

Audrey is saving for a school trip.

She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals.

$68 + $31.50 + $158 + $74.75 = 332.25.

180 + 215 + 80 = 475.

475 – 332 = 143.

so the more money does Audrey needs for the trip = $143.

### Topic 2 Fluency Review Activity

**Point & Tally**

Find a partner. Get paper and a pencil. Each partner chooses either light blue or dark blue.

Partner 1 and Partner 2 each point to a black number at the same time. Each partner subtracts the lesser number from the greater number.

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

**Topic 2 Vocabulary Review**

**Glossary**

**Understand Vocabulary**

**Word List**

• Associative Property of Addition

• Commutative Property of Addition

• compatible numbers

• compensation

• equivalent decimals

• inverse operations

Choose the best term from the Word List. Write it on the blank.

Question 1.

When you adjust one number and change another number in the problem to make a computation easier, you use ____.

Answer:

We will use the compensation.

Explanation:

In the above-given question,

given that,

when you adjust one number and change another number in the problem to make computation easier.

for example:

2 + 3 + 4.

2 + (3 + 4).

(2 + 3) + 4.

5 + 4 = 9.

so we will use the compensation.

Question 2.

You can replace the values in a problem with _____ so that it’s easier to use mental math to complete the computation.

Answer:

We can replace the values in a problem with compatible numbers.

Explanation:

In the above-given question,

given that,

you can replace the values in a problem with compatible numbers.

for example:

3.9 = 4.

4.8 = 5.

4 + 5 = 9.

so we can replace the values in a problem with compatible numbers.

Question 3.

To align decimal points in a decimal addition problem, annex zeros to write ____ so that all addends have the same number of decimal places.

Answer:

To align decimal points in a decimal addition problem, annex zeros to write compensation so that all addends have the same number of decimal places.

Explanation:

In the above-given question,

given that,

for example:

2.99 + 3.79.

3 + 4 = 7.

Question 4.

Because of the ____, I know that 477.75 + (76.89 + 196.25) = (76.89 + 196.25) + 477.75 without adding.

Answer:

We can use associative and commutative properties.

Explanation:

In the above-given question,

given that,

477.75 + (76.89 + 196.25).

(76.89 + 196.25) + 477.75.

so we can use associative and commutative properties.

Question 5.

Cross out the numbers below that are NOT equivalent to 500.0.

500.00 5 × 10 5 × 10^{2} 50.05 500.500

Answer:

500, 5 x 10 x 10.

Explanation:

In the above-given question,

given that,

the numbers are 500, 5 x 10, 5 x 10 x 10, 50.05.

5 x 10 x 10 = 500.

so the numbers that are not equivalent to 500.

Question 6.

Cross out the numbers below that are NOT equivalent to 53.2 + 16.8.

7 × 10^{1} 0.070 7.0 7 × 7 (7 × 10) + (0 × 1)

Circle the problem that uses compensation.

Question 7.

32.7 + 15.6 = 32.6 + 15.7 45.7 + 26.2 = 45.7 + 26.3 – 0.1

Answer:

Yes, this problem uses the compensation.

Explanation:

In the above-given question,

given that,

the expressions are 32.7 + 15.6 = 32.6 + 15.7.

45.7 + 26.2 = 45.7 + 26.3 – 0.1.

so this uses a compensation.

Question 8.

14.24 – 11.8 = 14.24 – 12 + 0.2 168.3 – 53.8 = 168.3 – 53.4 – 0.4

Answer:

Yes this problem also uses the compensation.

Explanation:

In the above-given question,

given that,

the expressions are 14.24 – 11.8.

14.24 – 12 + 0.2.

168.3 – 53.8 = 168.3 – 53.4 – 0.4.

so this problem also uses the compensation method.

**Use Vocabulary in Writing**

Question 9.

Explain how the Commutative Property of Addition, the Associative Property of Addition and mental math can help you find 75.2 + (57.376 + 24.8). What is the sum?

Answer:

The sum is 157.376.

Explanation:

In the above-given question,

given that,

by using the Associative property of addition and Commutative property of addition.

75.2 + (57.376 + 24.8).

(75.2 + 57.376) + 24.8.

132.576 + 24.8 = 157.376.

so the sum is 157.376.

### Topic 2 Reteaching

**Set A**

pages 45-48

Add 15.3 + 1.1 + 1.7 using mental math.

15.3 and 1.7 are compatible numbers because they are easy to calculate mentally.

The Commutative Property of Addition enables us to add in any order.

15.3 + 1.1 + 1.7 = 15.3 + 1.7 + 1.1

= 17.0 + 1.1

= 18.1

**Remember** that you can use compatible numbers or compensation to find sums and differences.

Use mental math to add or subtract.

Question 1.

8.6 + 23.4 + 1.4

Answer:

8.6 + 23.4 + 1.4 = 33.4.

Explanation:

In the above-given question,

given that,

by using the Associative property of addition and Commutative property of addition.

8.6 + (23.4 + 1.4).

(8.6 + 23.4) + 1.4.

32 + 1.4 = 33.4.

Question 2.

27 – 9.9

Answer:

27 – 9.9 = 17.1.

Explanation:

In the above-given question,

given that,

by using the Associative property of addition and Commutative property of subtraction.

27 – 9.9 = 17.1.

Question 3.

13.5 + 5.7 + 36.5

Answer:

13.5 + 5.7 + 36.5 = 55.7.

Explanation:

In the above-given question,

given that,

by using the Associative property of addition and Commutative property of addition.

13.5 + (5.7 + 36.5).

(13.5 + 5.7) + 36.5.

19.2 + 36.5 = 55.7.

Question 4.

205.4 – 99.7

Answer:

205.4 – 99.7 = 105.7.

Explanation:

In the above-given question,

given that,

the two numbers are 205.4 and 99.7.

subtract the numbers.

205.4 – 99.7 = 105.7.

**Set B**

pages 49-52

Estimate 22.4 – 16.2.

22.4 – 16.2 is about 5.

**Remember** that compatible numbers can give a different estimate than rounding. Estimate each sum or difference.

Question 1.

358 + 293

Answer:

358 + 293 = 651.

Explanation:

In the above-given question,

given that,

the two numbers are 358 + 293.

add the two numbers.

358 + 293 = 651.

Question 2.

15.01 – 4.4

Answer:

15.01 – 4.4 = 10.61.

Explanation:

In the above-given question,

given that,

the two numbers are 15.01 and 4.4.

subtract the two numbers.

15.01 – 4.4 = 10.61.

Question 3.

80.01 + 2.89

Answer:

80.01 + 2.89 = 82.9.

Explanation:

In the above-given question,

given that,

the two numbers are 80.01 and 2.89.

add the two numbers.

80.01 + 2.89 = 82.9.

Question 4.

25,003 – 12,900

Answer:

25003 – 12900 = 12103.

Explanation:

In the above-given question,

given that,

the two numbers are 25003 and 12900.

subtract the two numbers.

25003 – 12900 = 12103.

**Set C**

pages 53-56

Use place-value blocks to subtract 1.86 – 0.95.

Show 1 flat, 8 longs, and 6 small squares to represent 1.86.

Remove 9 tenths and 5 hundredths, regrouping as needed.

Count what is left.

1.86 – 0.95 = 0.91

Add or subtract. Use place-value blocks for help.

Question 1.

0.02 + 0.89

Answer:

0.02 + 0.89 = 0.91.

Explanation:

In the above-given question,

given that,

the two numbers are 0.02 and 0.89.

add the two numbers.

0.02 + 0.89 = 0.91.

Question 2.

0.67 – 0.31

Answer:

0.67 – 0.31 = 0.36.

Explanation:

In the above-given question,

given that,

the two numbers are 15.01 and 4.4.

subtract the two numbers.

0.67 – 0.31 = 0.36.

Question 3.

0.34 + 0.34

Answer:

0.34 + 0.34 = 0.68.

Explanation:

In the above-given question,

given that,

the two numbers are 0.34 and 0.34.

add the two numbers.

0.34 + 0.34 = 0.68.

Question 4.

0.81 – 0.78

Answer:

0.81 – 0.78 = 0.03.

Explanation:

In the above-given question,

given that,

the two numbers are 0.81 and 0.78.

subtract the two numbers.

0.81 – 0.78 = 0.03.

**Set D**

pages 57-60, 61-64

Lucy bought 2.12 pounds of pears and 3 pounds of apples. Find how many more pounds of apples than pears Lucy bought.

Use place-value blocks to help.

Add or subtract. Use place-value blocks to help.

Question 1.

7.06 + 0.85

Answer:

7.06 + 0.85 = 7.91.

Explanation:

In the above-given question,

given that,

the two numbers are 7.06 and 0.85.

add the two numbers.

7.06 + 0.85 = 7.91.

Question 2.

24.07 – 5.31

Answer:

24.07 – 5.31 = 18.76.

Explanation:

In the above-given question,

given that,

the two numbers are 24.07 and 5.31.

subtract the two numbers.

24.07 – 5.31 = 18.76.

Question 3.

51.92 – 28.03

Answer:

51.92 – 28.03 = 23.89.

Explanation:

In the above-given question,

given that,

the two numbers are 51.92 and 28.03.

subtract the two numbers.

51.92 – 28.03 = 23.89.

Question 4.

8.71 – 0.4

Answer:

8.71 – 0.4 = 8.31.

Explanation:

In the above-given question,

given that,

the two numbers are 8.71 and 0.4.

subtract the two numbers.

8.71 – 0.4 = 8.31.

Question 5.

98 + 3.79

Answer:

98 + 3.79 = 101.79.

Explanation:

In the above-given question,

given that,

the two numbers are 98 and 3.79.

add the two numbers.

98 + 3.79 = 101.79.

Question 6.

Talia measured two strings. The green string was 2.37 cm long. The blue string was 4 cm long. How many centimeters longer was the blue string than the green string?

Answer:

The number of centimeters longer was the blue string than the green string = 1.63 cm long.

Explanation:

In the above-given question,

given that,

Talia measured two strings.

The green string was 2.37 cm long.

The blue string was 4 cm long.

4 – 2.37 = 1.63.

so the number of centimeters longer was the blue string than the green string = 1.63 cm long.

**Set E**

pages 65-68

Think about these questions to help you model with math.

**Thinking Habits**

• How can I use math I know to help solve the problem?

• How can I use pictures, objects, or an equation to represent the problem?

• How can I use numbers, words, and symbols to solve the problem?

**Remember** a good model clearly shows how the quantities in the problem are related. Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday. Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday. Who ran farther? How much farther?

Question 1.

What do you need to find before you can solve the problem?

Answer:

Alberto ran farther than Dennis.

Explanation:

In the above-given question,

given that,

Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday.

Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday.

15.6 + 12.8 + 6.5 = 34.9.

11.25 + 14.6 + 8 = 33.85.

Alberto ran farther than Dennis.

34.9 – 33.85 = 1.05.

Question 2.

Write equations to model this problem. Then solve the problem.

Answer:

Alberto ran farther than Dennis.

Explanation:

In the above-given question,

given that,

Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday.

Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday.

15.6 + 12.8 + 6.5 = 34.9.

11.25 + 14.6 + 8 = 33.85.

Alberto ran farther than Dennis.

34.9 – 33.85 = 1.05.

### Topic 2 Assessment Practice

Question 1.

Kayla’s dollhouse has 15.15 square feet downstairs and 6.45 square feet upstairs. What is the estimated total area if you round the decimals to the nearest tenth?

A. 21.0

B. 21.6

C. 21.7

D. 22.0

Answer:

Option C is correct.

Explanation:

In the above-given question,

given that,

Kayla’s dollhouse has 15.15 square feet downstairs and 6.45 square feet upstairs.

15.15 = 15.2.

6.45 = 6.5.

15.2 + 6.5 = 21.7.

so option C is correct.

Question 2.

Estimate the sum of $12.15, $16.85, and $1.74 by rounding each number to the nearest tenth.

A. $30.70

B. $30.80

C. $31.00

D. $30.00

Answer:

Option B was correct.

Explanation:

In the above-given question,

given that,

estimate the sum by rounding each number to the nearest tenth.

$12.15 + $16.85 + $1.74 = $30.80.

so option B was correct.

Question 3.

What is the sum of 2.65 +3.78?

A. 5.33

B. 5.43

C. 6.33

D. 6.43

Answer:

Option D is correct.

Explanation:

In the above-given question,

given that,

the two numbers are 2.65 and 3.78.

add the two numbers.

2.65 + 3.78 = 6.43.

so option D is correct.

Question 4.

Which decimal makes this equation true? 4.95 + = 12.1

A. 7.15

B. 7.85

C. 8.15

D. 8.85

Answer:

Option A is correct.

Explanation:

In the above-given question,

given that,

the two numbers are 4.95 and 12.1.

4.95 – 12.1 = 7.15.

so option A is correct.

Question 5.

Lawrence spent $1.89 on a bottle of paint and $0.45 on a brush.

A. What was the total amount he spent? Use the model to help you.

B. Explain how the model helps you find the sum.

Answer:

The total amount he spent = $2.34.

Explanation:

In the above-given question,

given that,

Lawrence spent $1.89 on a bottle of paint and $0.45 on a brush.

$1.89 + $0.45 =

so the total amount he spent = $2.34.

Question 6.

Match each expression on the left with the equivalent decimal.

Answer:

3.05 + 1.65 = 4.7.

8.5 – 4.8 = 3.7.

4.25 + 1.55 = 5.8.

11.4 – 6.6 = 4.8.

Explanation:

In the above-given question,

given that,

match the expressions on the left with an equivalent symbol.

3.05 + 1.65 = 4.7.

8.5 – 4.8 = 3.7.

4.25 + 1.55 = 5.8.

11.4 – 6.6 = 4.8.

Question 7.

Ed is training for a race. He ran 12.56 miles on one day, 12.98 miles the second, and 13.04 miles the third day.

A. What is his combined distance for the first three days?

B. How much farther did he run the second day than the first day?

Answer:

A. The combined distance for the first three days = 38.58 miles.

B. The farther he runs the second day than the first day = 0.42 miles.

Explanation:

In the above-given question,

given that,

Ed is training for a race.

He ran 12.56 miles on one day, 12.98 miles on the second, and 13.04 miles on the third day.

12.56 + 12.98 + 13.04 = 38.58.

12.98 – 12.56 = 0.42.

the combined distance for the first three days = 38.58 miles.

the farther he runs the second day than the first day = 0.42 miles.

Question 8.

The Thomas Jefferson Memorial is on 18.36 acres of land, the Franklin Delano Roosevelt Memorial is on 7.5 acres of land, the Vietnam Veterans Memorial is on 8.9 acres of land, and the World War I Memorial is on 9.6 acres of land. Which two memorials have the greatest difference in area?

What is the difference between the areas of these two memorials? Explain.

Answer:

The difference between the areas of these two memorials = 10.86.

Explanation:

In the above-given question,

given that,

The Thomas Jefferson Memorial is on 18.36 acres of land,

the Franklin Delano Roosevelt Memorial is on 7.5 acres of land,

the Vietnam Veterans Memorial is on 8.9 acres of land,

and the World War I Memorial is on 9.6 acres of land.

18.36 – 7.5 = 10.86.

8.9 – 9.6 = 0.7.

so the difference between the areas of these two memorials = 10.86.

Question 9.

Amber bought a hardcover book for $23.70 and a paperback for $6.91. How much did she spend in all? If she paid with 2 twenty-dollar bills, how much change did she get?

Answer:

The much change did she get = $10.61.

Explanation:

In the above-given question,

given that,

Amber bought a hardcover book for $23.70 and a paperback for $6.91.

23.70 + 6.91 = 30.61.

If she paid with 2 twenty-dollar bills.

2 x 20 = 40.

$40 – $30.61 = $10.61.

Question 10.

Kassandra has a rectangular patio in her backyard. The patio is 12.74 meters long and 5.45 meters wide.

A. Round the length and width to the nearest whole number. Then estimate the perimeter of Kassandra’s patio. Write an equation to model your work.

B. Round the length and width to the nearest tenth. Then estimate the perimeter of Kassandra’s patio. Write an equation to model your work.

C. Find the exact perimeter. Which estimate is closer? Explain why you think that estimate is closer.

Answer:

The length and width to the nearest whole number = 5.5 and 13.

the length and width to the nearest tenth = 5.5 and 12.7.

the perimeter is 69.433.

Explanation:

In the above-given question,

given that,

Kassandra has a rectangular patio in her backyard.

The patio is 12.74 meters long and 5.45 meters wide.

the nearest whole number is 5.5 and 13.

the nearest tenth is 5.5 and 12.7.

the perimeter is 69.433.

### Topic 2 Performance Task

**Video Games**

Four students are playing the same video game. Their scores for the first three levels are added together to see if the student has enough points to move on to Round 2.

Question 1.

The students’ scores are shown in the table below.

**Part A**

A student must have at least 18 points to advance to Round 2. Use estimation to decide if any of the students did not get 18 points.

**Part B**

Use estimation to decide which student had the greatest number of points. Explain your reasoning.

Answer:

The student has the greater number of points = Zoey.

Explanation:

In the above-given question,

given that,

kim had 7.18 + 6.55 + 6.45 = 20.18.

Sally had 5.49 + 6.18 + 5.72 = 17.39.

Tina had 8.02 + 7.94 + 8.38 = 24.34.

zoey had 8.64 + 8.32 + 8.13 = 25.09.

Question 2.

Complete the table to find the total number of points for each student.

Answer:

The total number of points of Kim = 20.18.

the total number of points of Sally = 17.39.

the total number of points Tina = 24.34.

the total number of points Zoey = 25.09.

Explanation:

In the above-given question,

given that,

kim had 7.18 + 6.55 + 6.45 = 20.18.

Sally had 5.49 + 6.18 + 5.72 = 17.39.

Tina had 8.02 + 7.94 + 8.38 = 24.34.

zoey had 8.64 + 8.32 + 8.13 = 25.09.

Question 3.

How many more points did Zoey score than Sally? Write an equation to model your work.

Answer:

The more points did Zoey score than Sally = 7.7.

Explanation:

In the above-given question,

given that,

kim had 7.18 + 6.55 + 6.45 = 20.18.

Sally had 5.49 + 6.18 + 5.72 = 17.39.

Tina had 8.02 + 7.94 + 8.38 = 24.34.

zoey had 8.64 + 8.32 + 8.13 = 25.09.

25.09 – 17.39 = 7.7.

Question 4.

Use the total points scored for each student.

**Part A**

About how many points did the four students score in Round 1? Estimate by rounding each point total to the nearest whole number.

**Part B**

Complete the bar diagram to show the exact total number of points the students scored.

Answer:

The total number of points the students scored = 87.

Explanation:

In the above-given question,

given that,

kim had 7.18 + 6.55 + 6.45 = 20.18.

Sally had 5.49 + 6.18 + 5.72 = 17.39.

Tina had 8.02 + 7.94 + 8.38 = 24.34.

zoey had 8.64 + 8.32 + 8.13 = 25.09

20.18 + 17.39 + 24.34 + 25.09 = 87.

Question 5.

In Round 2, Zoey had a total of 23.43 points. She got a score of 7.96 in Level 2 and a score of 8.03 in Level 3.

**Part A**

What score did she receive in Level 1?

**Part B**

Explain how you found your answer.

Answer:

In level 1 Zoey scored 20.18 points.

Explanation:

In the above-given question,

given that,

Zoey had a total of 23.43 points.

She got a score of 7.96 in Level 2.

the score of 8.03 in Level 3.

23.43 + 7.96 + 8.03 = 20.18.

so the total score is 20.18 points.

Question 6.

Kim recorded her scores for Round 2. To estimate her total, she rounds to the nearest whole number and says, “7 + 9 + 7 = 23, so my total is at least 23 points.” Do you agree? Explain your reasoning.

Answer:

No, it was not correct.

Explanation:

In the above-given question,

given that,

Kim recorded her scores for Round 2.

7 + 9 + 7 = 23.

but the scores are 6.77, 8.48, and 7.13.

6.77 + 8.48 + 7.13 = 22.38.

so it was not correct.