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## Big Ideas Math Book 3rd Grade Answer Key Chapter 8 Add and Subtract Multi-Digit Numbers

BIM 3rd Grade 8th Chapter Add and Subtract Multi-Digit Numbers Answers are not only useful for the children but also for teachers and parents. If parents or teachers find any question difficult to solve, then they can refer to Big Ideas Math Book Grade 3 Chapter 8 Add and Subtract Multi-Digit Numbers Solution Key.

The topics included in the answer key are Identify Addition Properties, Use Number Lines to Addition, Use Mental Math to Add, Use Partial Sums to Add, Add Three-Digit Numbers, Add Three or More Numbers, Use Number Lines to Subtract, Use Mental Math to Subtract, Subtract Three-Digit Numbers, Relate Addition and Subtraction. The problem solving or performance task sections mentioned after these lessons are helpful to check skills.

**Lesson 1 – Identify Addition Properties**

**Lesson 2 – Use Number Lines to Addition**

**Lesson 3 – Use Mental Math to Add**

**Lesson 4 – Use Partial Sums to Add**

**Lesson 5 – Add Three-Digit Numbers**

**Lesson 6 – Add Three or More Numbers**

**Lesson 7 – Use Number Lines to Subtract**

**Lesson 8 – Use Mental Math to Subtract**

**Lesson 9 – Subtract Three-Digit Numbers**

**Lesson 10 – Relate Addition and Subtraction**

- Lesson 8.10 Relate Addition and Subtraction
- Relate Addition and Subtraction Homework & Practice 8.10

**Lesson 11 – Problem Solving: Addition and Subtraction**

- Lesson 8.11 Problem Solving: Addition and Subtraction
- Problem Solving: Addition and Subtraction Homework & Practice 8.11

**Performance Task**

- Add and Subtract Multi-Digit Numbers Performance Task
- Add and Subtract Multi-Digit Numbers Activity
- Add and Subtract Multi-Digit Numbers Chapter Practice
- Add and Subtract Multi-Digit Numbers Cumulative Practice 1 – 8
- Add and Subtract Multi-Digit Numbers Steam Performance Task 1-8

### Lesson 8.1 Identify Addition Properties

**Explore and Grow**

Use the addition table to write all of the addition equations that have a sum of 13.

What do you notice now?

Answer:

By adding a vertical number and the horizontal number we can find the sum of 13.

0 + 0 = 0

0 + 1 = 0

Add blue line and yellow line.

Add 10 in the blue column and 3 in the yellow column.

10 + 3 = 13

Thus the addition equation has the sum of 13.

**Structure**

Use the addition table to write all of the equations that have a sum of 12. What do you notice?

Answer:

Add blue line and yellow line.

Add 10 in the blue column and 2 in the yellow column.

10 + 2 = 12

Thus the addition equation has the sum of 12.

**Think and Grow: Addition Properties**

Changing the order of addends does not change the sum.

3 + 5 = 5 + 3

Associative Property of Addition

Changing the grouping of addends does not change the sum.

(7 + 6) + 4 = 7 + (6 + 4)

Addition Property of Zero

The sum of any number and 0 is that number.

9 + 0 = 9

**Example**

Identify the property.

56 + 0 = ___

12 + 29 = 29 + 12 _____

(24 + 17) + 23 = 24 + (17 + 23) ____

Answer:

56 + 0 = 56

It shows Addition Property of Zero. The Addition Property of Zero defines the sum of any number and 0 is that number.

12 + 29 = 29 + 12

Changing the order of addends does not change the sum.

(24 + 17) + 23 = 24 + (17 + 23)

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

**Show and Grow**

Identify the property.

Question 1.

16 + (14 + 19) = (16 + 14) + 19

Answer:

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 2.

11 + 54 = 54 + 11

Answer:

Associative Property of Addition defines the changing the order of addends does not change the sum.

Question 3.

0 + 43 = 43

Answer: Addition Property of Zero

The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 4.

(27 + 18) + 22 = 27 + (18 + 22)

Answer:

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

**Apply and Grow: Practice**

Identify the property.

Question 5.

(28 + 16) + 14 = 28 + (16 + 14)

Answer:

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 6.

12 + 35 = 35 + 12

Answer:

Associative Property of Addition defines the changing the order of addends does not change the sum.

Question 7.

36 + 0 = 36

Answer:

The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 8.

11 + (9 + 57) = (11 + 9) + 57

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Find the missing number.

Question 9.

23 + 45 = 45 + ___

Answer: 23

Explanation:

Let the missing number be x.

By using the Associative Property of Addition property we can find the missing number.

23 + 45 = 45 + x

23 + 45 = 45 + 23

Thus the missing number is 23.

Question 10.

(13 + 12) + __ = 13 + (12 + 45)

Answer: 45

Explanation:

Let the missing number be x.

By using the Associative Property of Addition property we can find the missing number.

(13 + 12) + x = 13 + (12 + 45)

Thus the missing number is 45.

Question 11.

4 + (76 + 10) = (___ + 76) + 10

Answer: 4

Explanation:

Let the missing number be x.

By using the Associative Property of Addition property we can find the missing number.

4 + (76 + 10) = (x + 76) + 10

4 + (76 + 10) = (4 + 76) + 10

Thus the missing number is 4.

Question 12.

98 + ___ = 98

Answer: 0

Explanation:

Let the missing number be x.

The Addition Property of Zero defines the sum of any number and 0 is that number.

98 + x = 98

x = 98 – 98

x = 0

Thus the missing number is 0.

Question 13.

(___ + 0) + 32 = 6 + 32

Answer: 6

Explanation:

Let the missing number be x.

By using the Associative Property of Addition property we can find the missing number.

(x + 0) + 32 = 6 + 32

x + 32 = 38

x = 38 – 32

x = 6

Thus the missing number is 6.

Question 14.

64 + (5 + 23) = (23 + ___) + 64

Answer: 5

Explanation:

Let the missing number be x.

By using the Associative Property of Addition property we can find the missing number.

64 + (5 + 23) = (23 + x) + 64

64 + 28 = 23 + x + 64

82 = x + 87

x = 87 – 82

x = 5

Thus the missing number is 5.

Question 15.

**DIG DEEPER!**

Use the numbers 24, 54, and 11 to write an equation that shows the Associative Property of Addition.

Answer:

We can write the equation by using the Associative Property of Addition.

24 + (54 + 11) = (24 + 54) + 11

**Writing**

Use a property to find the sum. Which property did you use? Why?

Question 16.

54 + 0 = __

Answer: 54

Explanation:

We can find the sum of the 54 + 0 by using the addition property of zero.

The Addition Property of Zero defines the sum of any number and 0 is that number.

54 + 0 = 54

Question 17.

(46 + 17) + 33 = ___

Answer: 96

Explanation:

We can find the sum of the (46 + 17) + 33 by using the Associative Property of Addition.

(46 + 17) + 33 = 96

Question 8.

20 + 63 = ___

Answer: 83

Explanation:

We can find the sum of the Associative Property of Addition.

20 + 63 = 83

**Think and Grow: Modeling Real Life**

A tourist visits 13 museums, 19 memorials, and 11 monuments. Explain how to use a property to find the total number of sites the tourist visits.

(13 + 19) + 11 = ?

Explain:

The tourist visits ___ sites.

Answer:

Given,

A tourist visits 13 museums, 19 memorials, and 11 monuments.

We can find the total number of sites the tourist visits.

(13 + 19) + 11 = 13 + (19 + 11) = 43

Thus the tourist visits 43 sites.

**Show and Grow**

Question 19.

A farmer sells 34 cucumbers, 48 ears of corn, and 26 bell peppers at a farmer’s market. Explain how to use properties to find the total number of vegetables the farmer sells.

(34 + 48) + 26 = ?

Answer:

Given,

A farmer sells 34 cucumbers, 48 ears of corn, and 26 bell peppers at a farmer’s market.

We can find the sum of the Associative Property of Addition.

(34 + 48) + 26 = 34 + (48 + 26)

34 + 48 + 26 = 108

Thus the total number of vegetables the farmer sells is 108.

Question 20.

How many people go on the field trip?

Answer:

The number of adults = 20

The number of grade 2 students = 47

The number of grade 3 students = 53

20 + 47 + 53 = 120

Thus 120 people go on the field trip.

**DIG DEEPER!**

The Grade 2 and Grade 3 students are divided into 10 equal groups. How many students are in each group? Explain.

Answer:

Given that,

The Grade 2 and Grade 3 students are divided into 10 equal groups.

The number of grade 2 students = 47

The number of grade 3 students = 53

47 + 53 = 100

100/10 = 10

Thus there are 10 students in each group.

### Identify Addition Properties Homework & Practice 8.1

Identify the property.

Question 1.

(79 + 12) + 13 = 79 + (12 + 13)

Answer: Associative property of addition

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 2.

24 + 63 = 63 + 24

Answer: Associative property of addition

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 3.

0 + 64 = 64

Answer: Associative property of zero

The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 4.

37 + (43 + 19) = (37 + 43) + 19

Answer: Associative property of addition

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 5.

17 + 38 = 38 + 17

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 6.

18 + 48 = 48 + 18

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Find the missing number.

Question 7.

36 + __ = 36

Answer: 0

Explanation:

Let the missing number be x.

36 + x = 36

x = 36 – 36

x = 0

Thus the missing number is 0.

Question 8.

25 + __ + 11 = 25 + 11

Answer: 0

Explanation:

Let the missing number be y.

25 + y + 11 = 25 + 11

y + 36 = 36

y = 36 – 36

y = 0

Thus the missing number is 0.

Question 9.

0 + 43 = __ + 0

Answer: 43

Explanation:

Let the missing number be t.

0 + 43 = t + 0

43 = t

Thus the missing number is 43.

Question 10.

(22 + 19) + 28 = 19 + (___ + 28)

Answer: 22

Explanation:

Let the missing number be p.

22 + 19 + 28 = 19 + p + 28

69 = 47 + p

p = 69 – 47

p = 22

Thus the missing number is 22.

Question 11.

**Number Sense**

Newton uses two properties. Identify the properties he uses.

Answer:

Given the expression (18 + 27) + 12 = 27 + (18 + 12)

By seeing the above expression we can say that Newton used Associative Property of Addition and Commutative Property of Addition.

Question 12.

**Open-Ended**

Write an equation that shows the Commutative Property of Addition.

Answer: 4 + 2 = 2 + 4

Commutative property of addition: Changing the order of addends does not change the sum.

Question 13.

**Structure**

Explain how the Associative Property of Addition and the Associative Property of Multiplication are alike and how they are different.

Answer:

Associative property explains that addition and multiplication of numbers are possible regardless of how they are grouped.

Example:

2 × (3 × 5) = (2 × 3) × 5

2 + (3 + 5) = (2 + 3) + 5

The method is same but the solution for both the equations are different.

Question 14.

**Modeling Real Life**

A florist uses 11 roses, 12 lilies, and 19 daisies to make bouquets. How many flowers does he use?

Answer:

Given that,

A florist uses 11 roses, 12 lilies, and 19 daisies to make bouquets.

Add all the flowers to find the total number of flowers he used.

11 + 12 + 19 = 42

Thus he used 42 flowers.

**DIG DEEPER!**

The florist uses 6 flowers for each bouquet. How many bouquets does he make? Explain.

Answer:

Given,

The florist uses 6 flowers for each bouquet.

Total flowers = 42

Divide the total number of flowers by the number of flowers in each bouquet

42/6 = 7

Thus he made 7 bouquets.

**Review & Refresh**

Find the product.

Question 15.

Answer:

Multiply the two numbers 0 and 3.

0 × 3 = 0

Question 16.

Answer:

Multiply the two numbers 7 and 7.

7 × 7 = 49

Question 17.

Answer:

Multiply the two numbers 10 and 4.

10 × 4 = 40

Question 18

Answer:

Multiply the two numbers 7 and 6.

7 × 6 = 42

### Lesson 8.2 Use Number Lines to Addition

**Explore and Grow**

Color to find 33 + 25. Then model your jumps on the number line.

Answer:

First, you have to color the two numbers 33 and 25.

Now add 33 and 25

33 + 25 = 58

Now try to solve the problem by using the number line.

Start at 33. Count by twenties, then by 5s.

33 + 20 + 5 = 58

**Reasoning**

How can finding 33 + 25 help you find 533 + 25?

Answer:

We can find the sum of 533 and 25 with the help of the above problem.

33 + 25 = 58

533+ 25 = 538

Just add 5 on the left side to get the sum.

**Think and Grow: Adding on a Number Line**

**Example**

Find 245 + 38

**One Way:** Use the count on strategy. Start at 245. Count on by tens, then by ones.

Answer:

**Another Way:** Use the make a ten strategy. Start at 245. Count on to the nearest ten. Then count on by tens and by ones.

Answer:

**Show and Grow**

Question 1.

Use the count on strategy to find 368 + 24.

Answer: 392

Use the count on strategy. Start at 368. Count on by tens, then by ones.

368 + 10 + 10 + 2 + 2 = 392

Question 2.

Use the count on strategy to find 57 + 179.

Answer: 236

Use the count on strategy. Start at 57. Count on by hundreds, tens, then by ones.

**Apply and Grow: Practice**

Question 3.

Use the count on strategy to find 47 + 216.

Answer: 263

Use the count on strategy. Start at 47. Count on by hundreds, tens, then by ones.

47 + 100 + 100 + 10 + 6 = 263

Question 4.

Use the make a ten strategy to find 478 + 64.

Answer: 542

Use the count on strategy. Start at 478. Count on by tens, then by ones.

Find the sum

Question 5.

395 + 85 = ___

Answer: 480

Use the count on strategy. Start at 395. Count on by tens, then by ones.

Question 6.

653 + 109 = ___

Answer: 762

Use the count on strategy. Start at 353. Count on by tens, then by ones.

Question 7.

Humans have 24 rib bones and 182 other types of bones. How many bones do humans have in all?

Answer:

Given,

Humans have 24 rib bones and 182 other types of bones.

182 + 24 = 206

Thus Humans have 206 bones.

Question 8.

**Structure**

Write the equation shown by the number line.

Answer:

436 + 4 + 20 + 4

440 + 20 + 4 = 464

Question 9.

**Structure**

Show two different ways to find 225 + 39 using a number line.

Answer:

Use the count on strategy. Start at 225. Count on by tens, then by ones.

225 + 30 + 9 = 264

**Think and Grow: Modeling Real Life**

The Leaning Tower of Pisa has 294 steps. A visitor climbs 156 steps, takes a break, and then climbs 78 more steps. Does the visitor reach the top of the tower?

**Addition equation:**

The visitor ___ reach the top of the tower.

Answer:

156 + 78 = 234

294 – 234 = 60

Thus the visitor does not reach the top of the tower.

**Show and Grow**

Question 10.

A book has 216 pages. You have already read 167 pages. You read 49 more pages. Do you finish reading the book?

Answer:

Given that,

A book has 216 pages. You have already read 167 pages. You read 49 more pages.

167 + 49 = 216 pages

216 – 216 = 0

Thus you finish reading the book.

Question 11.

**DIG DEEPER!**

A puzzle has 350 pieces. You put 95 pieces together. Your friend puts 185 pieces together. Do you and your friend complete the puzzle? If not, how many pieces are left?

Answer:

Given that,

A puzzle has 350 pieces. You put 95 pieces together. Your friend puts 185 pieces together.

95 + 185 = 280 pages

350 – 280 = 70 pages

No you and your friend do not complete the puzzle.

70 pieces are left to complete the puzzle.

Question 12.

A music library has 483 songs. You listen to162 different songs one week and 171 more songs the next week. How many songs are left?

Answer:

Given that,

A music library has 483 songs.

You listen to162 different songs one week and 171 more songs the next week.

162 + 171 = 333 songs

483 – 333 = 150 songs

Thus 150 songs are left.

### Use Number Lines to Addition Homework & Practice 8.2

Question 1.

Use the count on strategy to find 402 + 39.

Answer:

Use the count on strategy. Start at 402. Count on by tens, then by ones.

Question 2.

Use the make a ten strategy to find 81 + 647.

Answer:

Use the count on strategy. Start at 81. Count on by hundreds, tens, then by ones.

Question 3.

Find the sum.

Answer:

Question 4.

718 + 226 = __

Answer:

Use the count on strategy. Start at 718. Count on by hundreds, tens, then by ones.

718 + 226 = 944

Question 5.

**YOU BE THE TEACHER**

Your friend uses a number line to find 435 + 27. Is your friend correct? Explain.

Answer:

Your friend uses a number line to find 435 + 27.

435 + 27 = 462

Your friend is not correct.

Question 6.

**YOU BE THE TEACHER**

Your friend says she can find 64 + 691 by starting at 691 on a number line because of the Associative Property of Addition. Is your friend correct? Explain.

Answer:

Your friend says she can find 64 + 691 by starting at 691 on a number line because of the Associative Property of Addition.

Yes, your friend is correct.

Question 7.

**Modeling Real Life**

Your cousin needs to write a 400-word essay. She writes 318 words during class. She finishes her essay by writing 94 words at home. Does your cousin’s essay have enough words?

Answer:

Given,

Your cousin needs to write a 400-word essay.

She writes 318 words during class. She finishes her essay by writing 94 words at home.

318 + 94 = 412

412 – 400 = 12

Yes your cousin’s essay have enough words.

Question 8.

**DIG DEEPER!**

There are 275 apartments in an apartment building. There are 203 two-bedroom apartments rented, and 56 one-bedroom not apartments rented. How many apartments are rented?

Answer:

Given that,

There are 275 apartments in an apartment building.

There are 203 two-bedroom apartments rented, and 56 one-bedroom not apartments rented.

203 + 56 = 259

Thus 259 apartments are rented.

Find the quotient

Question 9.

18 ÷ 6 = ___

Answer: 3

Explanation:

Divide the two numbers 18 and 6.

18/6 = 3

Thus the quotient is 3.

Question 10.

32 ÷ 8 = ___

Answer: 4

Explanation:

Divide the two numbers 32 and 8.

32/4 = 4

Thus the quotient is 4.

Question 11.

72 ÷ 9 = __

Answer: 8

Explanation:

Divide the two numbers 72 and 9.

72/9 = 8

Thus the quotient is 8.

### Lesson 8.3 Use Mental Math to Add

**Explore and Grow**

What addition problem is shown? How can you find the sum?

Answer: 366 + 504 = 870

Explanation:

By seeing the above figure we can find the sum.

First count the number of blocks

There are 100 blocks in each figure

There are three 100 blocks, six 10 blocks, and 6 blocks.

300 + 60 + 6 = 366

There are five 100 blocks and 4 blocks.

500 + 4 = 504

Now add both

366 + 504 = 870

Reasoning

Show how to find 402 + 248.

Answer:

You can find the sum of 402 and 248 by using the above arrays.

Take 10 × 10 block

402 – Four 10 × 10 blocks, 2 blocks

248 – Two 10 × 10 blocks, Four 10 blocks, and eight blocks

402 + 248 = 650

**Think and Grow: Mental Math Strategies for Addition**

**Example**

Find 247 + 328.

Use compensation to add.

Answer:

You can find the sum of 247 and 328 by using mental math strategies.

247 + 3 = 250

328 – 3 = 325

250

+325

575

Thus the sum of 247 and 328 is 575.

**Example**

Find 119 + 163.

Make a ten and count on to add.

Answer:

119 + 163 = 119 + (1 + 100 + 60 + 2)

(119 + 1) + 100 + 60 + 2

120 + 100 + 60 + 2

382

**Show and Grow**

Question 1.

Use compensation to find 322 + 158.

Answer:

322 – 2 = 320

158 + 2 = 160

320

+160

480

So, 322 + 158 = 480

Question 2.

Make a ten and count on to find 695 + 187.

Answer:

695 + 187 = 695 + (5 + 100 + 80 + 2)

(695 + 5) + (100 + 80 + 2)

700 + 100 + 80 + 2

882

So, 695 + 187 = 882

**Apply and Grow: Practice**

Question 3.

Use compensation to find the sum.

Answer:

604 – 4 = 600

275 + 4 = 279

600

+279

879

Question 4.

Make a ten and count on to find the sum.

Answer:

359 + 1 = 360

360 + 300 = 660

660 + 17 = 677

So, 359 + 318 = 677

Use mental math to find the sum.

Question 5.

436 + 248 = __

Answer:

436 + 248 = 436 + (8 + 40 + 200)

436 + (4 + 4 + 40 + 200)

(436 + 4) + 4 + 40 + 200

440 + 244

684

So, 436 + 248 = 684

Question 6.

795 + 102 = ___

Answer:

102 – 2 = 100

795 + 2 = 797

797

+100

897

So, 795 + 102 = 897

Question 7.

503 + 71 = ___

Answer:

503 – 3 = 500

71 + 3 = 74

500

+74

574

So, 503 + 71 = 574

Question 8.

589 + 407 = ___

Answer:

589 + 1 = 590

407 – 1 = 406

590

+406

996

Question 9.

734 + 97 = ___

Answer:

734 – 3 = 731

97 + 3 = 100

731

+100

831

Question 10.

352 + 164 = ___

Answer:

352 – 2 = 350

164 + 2 = 166

350

+166

516

Question 11.

297 + 211 = ___

Answer:

297 + 3 = 300

211 – 3 = 208

300

+208

508

Question 12.

426 + 364 = ___

Answer:

426 + 4 = 430

364 – 4 = 360

430

+360

790

Question 13.

159 + 104 = ___

Answer:

159 + 1 = 160

104 – 1 = 103

160

+103

263

Question 14.

A community shelter collects 101 shirts and 109 pairs of pants from a clothing drive. How many clothing items does the community shelter collect?

Answer:

Given,

A community shelter collects 101 shirts and 109 pairs of pants from a clothing drive.

101 – 1 = 100

109 + 1 = 110

100

+110

210

Thus the community shelter collect 210 clothing items.

Question 15.

**Number Sense**

Descartes wants to use compensation to find 238 + 127. Which numbers could he use?

Answer:

Descartes wants to use compensation to find 238 + 127.

The number near 238 is 240, 127 is 130.

Thus he could use 240 and 130

**Think and Grow: Modeling Real Life**

A company manager has $900. Does he have enough money to buy the laptop and the cell phone?

**Addition equation:**

**Compare:**

The manager ___ have enough money.

Answer:

Given,

A company manager has $900.

The cost of the laptop is $595

The cost of the mobile is $249.

595 + 5 = 600

249 – 5 = 244

600

+244

844

900 – 844 = 56

Thus the manager does not have enough money.

**Show and Grow**

Question 16.

A USB drive holds 600 photos. You have 279 photos on a digital camera and 337 photos on a cell phone. Can the USB drive hold all of your photos?

Answer:

Given,

A USB drive holds 600 photos. You have 279 photos on a digital camera and 337 photos on a cell phone.

279 + 1 = 280

337 – 1 = 336

280

+336

616

Yes the USB drive can hold all of your photos

Question 17.

A school board president has $1,000. Which two items can she buy?

**DIG DEEPER!**

The president buys the two items. How much money does she have left?

Answer:

A school board president has $1,000.

The cost of a swing set is $648

The cost of the seesaw is $372

The cost of a Dome Climber is $498

498

+372

870

1000 – 870 = 130

Thus she has left $130.

### Use Mental Math to Add Homework & Practice 8.3

Use compensation to find the sum.

Question 1.

Answer:

248 + 2 = 250

137 – 2 = 135

250

+135

385

So, 248 + 137 = 385

Question 2.

Answer:

401 – 1 = 400

165 + 1 = 166

400

+166

566

Make a ten and count on to find the sum

Question 3.

506 + 369 = ?

Answer:

506 + 369 = 506 + (4 + 300 + 60 + 5)

(506 + 4) + 300 + 60 + 5

510 + 365

875

So, 506 + 369 = 875

Question 4.

617 + 348 = ?

Answer:

617 + 348 = 617 + (3 + 300 + 40 + 5)

(617 + 3) + 300 + 40 + 5

620 + 345

965

617 + 348 = 965

Use mental math to find the sum.

Question 5.

478 + 219 = ___

Answer:

478 + 2 = 480

219 – 2 = 217

480

+217

697

Question 6.

503 + 64 = ___

Answer:

503 – 3 = 500

64 + 3 = 67

500

+67

567

Question 7.

288 + 242 = ___

Answer:

288 + 2 = 290

242 – 2 = 240

290

+240

530

Question 8.

Structure

Explain how to make a ten to find the sum.

Answer:

738 + 126 = 738 + (6 + 20 + 100)

(738 + 2) + 4 + 20 + 100

740 + 124

864

Question 9.

**Writing**

How is compensation make a ten similar to the strategy? How is it different?

Answer:

Compensation is a mental math strategy for multi-digit addition that involves adjusting one of the addends to make the equation easier to solve. The methods are different but the solutions are the same.

Question 10.

**Modeling Real Life**

A binder holds 250 sheets of paper. You have 107 science papers and 142 math papers. Can the binder hold all of your papers?

Answer:

Given,

A binder holds 250 sheets of paper. You have 107 science papers and 142 math papers.

107 – 2 = 105

142 + 2 = 144

105 + 144 = 249

Yes, the binder can hold all of your papers.

Question 11.

**Modeling Real Life**

A school nurse has $450. Which two items can she buy?

**DIG DEEPER!**

The school nurse buys the two items. How much money does she have left?

Answer:

A school nurse has $450.

The cost of a Stethoscope = $119

The cost of thermometer = $ 308

119 + 1 = 120

308 – 1 = 307

120

+307

427

450 – 427 = 23

She has left $23

**Review & Refresh**

Question 12.

It costs $1 to get into each football game. Newton buys a chicken wrap for $2 and a drink for $1 each game. How much money does Newton spend in 4 games?

Answer:

Given,

It costs $1 to get into each football game. Newton buys a chicken wrap for $2 and a drink for $1 each game.

1 + 2 + 1 = 4

4 × $4 = $8

Thus Newton spent $8 for 4 games.

### Lesson 8.4 Use Partial Sums to Add

**Explore and Grow**

Model each number. Draw to show each model.

How can you use the models to find 341 + 227?

Answer:

You can find the sum of 341 and 227 is

300 + 40 + 1

200 + 20 + 7

500 + 60 + 8 = 568

**Reasoning**

How can breaking apart addends help you add three-digit numbers?

Answer: Breaking apart addends helps you add three-digit numbers easily. Mind math is possible with this breaking apart addends.

**Think and Grow: Use Partials Sums to Add**

**Example**

Find 356 + 408.

**Step 1:** Write each number in expanded form.

**Step 2:** Find the partial sums.

**Step 3:** Add the partial sums.

Answer: 764

**Show and Grow**

Use partial sums to add.

Question 1.

Answer:

319 = 300 + 10 + 9

234 = 200 + 30 + 4

553 = 500 + 40 + 13

Question 2.

Answer:

568 = 500 + 60 + 8

173 = 100 + 70 + 3

741 = 600 + 130 + 11

Question 3.

Answer:

424 = 400 + 20 + 4

450 = 400 + 50 + 0

874 = 800 + 70 + 4

Question 4.

Answer:

281 = 200 + 80 + 1

365 = 300 + 60 + 5

646 = 500 + 140 + 6

Question 5.

Answer:

127 = 100 + 20 + 7

609 = 600 + 0 + 9

736 = 700 + 20 + 16

Question 6.

Answer:

276 = 200 + 70 + 6

39 = 000 + 30 + 9

315 = 200 + 100 + 15

**Apply and Grow: Practice**

Question 7.

Answer:

759 = 700 + 50 + 9

202 = 200 + 00 + 2

961 = 900 + 50 + 11

Question 8.

Answer:

864 = 800 + 60 + 4

131 = 100 + 30 + 1

995 = 900 + 90 + 5

Question 9.

Answer:

387 = 300 + 80 + 7

94 = 000 + 90 + 4

481 = 300 + 170 + 11

Question 10.

Answer:

560 = 500 + 60 + 0

273 = 200 + 70 + 3

833 = 700 + 130 + 3

Question 11.

498 + 375 = ___

Answer:

498 = 400 + 90 + 8

375 = 300 + 70 + 5

873 = 700 + 160 + 13

Question 12.

209 + 158 = ___

Answer:

209 = 200 + 00 + 9

158 = 100 + 50 + 8

367 = 300 + 50 + 17

**Think and Grow: Modeling Real Life**

A giant panda weighs 696 pounds less than a polar bear. How much does the polar bear weigh?

Addition equation:

Answer:

Given,

A giant panda weighs 696 pounds less than a polar bear.

696 – 263 = 433

Thus the polar bear weighs 433 pounds.

**Show and Grow**

Question 15.

A herd of wildebeests has 258 fewer members than a herd of zebras has. There are 335 wildebeests in the herd. How many zebras are in their herd?

Answer:

Given,

A herd of wildebeests has 258 fewer members than a herd of zebras has. There are 335 wildebeests in the herd.

335 – 258 = 77

Therefore there are 77 zebras in their herd.

Question 16.

There are three candidates in an election. Candidate A receives 184 fewer votes than Candidate B. Who wins the election?

Answer:

Given,

There are three candidates in an election. Candidate A receives 184 fewer votes than Candidate B.

Number of votes candidate A receives = 347

347 + 184 = 631

Thus Candidate B wins the election.

Question 17.

**DIG DEEPER!**

You, your friend, and your cousin play a video game. Your friend scores 161 fewer points than you. Your cousin scores 213 more points than your friend. What is each player’s score? Who wins?

Answer:

Your friend score is 579

Your friend scores 161 fewer points than you.

579 + 161 = 740

Your score is 740

Your cousin scores 213 more points than your friend.

213 + 579 = 592

Your cousin’s score is the highest among all three.

So, your cousin wins the game.

### Use Partial Sums to Add Homework & Practice 8.4

Use partials sums to add

Question 1.

Answer:

We can find the sum by using the partial sum model.

479 = 400 + 70 + 9

356 = 300 + 50 + 6

835 = 700 + 120 + 15

So, 479 + 356 = 835

Question 2.

Answer:

We can find the sum by using the partial sum model.

674 = 600 + 70 + 4

321 = 300 + 20 + 1

995 = 900 + 90 + 5

Question 3.

Answer:

We can find the sum by using the partial sum model.

396 = 300 + 90 + 6

278 = 200 + 70 + 8

674 = 500 + 160 + 14

Question 4.

564 + 218 = ___

Answer:

We can find the sum by using the partial sum model.

564 = 500 + 60 + 4

218 = 200 + 10 + 8

782 = 700 + 70 + 12

Question 5.

190 + 123 = ___

Answer:

We can find the sum by using the partial sum model.

190 = 100 + 90 + 0

123 = 100 + 20 + 3

313 = 200 + 110 + 3

Question 6.

**YOU BE THE TEACHER**

Your friend uses partial sums to find 205 + 124. Is your friend correct? Explain.

Answer: Your friend is incorrect.

205 = 200 + 00 + 5

124 = 100 + 20 + 4

329 = 300 + 20 + 9

The sum of 205 + 124 = 329

Question 7.

Patterns

Write and solve the next problem in the pattern.

Answer:

The addend is increased by 100.

So, the next pattern is

516

+178

694

Question 8.

**Modeling Real Life**

There are worker bees and drone bees in a beehive. A hive has 268 fewer drones than workers. There are 351 drone bees. How many worker bees are there?

Answer:

Given,

There are worker bees and drone bees in a beehive. A hive has 268 fewer drones than workers. There are 351 drone bees.

351

-268

83

Therefore there are 83 worker bees.

Question 9.

**Modeling Real Life**

Three athletes compete in Olympic weight lifting. Weight lifter A lifts 104 fewer pounds than Weight lifter B. Who lifts the most weight?

Answer:

Three athletes compete in Olympic weight lifting. Weight lifter A lifts 104 fewer pounds than Weight lifter B.

Weight lifter A lifts 368 pounds

368 + 104 = 472

Therefore, Weight Lifter B lifts the most weight.

**Review & Refresh**

Circle the value of the underlined digit.

Question 10.

Answer:

In the given value 2 is in the ones place so the answer is 2.

Question 11.

Answer:

In the given value 4 is in the hundreds place so the answer is 400.

Question 12.

Answer:

In the given value 0 is in tens place so the answer is 0.

### Lesson 8.5 Add Three-Digit Numbers

**Explore and Grow**

Model the equation. Draw your model. Then find the sum.

195 + 308 = ___

Answer:

195 = 100 + 90 + 5

308 = 300 + 00 + 8

503 = 400 + 90 + 13

**Reasoning**

How can you use an estimate to check whether your answer reasonable?

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

195 = 200

308 = 300

200

+300

500

Ths sum is about 500.

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

195

+308

503

503 is close to 500. So, the answer is reasonable.

**Think and Grow: Add Three-Digit Numbers**

**Example**

Find 236 + 378. Check whether your answer is reasonable.

**Step 1:** Estimate. Round each addend to the nearest hundred.

**Show and Grow**

Find the sum. Check whether your answer is reasonable.

Question 11.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

457 – 500

133 – 100

500

+100

600

The sum is about 600.

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

457

+133

590

590 is close to 600. So, the answer is reasonable.

Question 2.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

269 – 300

354 – 300

300

+300

300

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

269

+354

623

623 is close to 600. So, the answer is reasonable.

Question 3.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

560 – 600

274 – 300

600

+300

900

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

560

+274

834

834 is close to 900. So, the answer is reasonable.

Question 4.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

345 – 300

286 – 300

300

+300

600

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

345

+286

631

631 is close to 600. So, the answer is reasonable.

Question 5.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

129 – 100

668 – 700

100

+700

800

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

129

+668

797

797 is close to 800. So, the answer is reasonable.

Question 6.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

383 – 400

539 – 500

400

+500

900

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

383

+539

922

922 is close to 900. So, the answer is reasonable.

**Apply and Grow: practice**

Find the sum. Check whether your answer is reasonable.

Question 7.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

803 – 800

179 – 200

800

+200

1000

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

803

+179

982

982 is close to 1000. So, the answer is reasonable.

Question 8.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

608 – 600

239 – 200

600

+200

800

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

608

+239

847

847 is close to 800. So, the answer is reasonable.

Question 9.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

427 – 400

385 – 400

400

+400

800

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

427

+385

812

812 is close to 800. So, the answer is reasonable.

Question 10.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

401 – 400

109 – 100

400

+100

500

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

401

+109

510

510 is close to 500. So, the answer is reasonable.

Question 11.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

265 – 300

157 – 100

300

+100

400

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

265

+157

422

422 is close to 400. So, the answer is reasonable.

Question 12.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

375 – 400

64 – 100

400

+100

500

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

375

+64

439

439 is close to 500. So, the answer is reasonable.

Question 13.

Estimate: ___

469 + 284 = ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

469 – 500

284 – 300

500

+300

800

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

469

+284

753

753 is close to 800. So, the answer is reasonable.

Question 14.

Estimate: ___

580 + 246 = __

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

580 – 600

246 – 200

600

+200

800

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

580

+246

826

826 is close to 800. So, the answer is reasonable.

Question 15.

Estimate: ___

796 + 135 = ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest hundred.

796 – 800

135 – 100

800

+100

900

**Step 2:** Find the sum. Add the ones, tens, then the hundreds.

796

+135

931

931 is close to 900. So, the answer is reasonable.

Question 16.

A truck driver travels 428 miles on Monday. He travels 473 miles on Tuesday. How many miles does he travel in all on Monday and Tuesday?

Answer:

Given that,

A truck driver travels 428 miles on Monday. He travels 473 miles on Tuesday.

428

+473

901

Thus he travels 901 miles on Monday and Tuesday.

Question 17.

**Reasoning**

Your friend finds a sum. Is her answer reasonable? If not, describe her mistake.

Answer:

119

+ 187

306

Your answer is not reasonable.

**Think and Grow: Modeling Real Life**

A construction team builds an 825-meter-long boardwalk on a beach. The team builds 408 meters one week and 377 meters the next week. Is the boardwalk complete?

**Addition equation:**

The boardwalk ___ complete.

Answer:

Given,

A construction team builds an 825-meter-long boardwalk on a beach. The team builds 408 meters one week and 377 meters the next week.

408

+377

785

The boardwalk did not complete.

**Show and Grow**

Question 18.

A road crew repaves the road on a 547-meter-long bridge. The crew repaves 318 meters the ﬁrst day and 229 meters the second day. Is the road on the bridge completely repaved?

Answer:

Given,

A road crew repaves the road on a 547-meter-long bridge.

The crew repaves 318 meters on the ﬁrst day and 229 meters on the second day.

318

+229

547

Yes, the road on the bridge completely repaved.

Question 19.

A family drives from St. Louis to Orlando for a vacation. The family drives 363 miles the first day and 386 miles the second day. How many miles does the family have left to drive?

Answer:

Given,

A family drives from St. Louis to Orlando for a vacation. The family drives 363 miles the first day and 386 miles the second day.

363 + 386 = 749 miles

922 miles – 749 miles = 173 miles

173 miles the family have left to drive.

Question 20.

Which booth had more visitors in all?

Answer:

Day 1 – 468 + 527 = 995

Day 2 – 416 + 374 = 790

995 – 790 = 205

Thus day 1 has more visitors in all.

### Add Three-Digit Numbers Homework & Practice 8.5

Find the sum. Check whether your answer is answerable.

Question 1.

Estimate: ___

Answer: 630

Explanation:

The estimated number of 493 is 490

The estimated number of 142 is 140.

490

+ 140

630

Question 2.

Estimate: ___

Answer: 820

Explanation:

The estimated number of 763 is 760.

The estimated number of 58 is 60.

760

+ 60

820

Question 3.

Estimate: ___

Answer: 580

Explanation:

The estimated number of 308 is 310

The estimated number of 273 is 270

310

+270

580

Question 4.

Estimate: ___

Answer: 420

Explanation:

The estimated number of 276 is 280

The estimated number of 138 is 140

280

+ 140

420

Question 5.

Estimate: ___

Answer: 700

Explanation:

The estimated number of 532 is 530

The estimated number of 167 is 170.

530

+170

700

Question 6.

Estimate: ___

Answer: 980

Explanation:

The estimated number of 680

The estimated number of 296 is 300.

680

+300

980

Question 7.

Estimate: ___

595 + 280 = ___

Answer: 880

Explanation:

The estimated number of 595 is 600

The estimated number of 280

600

+ 280

880

Question 8.

Estimate: ___

419 + 295

Answer: 720

Explanation:

The estimated number of 419 is 420

The estimated number of 295 is 300

420

+ 300

720

Question 9.

Estimate: ___

498 + 305 = ___

Answer: 800

Explanation:

The estimated number of 498 is 500

The estimated number of 305 is 300

500

+300

800

Question 10.

**Open-Ended**

Complete the addends so you need to regroup to add. Then find the sums.

Answer:

Let the addend be 3

479

+283

762

If you take 3 as addend then you need to regroup to find the sum.

Let the addend be 9

697

+135

832

If you take 9 as addend then you need to regroup to find the sum.

Question 11.

**DIG DEEPER!**

Find the missing digits.

Answer:

You will get 466 if you add 107 and 359.

You will get 982 if you add 748 and 234

You will get 962 if you add 670 and 292.

You will get 982 if you add 809 and 173.

Question 12.

**Modeling Real Life**

Newton wants to complete a 770-mile hike in 2 months. He hikes 423 miles the first month and 347 miles the second month. Does he complete the hike?

Answer:

Given,

Newton wants to complete a 770-mile hike in 2 months.

He hikes 423 miles the first month and 347 miles the second month

423

+347

770

Thus he Newton completed the hike.

Question 13.

**Modeling Real Life**

You ship a package 750 miles from San Diego to Salt Lake City. The package is now in Las Vegas. How many miles are left until your package is delivered?

Answer:

Given,

You ship a package 750 miles from San Diego to Salt Lake City. The package is now in Las Vegas.

121 + 270 = 391 miles until Las Vegas.

750 – 391 = 359 miles

Therefore 359 miles are left until your package is delivered.

**Review & Refresh**

Find the quotient.

Question 14.

Answer: 10

Explanation:

Divide the two numbers 100 and 10.

100/10 = 10

Thus the quotient is 10.

Question 15.

Answer: 9

Explanation:

Divide the two numbers 45 and 5.

45/5 = 9

Thus the quotient is 9.

Question 16.

Answer: 7

Explanation:

Divide the two numbers 14 and 7.

14/2 = 7

Thus the quotient is 7.

Question 17.

Answer: 8

Explanation:

Divide the two numbers 10 and 80.

80/10 = 8

Thus the quotient is 8.

Question 18.

Divide 25 by 5.

Answer: 5

Explanation:

Divide the two numbers 5 and 25.

25/5 = 5

Thus the quotient is 5.

Question 19.

Divide 30 by 10.

Answer: 3

Explanation:

Divide the two numbers 10 and 30.

30/10 = 3

Thus the quotient is 3.

Question 20.

Divide 8 by 2.

Answer: 4

Explanation:

Divide the two numbers 8 and 2.

8/2 = 4

Thus the quotient is 4.

### Lesson 8.6 Add Three or More Numbers

Find the sum of the numbers. Which two numbers should you add first?

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

348 = 350

478 = 480

152 = 150

350 + 480 + 150 = 980

The sum is about 980.

517 = 520

117 = 120

283 = 280

520 + 120 + 280 = 920

The sum is about 920

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

348

+478

+152

978

978 is close to 980. So, the answer is reasonable.

517

+117

+283

917

917 is close to 920, So, the answer is reasonable.

**Reasoning**

Why did you choose those numbers? Compare your strategy to your partner’s strategy.

Answer:

348 = 350

478 = 480

152 = 150

I choose these numbers because they are nearest to ten. This strategy will help to improve the mental math. After solving the problem you can verify the answer with the actual sum.

**Think and Grow: Add Three or More Numbers**

**Example**

Find 138 + 221 + 176 + 92. Check whether your answer is reasonable.

**Step 1:** Estimate. Round each addend to the nearest ten.

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

140 + 220 + 180 + 90 = 630

The sum is about 630.

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

138

+221

+176

+92

627

627 is close to 630. So, the answer is reasonable.

**Show and Grow**

Find the sum. Check whether your answer is reasonable.

Question 1.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

342 = 340

73 = 70

267 = 270

340 + 70 + 270 = 680

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

342

+73

+267

682

682 is close to 680. So, the answer is reasonable.

Question 2.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

191 = 190

452 = 450

206 = 210

190 + 450 + 210 = 850

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

849

849 is close to 850. So, the answer is reasonable.

Question 3.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

65 = 60

98 = 100

637 = 640

640

+100

+60

800

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

637

+98

+65

800

800 is close to 800. So, the answer is reasonable.

Question 4.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

241 = 240

394 = 390

85 = 80

193 = 190

390

240

190

+80

900

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

913

913 is close to 900. So, the answer is reasonable.

Question 5.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

136 = 140

51 = 50

64 = 60

410 = 410

140

410

+60

+50

660

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

661

661 is close to 660. So, the answer is reasonable.

Question 6.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

105 = 100

113 = 110

222 = 220

307 = 310

100 + 110 + 220 + 310 = 740

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

747

747 is close to 740. So, the answer is reasonable.

**Apply and Grow: Practice**

Find the sum. Check whether your answer is answerable.

Question 7.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

557 = 560

79 = 80

283 = 280

560 + 80 + 280 = 920

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

919

919 is close to 920. So, the answer is reasonable.

Question 8.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

382 = 380

357 = 360

160 + 380 + 360 = 900

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

160

382

357

899

899 is close to 900. So, the answer is reasonable.

Question 9.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

35 = 30

68 = 70

827 = 830

30 + 70 + 830 = 930

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

35 + 68 + 827 = 930

930 is close to 930. So, the answer is reasonable.

Question 10.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

153 = 150

235 = 230

458 = 460

67 = 70

150 + 230 + 460 + 70 = 910

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

153 + 235 + 458 + 67 = 913

913 is close to 910. So, the answer is reasonable.

Question 11.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

108 = 110

172 = 170

200 = 200

263 = 260

110 + 170 + 200 + 260 = 740

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

108 + 172 + 200 + 263 = 743

743 is close to 740. So, the answer is reasonable.

Question 12.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

181 = 180

629 = 630

140 = 140

23 = 20

180 + 630 + 140 + 20 = 970

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

181 + 629 + 140 + 23 = 973

973 is close to 970. So, the answer is reasonable.

Question 13.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

213 = 210

208 = 210

462 = 460

111 = 110

210 + 210 + 460 + 110 = 990

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

994

994 is close to 990. So, the answer is reasonable.

Question 14.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

108 = 110

172 = 170

200 = 200

263 = 260

110 + 170 + 200 + 260 = 740

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

743

743 is close to 740. So, the answer is reasonable.

Question 15.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each addend to the nearest ten.

259 = 260

233 = 230

223 = 220

147 = 150

260 + 230 + 220 + 150 = 860

**Step 2:** Find the sum, add the ones, then the tens, then the hundreds.

862

862 is close to 860. So, the answer is reasonable.

Question 16.

**Number Sense**

Use the Associative Property of Addition to find (345 + 234) + 206.

Answer:

We can find the (345 + 234) + 206 by using the Associative Property of Addition.

(a + b) + c = a + (b + c)

(345 + 234) + 206 = 345 + (234 + 206)

345 + 440 = 785

Question 17.

**YOU BE THE TEACHER**

Your friend finds 364 + 109 + 27. Is your friend correct? Explain.

Answer:

Your friend is incorrect. The order of the sum is wrong. 27 is placed in the wrong pattern. 2 and 7 must be places on tens place and ones place.

364

109

+27

503

**Think and Grow: Modeling Real Life**

An elevator has a weight limit of 1,000 pounds. A 186-pound man has three 265-pound boxes to deliver. Can he bring all 3 boxes on the elevator at once?

**Understand the problem:**

**Make a plan:**

**Solve:**

He ___ bring all 3 boxes on the elevator at once.

Answer:

Given that,

An elevator has a weight limit of 1,000 pounds.

A 186-pound man has three 265-pound boxes to deliver.

265 + 265 + 265 + 186 = 981

1000 – 981 = 19 pounds

Thus he can bring all 3 boxes on the elevator at once.

**Show and Grow**

Question 18.

An auditorium has 650 seats. 175 students from each of 3 schools compete in a math competition. 68 teachers assist. Are there enough seats for all of the students and teachers?

Answer:

Given,

An auditorium has 650 seats. 175 students from each of 3 schools compete in a math competition. 68 teachers assist.

175 + 175 + 175 + 68 = 593

Thus the seats are enough for all of the students and teachers.

Question 19.

**DIG DEEPER!**

Four students at a school organize a petition for more lunch food options. They need 500 signatures. How many more signatures do they need?

Answer:

Add the number of signatures of all the students

A + B + C + D = 77 + 108 + 112 + 96 = 393

500 – 393 = 107

Thus they need 107 signatures more.

### Add Three or More Numbers Homework & Practice 8.6

Find the sum. Check whether your answer is reasonable

Question 1.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest ten.

Step 2: Find the sum, add the ones, then the tens, then the hundreds.

862 is close to 860. So, the answer is reasonable.

Question 2.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest ten.

65 = 60

41 = 40

786 = 790

60 + 40 + 790 = 890

Step 2: Find the sum, add the ones, then the tens, then the hundreds.

892

892 is close to 890. So, the answer is reasonable.

Question 3.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest ten.

409 = 410

87 = 90

463 = 460

410 + 90 + 460 = 960

Step 2: Find the sum, add the ones, then the tens, then the hundreds.

959

959 is close to 960. So, the answer is reasonable.

Question 4.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest ten.

302 = 300

253 = 250

169 = 170

18 = 20

300 + 250 + 170 + 20 = 740

Step 2: Find the sum, add the ones, then the tens, then the hundreds.

742

742 is close to 740. So, the answer is reasonable.

Question 5.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest ten.

353 = 350

121 = 120

154 = 150

116 = 120

350 + 120 + 150 + 120 = 740

Step 2: Find the sum, add the ones, then the tens, then the hundreds.

744

744 is close to 740. So, the answer is reasonable.

Question 6.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest ten.

213 = 210

251 = 250

139 = 140

210 + 270 + 250 + 140 = 870

Step 2: Find the sum, add the ones, then the tens, then the hundreds.

873

873 is close to 870. So, the answer is reasonable.

Question 7.

Structure

Which problem can you solve without regrouping?

Answer:

Question 8.

**Reasoning**

You add 602 + 125 + 231. Your friend adds 231 + 602 + 125. Do you both get the same answer? Use an additional property to explain.

Answer:

There are four mathematical properties that involve addition. The properties are the commutative, associative, additive identity and distributive properties. Additive Identity Property: The sum of any number and zero is the original number.

602 + 125 + 231 = 958

231 + 602 + 125 = 958

The sum will be the same irrespective of the change of order.

Question 9.

**Modeling Real Life**

A firefighter’s ladder has a weight limit of 750 pounds. One firefighter weighs 196 pounds. Another firefighter weighs 243 pounds. They each have67 pounds of gear. If both firefighters wear their gear, can they climb the ladder at the same time?

Answer:

A firefighter’s ladder has a weight limit of 750 pounds.

One firefighter weighs 196 pounds. Another firefighter weighs 243 pounds. They each have 67 pounds of gear.

196 + 243 + 67 + 67 = 573

750 – 573 = 177 pounds

If both firefighters wear their gear, they can climb the ladder at the same time.

Question 10.

**DIG DEEPER!**

Your principal agrees to make a lip-sync video if the school’s social media page reaches 1,000 likes in 5 days. How many more likes does the school’s page need?

Answer:

Given,

Your principal agrees to make a lip-sync video if the school’s social media page reaches 1,000 likes in 5 days.

Add all the number of likes

573 + 168 + 201 + 47 = 989

1000 – 989 = 19 likes

Thus the school’s page needs 19 likes more.

**Review & Refresh**

Question 11.

Find the area of the shape

Answer:

From the figure, we can observe that each block = 1 sq. cm

We have to find the area of the shaded part.

The shaded region is in the form of a rectangle.

So, we have to find the area of the rectangle.

A = l × b

A = 7 × 3

A = 21 sq.cm

Thus the area of the shape is 21 sq. cm

### Lesson 8.7 Use Number Lines to Subtract

**Explore and Grow**

Color to find 79 – 47. Then model your jumps on the number line.

Answer:

**Reasoning**

How can finding 79 – 47 help you find 379 – 47?

Answer:

You can subtract 47 from 79 by using the number line.

79 – 47 = 32

Just add 300 to 79 or add 3 to the left and subtract 47 from 379.

379 – 47 = 332

**Think and Grow: Subtracting on a Number Line**

**Example**

Find 358 – 82.

**One Way:**

Use the count back strategy. Start at 358. Count back by tens, then by ones.

**Another Key:**

Use the count on strategy. Start at 82. Count on until you reach 358.

**Show and Grow**

Question 1.

Use the count back strategy to find 273 – 36.

Answer:

Use the count back strategy. Start at 273. Count back by tens, then by ones.

Question 2.

Use the strategy to find 124 – 45.

Answer:

Use the count on strategy. Start at 45. Count on until you reach 124.

**Apply and Grow: Practice**

Question 3.

Use the count back strategy to find 961 – 38.

Answer:

Use the count back strategy. Start at 961. Count back by tens, then by ones.

Question 4.

Use the count back strategy to find 853 – 77.

Answer:

Use the count back strategy. Start at 853. Count back by tens, then by ones.

Find the difference.

Question 5.

316 – 24 = ___

Answer:

Use the count back strategy. Start at 316. Count back by tens, then by ones.

Question 6.

548 – 113 = ___

Answer:

Use the count back strategy. Start at 548. Count back by tens, then by ones.

Question 7.

Your friend knows 154 words in Italian. You want to know just as many words as your friend. So far, you have learned 73 words. How many words do you have left to learn?

Answer:

Given,

Your friend knows 154 words in Italian. You want to know just as many words as your friend. So far, you have learned 73 words.

154 – 73 = 81

Thus 81 words are left to learn.

Question 8.

**Structure**

Write the equation shown by the number line.

Answer:

By seeing the above number line we can find the subtraction equation.

Use the count on strategy. Start at 36. Count on until you reach 407.

407 – 36 = 371

**Think and Grow: Modeling Real Life**

Each member of a marching band and a football team is awarded a ribbon. The marching band has 123 members. The football team has 66 members. How many more ribbons are needed for the marching band than for the football team?

**Subtraction equation:**

___ more ribbons are needed for the marching band.

Answer:

Given,

Each member of a marching band and a football team is awarded a ribbon. The marching band has 123 members. The football team has 66 members.

123 – 66 = 57

Thus 57 ribbons are needed for the marching band than for the football team.

**Show and Grow**

Question 9.

A marine biologist feeds 435 pounds of fish to an orca and 50 pounds of fish to a sea lion. How many more pounds did the orca eat than the sea lion?

Answer:

Given,

A marine biologist feeds 435 pounds of fish to an orca and 50 pounds of fish to a sea lion.

435 – 50 = 385

Thus 385 more pounds the orca eat than the sea lion.

Question 10.

There are 620 paper lanterns for a festival. Some are let go. There are 42 left. How many paper lanterns were let go?

Answer:

Given,

There are 620 paper lanterns for a festival. Some are let go. There are 42 left.

620 – 42 = 578

Therefore 578 paper lanterns were let go.

Question 11.

**DIG DEEPER!**

There are some guests at an amusement park. 387 of them leave when it rains. 474 of them stay. How many guests were there before it rained?

Answer:

Given that,

There are some guests at an amusement park. 387 of them leave when it rains. 474 of them stay.

387 + 474 = 861

Thus 861 guests were there before it rained.

### Use Number Lines to Subtract Homework & Practice 8.7

Question 1.

Use the count back strategy to find 232 – 53.

Answer:

Use the count back strategy. Start at 232. Count back by tens, then by ones.

Question 2.

Use the count back strategy to find 796 – 81.

Answer:

Use the count back strategy. Start at 796. Count back by tens, then by ones.

Find the difference

Question 3.

474 – 19 = ___

Answer:

Use the count back strategy. Start at 474. Count back by tens, then by ones.

Question 4.

615 – 204 = ___

Answer:

Use the count back strategy. Start at 615. Count back by tens, then by ones.

Question 5.

**Writing**

Write and solve a subtraction word problem using 995 and 238.

Answer:

There are 995 guests at an amusement park. 238 of them leave when it rains. How many guests were there before it rained?

995 – 238

We can solve the problem by using the number line.

Question 6.

**DIG DEEPER!**

Which number lines can you use to find 734 – 308?

Answer:

Among all the number lines option ii is used to find 734 – 308.

Question 7.

**Modeling Real Life**

You take 107 pictures on a field trip to a zoo. Your friend takes 73 pictures. How many more pictures do you take than your friend?

Answer:

Given that,

You take 107 pictures on a field trip to a zoo. Your friend takes 73 pictures.

107 – 73 = 34

You take 34 pictures than your friend.

Question 8.

**Modeling Real Life**

An author has 350 copies, not of her book. Some are signed. 115 copies are signed. How many copies are signed?

Answer:

Given,

An author has 350 copies, not of her book. Some are signed. 115 copies are signed.

350 – 115 = 235 copies

Therefore 235 copies are to be signed.

**Review & Refresh**

Find the quotient.

Question 9.

Divide 25 by 5.

Answer: 5

Explanation:

Divide the two numbers 25 and 5.

25/5 = 5

Thus the quotient is 5.

Question 10.

Divide 40 by 4.

Answer: 10

Explanation:

Divide the two numbers 40 and 4.

40/4 = 10

Thus the quotient is 10.

Question 11.

Divide 72 by 8.

Answer: 9

Explanation:

Divide the two numbers 72 and 8.

72/8 = 9

Thus the quotient is 9.

### Lesson 8.8 Use Mental Math to Subtract

**Explore and Grow**

750 – 300 = ___

650 – 200 = ____

750 – 300 = ___

700 – 250 = ____

750 – 300 = ___

740 – 290 = ____

What patterns do you notice? Explain.

Answer:

750 – 300 = 450

650 – 200 = 450

750 – 300 = 450

700 – 250 = 450

750 – 300 = 450

740 – 290 = 450

Here you notice that all the answers are 450 for different patterns.

**Think and Grow: Mental Math Strategies for Subtraction**

**Example**

Find 433 – 198.

**One Way:** Use compensation to change both numbers.

433 + 2 = 435

198 + 2 = 200

435

-200

235

So, 433 – 198 = 235

**Another Way: **Use compensation to change one number.

198 is close to 200 and it is easier to subtract 200.

433

-198 + 2 = 200

233

233 + 2 = 235

So, 433 – 198 = 235

**Show and Grow**

Use compensation to find the difference

Question 1.

Answer:

Use compensation to change both numbers.

Add 4 to both numbers and use mental math strategy.

Question 2.

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

Question 3.

Answer:

Use compensation to change one number.

219 is close to 220 and it is easier to subtract 220.

**Apply and Grow: Practice**

Use compensation to find the difference

Question 4.

Answer:

Use compensation to change both numbers.

Add 1 to both numbers and use mental math strategy.

Question 5.

Answer:

117 is close to 120. So it is easier to subtract 120.

Use mental math to find the difference

Question 6.

643 – 115 = ___

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

643 + 5 = 648

115 + 5 = 120

648

-120

528

So, 643 – 115 = 528

Question 7.

863 – 257 = ___

Answer:

Use compensation to change both numbers.

Add 3 to both numbers and use mental math strategy.

863 + 3 = 866

257 + 3 = 260

866

-260

606

Question 8.

768 – 543 = ___

Answer:

Use compensation to change both numbers.

Add 2 to both numbers and use mental math strategy.

768 + 2 = 770

543 + 2 = 545

770

-545

225

Question 9.

688 – 414 = ___

Answer:

Use compensation to change both numbers.

Add 1 to both numbers and use mental math strategy.

688 + 1 = 689

414 + 1 = 415

689

-415

274

Question 10.

499 – 106 = ___

Answer:

Use compensation to change both numbers.

Add 4 to both numbers and use mental math strategy.

499 + 4 = 503

106 + 4 = 110

503

-110

393

Question 11.

495 – 162 = ___

Answer:

Use compensation to change both numbers.

Add 3 to both numbers and use mental math strategy.

495 + 3 = 498

162 + 3 = 165

498

-165

333

Question 12.

874 – 515 = ___

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

874 + 5 = 879

515 + 5 = 520

879

-520

359

Question 13.

637 – 228 = ___

Answer:

Use compensation to change both numbers.

Add 2 to both numbers and use mental math strategy.

637 + 2 = 639

228 + 2 = 230

639

-230

409

Question 14.

986 – 432 = ___

Answer:

Use compensation to change both numbers.

Add 3 to both numbers and use mental math strategy.

986 + 3 = 989

432 + 3 = 435

989

-435

554

Question 15.

A movie theater has 225 seats. 108 seats are not taken. How many seats are not taken?

Answer:

Given that,

A movie theater has 225 seats. 108 seats are not taken.

225 – 108 = 117

Therefore 117 seats are not taken.

Question 16.

**Reasoning**

Your friend starts to ﬁnd 741 – 295. What is the next step? Explain.

Answer:

The next step is to subtract the original numbers.

741

-295

446

**Think and Grow: Modeling Real Life**

A softball coach has $325 for new equipment. She buys the catching gear. Does she have enough money left to buy the bat?

Subtraction equation:

Compare:

The coach ___ has enough money to buy the bat.

Answer:

Given A softball coach has $325 for new equipment. She buys the catching gear.

325 + 1 = 326

219 + 1 = 220

326

-220

106

The cost of the bat is $109.

Thus she does not have enough money.

**Show and Grow**

Question 17.

A store owner has 550 T-shirts. He sells 333 of them. Then he receives an order for 168 T-shirts. Does he have enough T-shirts to complete the order?

Answer:

Given that,

A store owner has 550 T-shirts. He sells 333 of them.

550 – 333 = 217

Then he receives an order for 168 T-shirts.

217 – 168 = 49

Yes, he has enough T-shirts to complete the order.

Question 18.

The manager of a gaming center has $700 for new electronics. She buys the game system. Does she have enough money left for either of the other two items? If so, which one?

Answer:

Given that,

The manager of a gaming center has $700 for new electronics. She buys the game system.

$399 + $169 = $568

700 – 568 = $132

Thus she has enough money left for either of the other two items.

She can buy the game system and a bundle of games.

**DIG DEEPER!**

How much more money does the manager need to buy both the television and the bundle of games?

Answer:

The cost of television is $379

The cost of the bundle of games = $169

379 + 169 = 548

Thus the manager need $548 to buy both the television and the bundle of games

### Use Mental Math to Subtract Homework & Practice 8.8

Use compensation to find the difference.

Question 1.

Answer:

Use compensation to change both numbers.

Add 3 to both numbers and use mental math strategy.

596 + 3 = 599

317 + 3 = 320

599

-320

279

So, 596 – 317 = 279

Question 2.

Answer:

Add 6 to 214 to make the subtraction easier.

685

-214 + 6 = 220

685

-220

465

So, 685 – 214 = 465

Use mental math to find the difference.

Question 3.

782 – 489 = ___

Answer:

Use compensation to change both numbers.

Add 1 to both numbers and use mental math strategy.

782 + 1 = 783

489 + 1 = 490

783

-490

293

So, 782 – 489 = 293

Question 4.

672 – 266 = ___

Answer:

Use compensation to change both numbers.

Add 4 to both numbers and use mental math strategy.

672 + 4 = 676

266 + 4 = 270

676

-270

406

So, 672 – 266 = 406

Question 5.

983 – 155 = ___

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

983 + 5 = 988

155 + 5 = 160

988

-160

820

So, 983 – 155 = 820

Question 6.

744 – 125 = ___

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

744 + 5 = 749

125 + 5 = 130

749

–130

619

So, 744 – 125 = 619

Question 7.

967 – 619 = ___

Answer:

Use compensation to change both numbers.

Add 1 to both numbers and use mental math strategy.

967 + 1 = 968

619 + 1 = 620

968

-620

348

So, 967 – 619 = 348

Question 8.

854 – 517 = ___

Answer:

Use compensation to change both numbers.

Add 3 to both numbers and use mental math strategy.

854 + 3 = 857

517 + 3 = 520

857

-520

337

So, 854 – 517 = 337

Question 9.

472 – 215 = ___

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

472 + 5 = 479

215 + 5 = 220

479

–220

259

So, 472 – 215 = 259

Question 10.

883 – 335 = ___

Answer:

Use compensation to change both numbers.

Add 5 to both numbers and use mental math strategy.

883 + 5 = 888

335 + 5 = 340

888

-340

548

So, 883 – 335 = 548

Question 11.

575 – 198 = ___

Answer:

Use compensation to change both numbers.

Add 2 to both numbers and use mental math strategy.

575 + 2 = 577

198 + 2 = 200

577

-200

377

So, 575 – 198 = 377

Question 12.

Reasoning

To find 765 – 246, Newton adds 5 to each number and then subtracts. To find the difference, Descartes adds 4 to each number, and then subtracts. Will they both get the correct answer? Explain.

Answer:

Given,

To find 765 – 246, Newton adds 5 to each number and then subtracts.

765 + 5 = 770

246 + 5 = 251

770 – 251 = 519

To find the difference, Descartes adds 4 to each number, and then subtracts.

765 + 4 = 769

246 + 4 = 250

769 – 250 = 519

Yes they both get the correct answer.

Question 13.

**Modeling Real Life**

A custodian has 350 desks to clean. She cleans 124 desks on the first floor and 147 desks on the second floor. Does she clean all of the desks?

Answer:

Given that,

A custodian has 350 desks to clean.

She cleans 124 desks on the first floor and 147 desks on the second floor.

124 + 147 = 271

350

-271

79

No, she did not clean all of the desks.

Question 14.

**Modeling Real Life**

A fashion designer has $ 725 to spend on new supplies. She buys the sewing machine. Does she have enough money left for either of the other two items? If so, which one?

Answer:

Given,

A fashion designer has $ 725 to spend on new supplies. She buys the sewing machine.

725 – 495 = 230

Yes she has enough money left for either of the other two items

She can buy a Mannequin.

**DIG DEEPER!**

How much more money does the fashion designer need to buy both the mannequin and the fashion design software?

Answer:

Given,

The cost of the Mannequin is $129

The cost of the fashion design software is $329

129 + 329 = 458

458 – 230 = 228

Thus she needs 228 to buy both the mannequin and the fashion design software.

**Review & Refresh**

Draw equal groups. Then complete the equations.

Question 15.

3 groups of 6

Answer:

3 groups of 6 means 3 times 6.

6 + 6 + 6 = 18

3 × 6 = 18

Question 16.

4 groups of 9

Answer:

4 groups of 9 means 4 times 9.

9 + 9 + 9 + 9 = 36

4 × 9 = 36

### Lesson 8.9 Subtract Three-Digit Numbers

**Explore and Grow**

Model the equation. Draw to show your model. Then find the difference.

694 – 418 = ___

**Reasoning**

How can you use an estimate to check whether your answer is reasonable?

Answer:

Find 694 – 418. Check whether your answer is reasonable.

694 = 700

418 = 400

700

-400

300

The difference is about 300.

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup

Step 3: Check 276 is close to 300, so the answer is reasonable.

**Think and Grow: Subtract Three-Digit Numbers**

**Example**

Find 604 – 215. Check whether your answer is reasonable.

**Step 1:** Estimate. Round each number to the nearest hundred.

600

-200

400

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup

Step 3: Check 389 is close to 400, so the answer is reasonable.

**Show and Grow**

Find the difference. Check whether your answer is reasonable.

Question 1.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

300

200

100

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 136 is close to 100, so the answer is reasonable.

Question 2.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

538 = 500

371 = 400

500 – 400 = 100

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 167 is close to 100, so the answer is reasonable.

Question 3.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

500 – 300 = 200

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 238 is close to 200, so the answer is reasonable.

Question 4.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

963 = 1000

429 = 400

1000 – 400 = 600

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 534 is close to 600, so the answer is reasonable.

Question 5.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

641 = 600

287 = 300

600 – 300 = 300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 354 is close to 300, so the answer is reasonable.

Question 6.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

832 = 800

359 = 300

800 – 300 = 500

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 473 is close to 500, so the answer is reasonable.

**Apply and Grow: Practice**

Find the difference. Check whether your answer is reasonable.

Question 7.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

518 = 500

232 = 200

500 – 200 = 300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 286 is close to 300, so the answer is reasonable.

Question 8.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

971 = 1000

320 = 300

1000 – 300 = 700

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 651 is close to 700, so the answer is reasonable.

Question 9.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

565 = 600

289 = 300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 276 is close to 300, so the answer is reasonable.

Question 10.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

546 = 500

341 = 300

500 – 300 = 200

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 205 is close to 200, so the answer is reasonable.

Question 11.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

707 = 700

453 = 400

700 – 400 = 300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 254 is close to 300, so the answer is reasonable.

Question 12.

Estimate: ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

406 = 400

77 = 100

400 – 100 = 300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 329 is close to 300, so the answer is reasonable.

Question 13.

Estimate: ____

552 – 381 = ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

552 = 600

381 = 400

600 – 400 = 200

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 171 is close to 200, so the answer is reasonable.

Question 14.

Estimate: ___

725 – 146 = ____

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

725 = 700

146 = 100

700 – 100 = 600

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 579 is close to 600, so the answer is reasonable.

Question 15.

Estimate: ___

800 – 486 = ___

Answer:

**Step 1:** Estimate. Round each number to the nearest hundred.

486 = 500

800 – 500 = 300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

Step 3: Check 314 is close to 300, so the answer is reasonable.

Question 16.

The number of rings on a tree is equal to its age. A redwood tree has 473 rings. A bristlecone pine tree has 806 rings. How much older is the bristlecone pine tree than the redwood tree?

Answer:

Given that,

The number of rings on a tree is equal to its age. A redwood tree has 473 rings. A bristlecone pine tree has 806 rings

806

-473

333

Thus 333 older is the bristlecone pine tree than the redwood tree.

Question 17.

**Writing**

Explain how to regroup 408 to subtract 259.

Answer:

Working each column from right to left

9 is greater than 8 so you must regroup:

Take 1 from 4, so 4 becomes 3.

Add 10 to 0, so 0 becomes 10.

Take 1 from 10, so 10 becomes 9.

Add 10 to 8, so 8 becomes 18.

18 minus 9 is 9.

9 minus 5 is 4.

3 minus 2 is 1.

408

-259

149

**Think and Grow: Modeling Real Life**

How many more pennies does the class need to reach the goal?

**Subtraction equation:**

The class needs to collect ___ more pennies.

Answer:

800

-444

356

The class needs to collect 356 more pennies.

**Show and Grow**

Question 18.

How many more campers can attend the summer camp?

Answer:

Total summer camp openings = 405

Filled = 316

400 – 316 = 84

84 more campers can attend the summer camp.

Question 19.

A musician wants to buy a set of speakers that costs $672. She saves $224 each month for 2 months. How much money does she still need to save?

Answer:

Given that,

A musician wants to buy a set of speakers that costs $672.

She saves $224 each month for 2 months.

224 + 224 = 448

672 – 448 = 224

Thus she still need to save $224.

Question 20.

**DIG DEEPER!**

Newton has 442 packages to deliver. Descartes has 464. Newton delivers 174 packages, and Descartes delivers 188. Who is closer to finishing his deliveries?

Answer:

Given,

Newton has 442 packages to deliver. Descartes has 464. Newton delivers 174 packages, and Descartes delivers 188.

442 – 174 = 268

464 – 188 = 276

Thus Newton is closer to finishing his deliveries.

### Subtract Three-Digit Numbers Homework & Practice 8.9

Find the difference. Check whether your answer is reasonable.

Question 1.

Estimate: ___

Answer:

The estimated number for 571 is 600.

The estimated number for 220 is 200.

600

-200

400

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

352 is close to 400. So the answer is reasonable.

Question 2.

Estimate: ___

Answer:

The estimated number for 421 is 400.

The estimated number for 277 is 300.

400

-300

100

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

144 is close to 100. So the answer is reasonable.

Question 3.

Estimate: ___

Answer:

The estimated number for 534 is 500.

The estimated number for 186 is 200

500

-200

300

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

348 is close to 300. So the answer is reasonable.

Question 4.

Estimate: ___

690 – 298 = ___

Answer:

The estimated number for 690 is 700

The estimated number for 298 is 300.

700

-300

400

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

392 is close to 400. So the answer is reasonable.

Question 5.

Estimate: ___

613 – 472 = ___

Answer:

The estimated number for 613 is 600.

The estimated number for 472 is 500

600

-500

100

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

141 is close to 100. So the answer is reasonable.

Question 6.

Estimate: ___

835 – 189 = ___

Answer:

The estimated number for 835 is 800.

The estimated number for 189 is 200.

800

-200

600

**Step 2:** Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

646 is close to 600. So the answer is reasonable.

Question 7.

**YOU BE THE TEACHER**

Your friend says you have to regroup every time you subtract from a number that has a zero. Is your friend correct? Explain.

Answer:

Your friend says you have to regroup every time you subtract from a number that has a zero.

Yes, your friend is correct. Because whenever you subtract a number from 0 you have to regroup.

Question 8.

**Modeling Real Life**

How many more soup can labels does the school need to reach the goal?

Answer:

To find how many more soup can label does the school need to reach the goal you have to subtract label collected from school soup.

1000 – 638 = 362

Question 9.

**Modeling Real Life**

Newton wants to buy a couch that costs $594. He saves $198 each month for 2 months. How much money does he still need to save?

Answer:

Given,

Newton wants to buy a couch that costs $594. He saves $198 each month for 2 months.

198 × 2 = $396

594 – 396 = -198

Therefore Newton need to save $198 to buy the couch.

Question 10.

**DIG DEEPER!**

Find the missing digits.

Answer:

**Review & Refresh**

Round the number to the nearest ten and to the nearest hundred.

Question 11.

64

Answer:

The number 64 nearest ten is 60.

The number nearest hundred to 64 is 60.

Question 12.

411

Answer:

The number 411 nearest ten is 410

The number nearest hundred to 411 is 400.

### Lesson 8.10 Relate Addition and Subtraction

**Explore and Grow**

How can you find the missing number? How do you know you are correct?

**Reasoning**

How are addition and subtraction related?

Answer:

497 – 358 = 136

Check the answer by using the addition model.

136

+358

497

So, the answer is reasonable.

**Think and Grow: Relate Addition and Subtraction**

Inverse operations are operations that “undo” each other. Addition and subtraction are inverse operations.

**Example**

Find 846 – 283. Use the inverse operation to check.

Answer:

First, subtract 283 from 846 and then use the inverse operation to check the solution.

**Example**

Find 355 + 437. Use the inverse operation to check.

Answer:

First, add 355 from 437 and then use the inverse operation to check the solution.

**Show and Grow**

Find the sum or difference. Use the inverse operation to check.

Question 1.

Answer:

First, subtract 682 from 419 and then use the inverse operation to check the solution.

So, the answer is reasonable.

Question 2.

Answer:

First, add 169 from 745 and then use the inverse operation to check the solution.

So, the answer is reasonable.

Question 3.

Answer:

First, add 376 from 238 and then use the inverse operation to check the solution.

So, the answer is reasonable.

Question 4.

Answer:

First, subtract 547 from 285 and then use the inverse operation to check the solution.

So, the answer is reasonable.

Question 5.

Answer:

First, add 463 from 349 and then use the inverse operation to check the solution.

463

+349

812

Use the inverse operation to check the solution

812

-349

463

So, the answer is reasonable.

Question 6.

Answer:

First, subtract 790 from 317 and then use the inverse operation to check the solution.

790

-317

473

Use the inverse operation to check the solution

473

+317

790

So, the answer is reasonable.

**Apply and Grow: Practice**

Find the sum or difference. Use the inverse operation to check.

Question 7.

Answer:

First, subtract 857 from 567 and then use the inverse operation to check the solution.

857

-567

290

Use the inverse operation to check the solution

290

+567

857

So, the answer is reasonable.

Question 8.

Answer:

First, add 762 from 143 and then use the inverse operation to check the solution.

762

+143

905

Use the inverse operation to check the solution

905

-143

762

So, the answer is reasonable.

Question 9.

Answer:

First, add 653 from 217 and then use the inverse operation to check the solution.

653

+217

870

Use the inverse operation to check the solution

870

-217

653

So, the answer is reasonable.

Question 10.

Answer:

First, subtract 294 from 156 and then use the inverse operation to check the solution.

294

-156

138

Use the inverse operation to check the solution

138

+156

294

So, the answer is reasonable.

Question 11.

Answer:

First, add 475 from 438 and then use the inverse operation to check the solution.

475

+438

913

Use the inverse operation to check the solution

913

-438

475

So, the answer is reasonable.

Question 12.

Answer:

First, subtract 514 from 386 and then use the inverse operation to check the solution.

514

-386

128

Use the inverse operation to check the solution

128

+386

514

So, the answer is reasonable.

Question 13.

Which one Doesn’t Belong? Which equation does not belong with the other three?

Answer:

The fourth equation does not belong with the other three. Because it is not using the inverse operation of addition and subtraction.

Question 14.

**Open-Ended**

Write a subtraction equation that has a difference of 381.

Answer: 901 – 520 = 381

Take the number on your own and write the subtraction equation with the difference of 381.

**Think and Grow: Modeling Real Life**

A kayak costs $321. A customer pays $196 for the kayak after using a gift card. How much money is the gift card worth?

The gift card is worth $___.

Check:

Answer:

Given that,

A kayak costs $321. A customer pays $196 for the kayak after using a gift card.

321 – 196 = 125

Thus the gift card worth $125.

**Show and Grow**

Question 15.

You print 600 flyers for an event. You hand out some of them. There are 237 left. How many flyers did you hand out?

Answer:

Given that,

You print 600 flyers for an event. You hand out some of them. There are 237 left.

600 – 237 = 363

Thus you hand out 363 flyers.

363 + 237 = 600

Question 16.

A building has 163 floors. You start on the 28th floor. You go up in the elevator 126 floors. Then you go down 145 floors. On which floor do you end?

Answer:

Given that,

A building has 163 floors. You start on the 28th floor. You go up in the elevator 126 floors. Then you go down 145 floors.

126 – 28 = 98 floors

145 – 98 = 47

Thus you end at 47th floor.

Question 17.

**DIG DEEPER!**

A bus travels from Boston to Washington, D.C. On the way back, the bus stops in New York City. How many miles has the bus traveled in all? How many miles does the bus have left to travel?

Answer:

Given that,

A bus travels from Boston to Washington, D.C. On the way back, the bus stops in New York City.

We have to find How many miles has the bus traveled in all

441 + 225 = 666 miles

Thus a bus travels 666 miles.

666 – 225 = 441 miles

### Relate Addition and Subtraction Homework & Practice 8.10

Find the sum or difference. Use the inverse operation to check.

Question 1.

Answer:

931

-544

387

Now you have to do the inverse operation.

387

+544

931

Question 2.

Answer:

623

+285

908

Now you have to do the inverse operation.

908

-285

623

Question 3.

Answer:

523

+237

760

Now you have to do the inverse operation.

760

-237

523

Question 4.

Answer:

403

-252

151

Now you have to do the inverse operation.

151

+252

403

Question 5.

Answer:

612

+387

999

Now you have to do the inverse operation.

999

-387

612

Question 6.

Answer:

511

-371

140

Now you have to do the inverse operation.

140

+371

511

Question 7.

Answer:

437

+156

593

Now you have to do the inverse operation.

593

-156

437

Question 8.

Answer:

726

-362

364

Now you have to do the inverse operation.

364

+362

726

Question 9.

**YOU BE THE TEACHER**

Your friend uses an inverse operation to check her answer. Is your friend correct? Explain.

Answer:

No, your friend is incorrect.

380

-159

221

Now you have to do the inverse operation.

221

+159

380

Question 10.

Which One Doesn’t Belong? Which does not belong with the other three?

Answer:

208 + 475 = 683

Now you have to do the inverse operation.

683 – 475 = 208

The second figure does not belong to the other three expressions.

Question 11.

**Modeling Real Life**

A telescope costs $169. A customer pays $119 for the telescope after using a gift card. How much money is the gift card worth?

Answer:

Given that,

A telescope costs $169. A customer pays $119 for the telescope after using a gift card.

169

-119

50

The cost of the gift card is $50.

Question 12.

**DIG DEEPER!**

A train travels from Dallas to San Antonio. On the way back, the train stops in Austin. How many miles has the train travel? How many miles does the train have left to travel?

Answer:

Given,

A train travels from Dallas to San Antonio. On the way back, the train stops in Austin.

274 – 79 = 195 miles

The train has traveled 195 miles.

79 miles left to travel from Austin to San Antonio.

**Review & Refresh**

Question 13.

Use the Distributive Propertytoﬁnd the area of the rectangle.

Answer:

4 × 8 = 4 × (4 + 4)

4 × 8 = (4 × 4) + (4 × 4)

4 × 8 = 16 +16

4 × 8 = 32

Thus the area of the rectangle = 32 square foot.

### Lesson 8.11 Problem Solving: Addition and Subtraction

**Explore and Grow**

You read 150 pages in three weeks.

what does p represent?

p = ___

Answer:

Let 9 be the number of pages read

56 + 47 + p = 150

103 + p = 150

p = 150 – 103

p = 47

**Construct Arguments**

Explain to your partner how to find what n represents.

250 + n = 580

Answer:

Given the expression 250 + n = 580

n = 580 – 250

n = 330

**Think and Grow: Using the Problem-Solving Plan**

**Example**

Newton has 368 baseball cards. He gives away 139 of them. He buys 26 more. How many cards does he have now?

**Understand the Problem**

- Newton has ___ cards.
- He gives away of them.
- He buys ___ more.
- You need to find how many ___ he has now.

Answer:

- Newton has 368 cards.
- He gives away of them.
- He buys 26 more.
- You need to find how many cards he has now.

**Make a Plan**

How will you solve?

- Subtract ___ from ___ to find how many ___ he has left after he gives some away.
- Then add ___ to the difference to find how many he has now.

Answer:

- Subtract
__139__from 368 to find how many cards he has left after he gives some away. - Then add 26 to the difference to find how many he has now.

**Solve**

Draw a part-part-whole model and write an equation.

Use a letter to represent the unknown number.

Newton has __ cards now.

Answer:

Step 1:

c is the unknown difference.

368 – 139 = c

c = 229

Step 2:

c = 229

229 + 26 = n

n = 225

Thus the unknown sum is 225.

**Show and Grow**

Question 1.

Explain how you can check whether your answer above is reasonable.

Answer:

You can check the answer by using addition and subtraction.

368

-139

229

Now check whether the answer is correct or not.

229

+139

368

So, the answer is reasonable.

**Apply and Grow: Practice**

Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.

Question 2.

A baker makes 476 muffins. He sells 218 of them. Then he makes 390 more. How many muffins does the baker have now?

Answer:

Given,

A baker makes 476 muffins. He sells 218 of them.

476

-218

258

Then he makes 390 more.

390

+258

648

Thus the baker has 348 muffins now.

Question 3.

Newton knocks down 146 pins in his first bowling game. He knocks down 19 more pins in his second game than in his first game. How many pins does he knock down in all?

Answer:

Given that,

Newton knocks down 146 pins in his first bowling game. He knocks down 19 more pins in his second game than in his first game.

146

+19

165

He knocks down 165 pins in his second game.

To find the total number of pins we have to the points in the first game and second game.

146

+165

311

Thus he knockdowns 311 pins in all.

Question 4.

You are traveling to a campground that is 243 miles away. You travel 155 miles in the morning and 59 miles in the afternoon. How many more miles do you need to travel before you get to the campground?

Answer:

Given that,

You are traveling to a campground that is 243 miles away.

You travel 155 miles in the morning and 59 miles in the afternoon.

155

+59

214

243

-214

029

Thus you need to travel 29 miles to get to the campground.

Question 5.

There are 205 lawn tickets and 585 bleacher tickets sold for a concert. There are 680 fewer VIP tickets sold than lawn and bleacher tickets combined. How many VIP tickets are sold?

Answer:

Given,

There are 205 lawn tickets and 585 bleacher tickets sold for a concert.

205 + 585 = 790

There are 680 fewer VIP tickets sold than lawn and bleacher tickets combined.

790

-680

110

Thus 110 VIP tickets are sold.

**Think and Grow: Modeling Real Life**

How many more people went to see the movie on Friday than on Thursday and Saturday combined?

**Understand the problem:**

**Make a plan:**

**Solve:**

__ more people went to see the movie on Friday than on Thursday and Saturday combined.

Answer:

Thursday – 346 people

Saturday – 512 people

346 + 512 = 858 people

897

-858

39

39 more people went to see the movie on Friday than on Thursday and Saturday combined.

**Show and Grow**

Question 6.

How many more people used the ferry on Friday than on Saturday and Sunday combined?

Explain how you can check whether your answer is reasonable.

Answer:

Friday – 903 passengers

Saturday – 624 passengers

Sunday – 255 passengers

624

+255

879

Now subtract 879 from 903.

903

-879

024

### Problem Solving: Addition and Subtraction Homework & Practice 8.11

Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.

Question 1.

Newton has 387 tokens, and Descartes has 295. They use a total of 461 tokens. How many tokens do they have now?

Answer: 222 tokens

Explanation:

Given that,

Newton has 387 tokens, and Descartes has 295.

387 + 295 = 682

They use a total of 461 tokens.

682 – 461 = 222 tokens

Thus they have 222 tokens now.

Question 2.

There are 125-second graders and 118 third graders at a museum. There are 249 more adults than students at the museum. How many adults are at the museum?

Answer:

Given that,

There are 125-second graders and 118 third graders at a museum.

125 + 118 = 243 graders

There are 249 more adults than students at the museum.

243 + 249 = 492

Therefore 492 adults are at the museum.

Question 3.

You received 171 votes in a coloring contest. Your friend received 24 fewer votes than you. How many people voted for you and your friend in all?

Answer:

Given,

You received 171 votes in a coloring contest. Your friend received 24 fewer votes than you.

171 + 24 = 195 votes

The number of votes for your friend is 195.

171+ 195 = 366 votes

Thus 366 people voted for you and your friend.

Question 4.

**Writing**

Write and solve a two-step problem that can be solved using addition or subtraction.

Answer:

You bought 10 packs of sketches and your friend bought 4 packs less than you. Each pack contains 10 sketches. Find how many sketches you and your friend bought in all.

Sol: You bought 10 packs of sketches and your friend bought 4 packs less than you.

10 – 4 = 6 packs

Your friend bought 6 packs.

Each pack contains 10 sketches.

10 + 6 = 16

16 × 10 = 160

Thus you and your friend bought 160 sketches.

Question 5.

**Modeling Real Life**

How many more fish were caught on Sunday than on Friday and Saturday combined?

Explain how you can check whether your answer is reasonable.

Answer:

Number of fish caught on Friday and Saturday = 127 + 244 = 371

Number of fish caught on Sunday = 564

564 – 371 = 193

193 more fish were caught on Sunday than on Friday and Saturday combined.

**Review & Refresh**

Question 6.

Use the multiplication table.

Describe the pattern in the shaded row and column.

What property explains this pattern?

Answer: The pattern shows that it is the multiple of 5.

5 × 1 = 5

5 × 2 = 10

5 × 3 = 15

5 × 4 = 20

5 × 5 = 25

### Add and Subtract Multi-Digit Numbers Performance Task

Your school holds a talent show.

Question 1.

You and your friend hand out programs to guests before the show. You each start with 250 programs. There are 114 programs left. How many programs did you and your friend hand out?

Answer:

250 – 114 = 136 programs

Thus you and your friend hand out 136 programs.

136 + 114 = 250 programs

Question 2.

75 students wait backstage to perform in the show. There are 336 children, 125 adults, and 14 teachers in the audience.

a. How many people are at the talent show in all? Explain how to use addition properties to find the sum.

Answer:

Given,

75 students wait backstage to perform in the show. There are 336 children, 125 adults, and 14 teachers in the audience.

75 + 336 + 125 + 14 = 550

Thus there are 550 people are in the talent show.

b. Four students perform in each of the ﬁrst 4 acts. How many students still need to perform?

Answer: 16 students

Explanation:

Given,

Four students perform in each of the ﬁrst 4 acts.

4 × 4 = 16

Thus 16 students need to perform.

c. Each performer is given a juice box backstage. Juice boxes come in packages of 10. How many packages did the teachers buy? How many juice boxes are left?

Answer:

Given,

Each performer is given a juice box backstage. Juice boxes come in packages of 10.

1 box – 10 packages

16 × 1 = 16 boxes

16 × 10 = 160 packages

### Add and Subtract Multi-Digit Numbers Activity

**Three in a Row: Addition and Subtraction**

**Directions:**

1. Players take turns.

2. On your turn, spin both spinners. Add or subtract the two numbers. Cover the sum or difference.

3. If the sum or difference is already covered, then you lose your turn.

4. The first player to get three counters in a row, horizontally, vertically, or diagonally, wins!

Answer:

Sums:

547 + 107 = 654

547 + 338 = 885

547 + 262 = 809

I got the three counters vertically.

### Add and Subtract Multi-Digit Numbers Chapter Practice

**8.1 Identify Addition Properties**

Identify the property.

Question 1.

59 + 0 = 59

Answer:

It shows the Addition Property of Zero. The Addition Property of Zero defines the sum of any number and 0 is that number.

Question 2.

(14 + 32) + 6 = 14 + (32 + 6)

It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

Question 3.

27 + 51 = 51 + 27

Answer:

Commutative Property of addition Changing the grouping of addends does not change the sum.

Question 4.

Structure

Which equations show the Commutative Property of Addition?

Answer:

64 + 12 = 12 + 64 – Commutative Property of addition changing the grouping of addends does not change the sum.

71 + 0 = 71 – It shows the Addition Property of Zero. The Addition Property of Zero defines the sum of any number and 0 is that number.

(56 + 21) + 34 = 56 + (21 + 34) – It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

26 + (41 + 4) = 4 + (26 + 41) – It satisfies the Associative Property of Addition. It is defined as changing the grouping of addends does not change the sum.

**8.2 Use Number Lines to Add**

Question 5.

Find 648 + 37.

Answer:

Use the count on strategy. Start at 648. Count on by tens, then by ones.

**8.3 Use Mental Math to Add**

Use mental math to find the sum.

Question 6.

192 + 107 = ___

Answer:

You can find the sum of 192 and 107 by using mental math strategies.

192 – 2 = 190

107 + 2 = 109

190

+109

299

Question 7.

676 + 114 = ___

Answer:

You can find the sum of 676 and 114 by using mental math strategies.

676 + 4 = 680

114 – 4 = 110

680

+110

790

Question 8.

716 + 279 = ___

Answer:

You can find the sum of 716 and 279 by using mental math strategies.

716 – 1 = 715

279 + 1 = 280

715

+280

995

Question 9.

501 + 468 = ___

Answer:

You can find the sum of 501 and 468 by using mental math strategies.

501 – 1 = 500

468 + 1 = 469

500

+469

969

Question 10.

527 + 343 = ___

Answer:

You can find the sum of 527 and 343 by using mental math strategies.

527 + 3 = 530

343 – 3 = 340

530

+340

870

Question 11.

441 + 189 = ___

Answer:

You can find the sum of 441 and 189 by using mental math strategies.

441 – 1 = 440

189 + 1 = 190

440

+190

630

**8.4 Use Partial Sums to Add**

Use partial sums to add.

Question 12.

Answer:

586 = 500 + 80 + 6

107 = 100 + 00 + 7

693 = 600 + 80 + 13

Question 13.

Answer:

647 = 600 + 40 + 7

293 = 200 + 90 + 3

940 = 800 + 130 + 10

Question 14.

**Modeling Real Life**

On Earth, your cousin weighs 207 pounds less than he would on Jupiter. Your cousin weighs 135 pounds on Earth. How much would he weigh on Jupiter?

Answer:

Given,

On Earth, your cousin weighs 207 pounds less than he would on Jupiter. Your cousin weighs 135 pounds on Earth.

207 + 135 = 342

Thus your cousin would weigh 342 pounds on Jupiter.

**8.5 Add Three-Digit Numbers**

Find the sum. Check whether your answer is reasonable.

Question 15.

Estimate: ___

326 + 490 = ___

Answer:

Step 1: Estimate. Round each addend to the nearest hundred.

326 = 300

490 = 500

300 + 500 = 800

The sum is about 800.

Step 2: Find the sum. Add the ones, tens, then the hundreds.

326

+490

816

816 is close to 800. So, the answer is reasonable.

Question 16.

Estimate: ___

657 + 189 = ___

Answer:

Step 1: Estimate. Round each addend to the nearest hundred.

657 = 700

189 = 200

600 + 200 = 800

The sum is about 800.

Step 2: Find the sum. Add the ones, tens, then the hundreds.

657 + 189 = 846

846 is close to 800. So, the answer is reasonable.

Question 17.

Estimate: ___

543 + 261 = ___

Answer:

Step 1: Estimate. Round each addend to the nearest hundred.

543 = 500

261 = 300

500 + 300 = 800

The sum is about 800.

Step 2: Find the sum. Add the ones, tens, then the hundreds.

543 + 261 = 804

804 is close to 800. So, the answer is reasonable.

**8.6 Add Three or More Numbers**

Question 18.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest hundred.

78 = 100

433 = 400

367 = 400

100 + 400 + 400 = 900

The sum is about 900.

Question 19.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest hundred.

194 = 200

151 = 200

244 = 200

231 = 200

200 + 200 + 200 + 200 = 800

The sum is about 800.

Question 20.

Estimate: ___

Answer:

Step 1: Estimate. Round each addend to the nearest hundred.

373 = 400

329 = 300

118 = 100

61 = 100

400 + 300 + 100 + 100 = 900

The sum is about 900.

**8.7 Use Number Lines to Subtract**

Question 21.

Find 856 – 29.

Answer:

Use the count back strategy. Start at 856. Count back by tens, then by ones.

Question 22.

Structure

Write the equation shown by the number line.

Answer:

By seeing the above number we can find the subtraction equation.

764 – 50 = 714

714 – 4 = 710

710 – 3 = 707

The subtraction equation is 764 – 57 = 707

**8.8 Use Mental Math to Subtract**

Use mental math to find the difference.

Question 23.

957 – 619 = ___

Answer:

957 – 7 = 950

619 + 7 = 626

950

-626

324

The difference is 324.

Question 24.

831 – 415 = ___

Answer:

831 – 1 = 830

415 + 1 = 416

830

-416

414

The difference is 414.

Question 25.

876 – 366 = ___

Answer:

876 – 6 = 870

366 + 6 = 372

870 – 372 = 498

Question 26.

636 – 317 = ___

Answer:

636 + 6 = 642

317 – 6 = 311

642 – 311 = 331

The difference is 331.

Question 27.

965 – 528 = ___

Answer:

528 – 8 = 520

965 + 8 = 973

973 – 520 = 453

The difference is 453.

Question 28.

384 – 118 = ____

Answer:

684 + 4 = 688

118 – 4 = 114

688 – 114 = 574

The difference is 574.

**8.9 Subtract Three-Digit Numbers**

Find the difference. Check whether your answer is reasonable.

Question 29.

Estimate: ___

963 – 51 = ___

Answer:

Step 1: Estimate. Round each number to the nearest hundred.

963 = 1000

51 = 100

1000 – 100 = 900

Step 2: Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

963 -51 = 912

912 is close to 900. So, the answer is reasonable.

Question 30.

Estimate: ___

878 – 594 = ___

Answer:

Step 1: Estimate. Round each number to the nearest hundred.

878 = 900

594 = 600

900 – 600 = 300

Step 2: Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

878 – 594 = 284

284 is close to 300. So, the answer is reasonable.

Question 31.

Estimate: ___

766 – 297 = ___

Answer:

Step 1: Estimate. Round each number to the nearest hundred.

766 = 800

297 = 300

800 – 300 = 500

Step 2: Find the difference.

Subtract the ones, then the tens, then the hundreds. There are not enough ones or tens to subtract, so regroup.

766 – 297 = 469

469 is close to 500. So, the answer is reasonable.

Question 32.

**YOU BE THE TEACHER**

Your friend ﬁnds 760 – 482. Is your friend correct? Explain.

Answer: No your friend is not correct.

**8.10 Relate Addition and Subtraction**

Find the sum or difference. Use the inverse operation to check.

Question 33.

Answer:

649

+227

876

Now you have to do the inverse operation of the sum.

876

-227

649

Question 34.

Answer:

288

Now you have to do the inverse operation of the difference.

288

+517

805

**8.11 Problem Solving: Addition and Subtraction**

Question 35.

There are 532 dogs enrolled in police academies. 246 dogs graduate in July, and 187 dogs graduate in August. How many dogs still need to graduate?

Answer:

Given that,

There are 532 dogs enrolled in police academies.

246 dogs graduate in July, and 187 dogs graduate in August.

246 + 187 = 433

532

-433

99

Thus 99 dogs are still needed to graduate.

### Add and Subtract Multi-Digit Numbers Cumulative Practice 1 – 8

Question 1.

Which numbers round to 300 when rounded to the nearest hundred?

Answer: The numbers round to 300 when rounded to the nearest hundred is

298, 309, 347

Thus the correct answer is the option a, b, c.

Question 2.

You buy 18 cups of yogurt. The yogurt is sold in packs of 6 cups. How many packs of yogurt do you buy?

Answer:

Given,

You buy 18 cups of yogurt. The yogurt is sold in packs of 6 cups.

18/6 = 3 packs

Thus the correct answer is option c.

Question 3.

A bedroom ﬂoor is 9 feet long and 8 feet wide. What is the area of the bedroom ﬂoor?

Answer:

Given,

A bedroom ﬂoor is 9 feet long and 8 feet wide.

The area of the rectangle = l × w

A = 9ft × 8ft

A = 72 sq. ft

Thus the area of the bedroom ﬂoor is 72 sq. ft.

Question 4.

Your friend says 458 – 298 = 160. How can you use inverse operations to check your friend’s answer? Is your friend correct?

Answer:

Your friend says 458 – 298 = 160.

Your friend is correct.

The correct answer is option a.

Question 5.

Your friend says she needs (9 × 3) + (3 × 9) = 27 × 27 = 54 tiles to make the design. Why is her thinking incorrect?

Answer:

Your friend says she needs (9 × 3) + (3 × 9) = 27 × 27 = 54 tiles to make the design.

Her thinking is incorrect because she needs to add 27 and 27 but she multiplied.

(9 × 3) + (3 × 9) = 27 + 27 = 54

Question 6.

**Part A**

What is the least number that can be made with the digits 7, 9, and 8 using each digit only once?

Your friend says the greatest number he can make with the digits 7, 9, and 8 using each digit only once is 879. Is he correct? If not, correct his answer. Explain.

Answer:

Given,

Your friend says the greatest number he can make with the digits 7, 9, and 8 using each digit only once is 879

Your friend is incorrect because the greatest number with the digits 7, 9, and 8 is 987.

Question 7.

Which equation is shown by the number line?

Answer:

The count starts from 0.

The count jumps from 0 and skips for every 3s.

3 × 7 = 21

Thus the correct answer is option c.

Question 8.

Find the sum.

Answer:

548

+372

920

Question 9.

Which equations show the Associative Property of Addition?

Answer:

According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Options A and D show the equation for the Associative Property of Addition.

Question 10.

A teacher takes 7 students on a field trip. Each student pays $5. How much money does the teacher collect in all?

Answer:

Given,

A teacher takes 7 students on a field trip. Each student pays$5.

7 × $5 = $35

Thus the teacher collects $35 in all.

The correct answer is option c.

Question 11.

What is the area of the shape?

Answer:

You can divide the figure into two parts.

Figure 1:

l = 4m

b = 3m

A = l × b

A = 4 × 3 = 12 sq. m

Figure 2:

l = 8m

b = 3m

A = l × b

A = 8 × 3 = 24 sq. m

Add the area of both the figures 12 + 24 = 36 sq.m

Thus the correct answer is option D.

Question 12.

There are 459 girls and 552 boys in a school. How many more boys are there than girls?

Answer:

Given that,

There are 459 girls and 552 boys in school.

Subtract the number of girls from the number of boys.

552

-459

93

Thus the correct answer is option b.

Question 13.

Look at the pattern. What rule was used to make the pattern?

Answer:

1, 3, 9, 27 are the multiples of 3.

Thus the correct answer is option c.

Question 14.

A smoothie shop sells 368 smoothies in July and 205 smoothies in August. About how many more smoothies did the shop sell in July than in August?

Answer:

Given that,

A smoothie shop sells 368 smoothies in July and 205 smoothies in August.

368

-205

163

Thus the shop sell 163 smoothies in July than in August.

Question 15.

Which shape does not have an area of 16 square units?

Answer:

There are 16 counters in the first figure

2 × 8 = 16

There are 16 counters in the second figure

4 × 4 = 16

There are 15 counters in the third figure

5 × 3 = 15

Thus the correct answer is option c.

Complete the table

Question 16.

Answer:

You can complete the table by multiplying the rows and columns.

Question 17.

Answer:

You can complete the table by multiplying the rows and columns.

### Add and Subtract Multi-Digit Numbers Steam Performance Task 1-8

Question 1.

The carpeting in the third-grade classrooms of an elementary school is being replaced. One roll of carpet covers 100 square yards. The map shows the classrooms that will receive the new carpet.

a. Explain two different ways to ﬁnd the area of Classroom A.

Answer:

You can find the area of classroom A by using the composite figure.

The shape of classroom A is square.

a = 10 yd

Area of the classroom is a × a

A = 10 × 10 = 100 sq.yd

Thus the area of the classroom A is 100 sq. yd

Another way:

l = 10 yd

w = 3 yd

A = 10 × 3 = 30 sq. yd

l = 10 yd

A = 8 × 4 = 32 sq. yd

l = 10 yd

w = 3 yd

A = 10 × 3 = 30 sq. yd

b. Find the total area of all of the classrooms in square yards.

Answer:

Area of the classroom is a × a

A = 10 × 10 = 100 sq.yd

Thus the area of the classroom A is 100 sq. yd

Area of Classroom D = 10 × 7 = 70 sq.yd

Area of Classroom B = 11 × 7 = 77 sq.yd

Area of Classroom C = 12 × 7 = 84 sq. yd, 8 × 3 = 24 sq.yd

Area of Classroom C = 84 + 24 = 108 sq. yd

Total area of the classrooms = 100 + 70 + 77 + 108 = 355 sq. yd

c. Estimate the number of rolls of carpet needed for the classrooms. Explain.

Answer:

There are 4 classrooms. So, the estimated number of rolls of carpet is 4.

d. Find the area of the hallway in square yards. Is there enough carpet for the hallway?

Answer:

First, divide the hallway into 3 parts.

i. It is in the form of a square.

a = 3 yd

A = 3 × 3 = 9 sq.yd

ii. It is in the form of rectangle

A = l × b

A = 5 × 4 = 20 sq.yd

iii. It is in the form of rectangle

A = l × b

A = 5 × 3 = 15 sq.yd

The area of the hallway in square yards = 9 + 20 + 15 = 44 sq.yd

Question 2.

Each school keeps a record of the total number of students in each class and grade.

a. Use the number of students in your class to estimate the total number of students in your grade. Explain.

Answer:

Let the number of students in your class is 47.

By this, we can estimate the total number of students in your grade i.e., 50.

The total number of students in your grade is 50.

b. Use the table to write the number of students in each grade of your school.

Answer:

You can prepare the table by estimating the number of students in your school.

c. How does your estimate compare to the actual number of students in your grade? Explain.

Answer: You can compare the number of students in the above table with the actual number of students in your grade.

d. What is the total number of students in your school?

Answer:

Add the number of students of all the grades

40+ 50 + 52 + 47 + 47 + 50 = 286

Thus there are 286 students in your school.

e. Write and answer a question using the information from the table above.

Answer:

Compare the number of students in grade 3 with the actual number of students in your school in grade 3?

The estimated number of students in grade 3 in the above table is 50.

The actual number of students in your school is 48.

50 – 48 = 2

f. What is one reason your principal may want to know the total number of students in your class, grade, or school?

Answer: Shaping a vision of academic success for all students.

*Conclusion:*

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