Multiply by One-Digit Numbers

6 Multiply by One-Digit Numbers How do you multiply by one-digit numbers? Multiply each digit by the one-digit number, starting with the ones place....
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Multiply by One-Digit Numbers How do you multiply by one-digit numbers?

Multiply each digit by the one-digit number, starting with the ones place. Regroup when necessary. Example A great white shark can swim 2,900 miles on a single meal. If a great white shark eats 3 meals a day, it could swim 2,900 × 3 or 8,700 miles. 2,900 × 3 −−−−− 6,000 Multiply 3 × 2,000. + 2,700 Multiply 3 × 900. −−−−−− 8,700 Add the partial products.

What will I learn in this chapter? ■

Multiply multiples of 10, 100, and 1,000.



Estimate products using rounding.



Multiply a multi-digit number by a one-digit number.



Determine reasonable answers.

Key Vocabulary multiply estimate product Distributive Property of Multiplication

Math Online

234

Student Study Tools at macmillanmh.com

Chapter 6 Multiply by One-Digit Numbers

Denis Scott/CORBIS

Make this Foldable to help you organize information about multiplying by one-digit numbers. Begin with one sheet of 11” × 17” paper. Fold the short sides so they meet in the middle.

Fold the top to the bottom.

Unfold and cut to make four tabs.

Label each tab as shown.

Chapter 6 Multiply by One-Digit Numbers

235

ARE YOU READY for Chapter 6? You have two ways to check prerequisite skills for this chapter.

Option 2 Math Online

Option 1

Take the Chapter Readiness Quiz at macmillanmh.com.

Complete the Quick Check below.

Multiply. Use models if needed. (Lessons 4-3 and 4-5) 1. 2 × 3 5.

9 × 4 −−−

2. 4 × $4 6.

8 × 3 −−−

3. 5 × 6 7.

$7 × 5 −−−

4. 7 × $8 8.

9 × 9 −−−

9. Evan’s photo album has 8 pages of pictures. How many photos are in Evan’s album if the same number of photos are on each page?

Identify the place value of the underlined digit. (Lesson 1-1) 10. 1,630

11. $5,367

12. 20,495

13. $89,196

14. Measurement Mount Everest’s tallest peak is 29,035 feet. It is the highest point on Earth. Identify the place value of each digit in 29,035.

Round each number to its greatest place value. (Lesson 1-6) 15. 26

16. $251

17. 4,499

19. There are 1,366 students at Sunrise Elementary School. Approximately how many students attend the school?

236

Chapter 6 Multiply by One-Digit Numbers

18. $33,103

6-1

MAIN IDEA I will multiply multiples of 10, 100, and 1,000 using basic facts and patterns.

Math Online macmillanmh.com • Extra Examples • Personal Tutor • Self-Check Quiz

Multiples of 10, 100, and 1,000 The whale shark is the world’s largest fish. Its mouth is 5 feet long, and each foot contains 600 teeth. How many teeth does a whale shark have?

You can use basic facts and number patterns to multiply.

Real-World EXAMPLE

Multiples of 100

1 ANIMALS How many teeth does a whale shark have? You need to find 5 × 600. Use basic facts and patterns. 5 × 6 = 30

5 × 6 ones = 30 ones = 30

5 × 60 = 300

5 × 6 tens = 30 tens = 300

5 × 600 = 3,000 5 × 6 hundreds = 30 hundreds = 3,000 So, a whale shark has 3,000 teeth. Notice that this answer is 5 × 6 with two zeros at the end.

EXAMPLE

Multiples of 1,000

2 Find 3 × 7,000. 3 × 7 = 21

3 × 7 ones = 21 ones = 21

3 × 70 = 210

3 × 7 tens = 21 tens = 210

3 × 700 = 2,100

3 × 7 hundreds = 21 hundreds = 2,100

3 × 7,000 = 21,000

3 × 7 thousands = 21 thousands = 21,000

So, 3 × 7,000 is 21,000. Notice that this answer is 3 × 7 with three zeros at the end.

Lesson 6-1 Multiples of 10, 100, and 1,000

237

When you know basic facts and number patterns, you can multiply mentally.

Real-World EXAMPLE

As the number of zeros in a factor increases, the number of zeros . in the product increases

Multiply Mentally

3 MEASUREMENT The weight of a fire truck is 8 × 4,000 pounds. What is its weight in pounds? To find its weight, you need to find 8 × 4,000. 8 × 4,000 THINK You know that 8 × 4 = 32. There are 3 zeros.

32,000 Since 8 × 4,000 = 32,000, the weight of the fire truck is 32,000 pounds.

Multiply. Use basic facts and patterns. See Examples 1 and 2 (p. 237) 1. 2 2 2 2

× × × ×

1 10 100 1,000

2. 6 6 6 6

× × × ×

3. 7 7 7 7

8 80 800 8,000

× × × ×

9 90 900 9,000

Multiply. Use mental math. See Example 3 (p. 238) 4. 3 × 20

5. 8 × 600

7. A zookeeper is in charge of feeding an anteater. Each day the anteater eats 5 × 6,000 ants. How many ants must the zookeeper give the anteater each day? 238

6. 9 × 9,000 8.

What is the product of 4 and 5,000? Explain why there are more zeros in the product than in the factors in the problem.

Chapter 6 Multiply by One-Digit Numbers

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Multiply. Use basic facts and patterns. See Examples 1 and 2 (p. 237) 9. 5 5 5 5

× × × ×

3 30 300 3,000

10. 3 3 3 3

× × × ×

4 40 400 4,000

11. 2 2 2 2

× × × ×

9 90 900 9,000

12. 6 6 6 6

× × × ×

7 70 700 7,000

13. 9 9 9 9

× × × ×

1 10 100 1,000

14. 8 8 8 8

× × × ×

5 50 500 5,000

Multiply. Use mental math. See Example 3 (p. 238) 15. 4 × 30

16. 6 × 40

17. 7 × 200

18. 4 × 500

19. 3 × 9,000

20. 9 × 6,000

Algebra Copy and complete. 21. If 6 ×  = 42, then 60 ×  = 4,200.

22. If 5 × 7 = , then 50 ×  = 3,500.

23. Mr. Singh’s car payments are $300 a month. How much money will he pay in 6 months?

24. Mia’s cell phone plan includes 2,000 monthly minutes. How many minutes does she get over 6 months?

Real-World PROBLEM SOLVING

Travel

The Williams family is going to a theme park.

25. Admission tickets cost $30 for each person. What is the total cost for the 5 family members for one day? 26. The cost for each person to eat for one week is $100. Find the total cost for the family to eat for one week. 27. Suppose each family member goes on 70 rides during the week. How many rides will they go on altogether?

28. OPEN ENDED Write two multiplication expressions that have a product of 20,000. 29.

How would you find 1 × 10,000? What is 1 × 10,000? Lesson 6-1 Multiples of 10, 100, and 1,000

239

6-2

Problem-Solving Skill MAIN IDEA

I will decide whether an answer to a problem is reasonable.

Odell donated 3 cases of dog treats to a dog shelter. Each case has 900 treats. The dogs eat 2,500 treats each month. Odell says he has donated enough treats for more than one month. Is his claim reasonable?

Understand

What facts do you know? • 3 cases of treats were donated. • Each case has 900 treats. • The animals eat 2,500 treats each month. What do you need to find? • Is it reasonable to say that the 3 cases of treats will last longer than one month?

Plan Solve

Find 3 × 900. Then determine if the amount is reasonable. 3 × 900 THINK 3 × 9 = 27 Place 2 zeros in the product.

2,700 Since 2,700 > 2,500, it is reasonable to say that the three cases will last longer than one month.

Check

240

You can add to check the multiplication. 900 + 900 + 900 = 2,700 So, the answer is correct.

Chapter 6 Multiply by One-Digit Numbers

Refer to the problem on the previous page. 1. Explain why 3 is multiplied by 900 to decide if Odell’s claim was reasonable.

3. Look back at the example. What would make Odell’s claim not reasonable?

2. Explain why there are 2 zeros at the end of the product of 3 and 900.

4. Suppose Odell donates 5 cases of treats. Is it reasonable to believe the treats will last 2 months? Explain. EXTRA

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Decide whether each answer is reasonable. Explain your reasoning. 5. Measurement The calendar shows the number of days each month Olivia rides her bike.

8. Measurement The distance from lan’s home to the museum is 2,640 yards. Is it reasonable to say that Ian’s home is more than 9,000 feet away from the museum? (3 feet = 1 yard) 9. Kiri spends 60 minutes a week walking to school. Is it reasonable to say that she spends 240 minutes walking to school in four weeks? 10. The table below shows the number of pennies collected by four children.

Each time she rides her bike, she travels 10 miles. Is it reasonable to C07-29A-105711 say that Olivia will bike more than 500 miles in 6 months? 6. Ben delivers 40 newspapers each day. Is 400 a reasonable estimate for the number of newspapers Ben delivers each week? 7. Jay makes $40 a week doing yard work. He is saving his money to buy a computer that costs $400. He has already saved $120. Is it reasonable to say that Jay will save enough money to buy the computer in 6 weeks?

Is it reasonable to say that the children collected about 200 pennies in all? 11.

Write a problem where $180 would be a reasonable answer.

Lesson 6-2 Problem-Solving Skill: Reasonable Answers

241

6-3

MAIN IDEA I will estimate products by rounding.

New Vocabulary estimate

Math Online macmillanmh.com • Extra Examples • Personal Tutor • Self-Check Quiz

Use Rounding to Estimate Products The fastest passenger train in the world actually floats above its track. This train in China can travel up to 267 miles per hour. About how far can the train travel in 3 hours?

To estimate products, round factors to their greatest place.

Real-World EXAMPLE

Estimate Products

1 TRAVEL About how far can the train travel in 3 hours? Estimate 3 × 267. Round the larger factor to its greatest place. Then use basic facts and patterns to multiply. 3 × 267 THINK 267 rounds to 300.

3 × 300 = 900 So, the train can travel about 900 miles in 3 hours. Since 267 was rounded up, the estimated product is greater than the actual product.

EXAMPLE

Estimate Greater Products

2 Estimate 8 × 2,496. First round, then multiply using basic facts and patterns. 8 × 2,496 THINK 2,496 rounds to 2,000.

8 × 2,000 = 16,000 So, 8 × 2,496 is about 16,000. Since 2,496 was rounded down, the estimated product is less than the actual product.

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Chapter 6 Multiply by One-Digit Numbers

You can also estimate products involving money.

Real-World EXAMPLE

, • When you round up ct du pro d the estimate the is greater than actual product. • When you round down, the estimated product is less than the actual product.

Estimate Money

3 MONEY Lacey’s older brother is going to a four-year college. The cost of his tuition is $8,562 each year. About how much will 4 years of college tuition cost? You need to estimate 4 × $8,562. First round, then multiply. 4 × $8,562

THINK 8,562 rounds to 9,000.

4 × $9,000 = $36,000 So, tuition will cost about $36,000.

Estimate each product. Then tell if the estimate is greater than or less than the actual product. See Examples 1–3 (pp. 242–243) 1. 449 × 5 −−−

2. $870 × 9 −−−

3. 3,293 × −−−−3

4. 7 × $1,395

5. 6 × 5,500

6. 9 × $7,420

For Exercises 7 and 8, use the data at the right. 7. Mr. and Mrs. Rivera are planning to go on an African safari. They have saved $1,125 a year for 8 years. If the trip costs $9,830, do they have enough money saved for the trip? Explain. 8.

Suppose Mr. and Mrs. Rivera saved $1,499 a year for 8 years. Why would an estimated answer be misleading for the amount saved? Lesson 6-3 Use Rounding to Estimate Products

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Estimate each product. Then tell if the estimate is greater than or less than the actual product. See Examples 1–3 (pp. 242–243) 9. 562 × 6 −−−

10. 896 × 2 −−−

11. 729 × 8 −−−

12. 949 × 4 −−−

13. 2 × $438

14. 8 × $647

15. 5 × $355

16. 7 × $450

17. 7 × 1,125

18. 3 × 5,489

19. 9 × 3,500

20. 6 × 8,816

21. 4 × $6,502

22. 7 × $8,856

23. 9 × $9,498

24. 7 × $9,310

25. There are 24 students in each class at Watson Elementary School. About how many students are there if there are 8 classes?

26. The round-trip distance from Woodward to Oklahoma City is 139 miles. Ms. Hodges travels this distance 6 days a week. About how many miles does she travel each week?

Real-World PROBLEM SOLVING

Entertainment

Toby and Lena like to go to the arcade. They earn points toward prizes. 27. Toby went to the arcade 2 times. He earned 5,150 points each time. What is the biggest prize Toby can get? 28. How many toy cars could Toby get with his points? 29. Lena went to the arcade 7 times. She earned 9,050 points each time. What are the two largest prizes she can get?

30. NUMBER SENSE Explain how you can tell if your estimated answer is more or less than the exact answer to a multiplication problem. 31.

244

Suppose you need to find the exact answer to 4 × $189. How can you use estimation to check the reasonableness of your answer? Chapter 6 Multiply by One-Digit Numbers

Estimation Station Estimate Products

Get Ready!

Players: 2 players You will need: spinner, 1 number cube, 2 whiteboards

,

x

Get Set!

Each player makes a spinner and a game board as shown. 2

Go!

• Player 1 rolls the number cube to find a one-digit factor. Record the number in the second row on the game board.

3

4

• Player 1 then spins to find how many digits will be in the second factor. • Player 1 rolls the number cube to find the digits in the second factor. Record each digit. • Player 1 estimates the product and gets 1 point if the estimate is correct. • Player 2 takes a turn. • Continue playing. The player who earns 10 points first wins.

Game Time Estimation Station

245

6-4

Multiply Two-Digit Numbers Hands-On Mini Activity Materials: base-ten blocks

MAIN IDEA I will multiply a two-digit number by a one-digit number.

Base-ten blocks can be used to explore multiplying two-digit numbers. In this activity, you will find 4 × 13. Step 1

Model 4 groups of 13.

Step 2

Combine the tens and ones. Regroup 12 ones as 1 ten and 2 ones.

Math Online macmillanmh.com • Extra Examples • Personal Tutor • Self-Check Quiz • Concepts in Motion

4 groups of 10

10

4 groups of 3

+

4

4

Step 3

= 3 12 ones = 1 ten, 2 ones

Add the partial products.

50 + 2 = 52

So, 4 × 13 = 52. Find each product. Use base-ten blocks. 1. 3 × 18

2. 4 × 19

3. 3 × 21

4. Multiplication can be a shortcut for which operation? 5. When is it necessary to regroup in a multiplication problem? When is regrouping not needed?

246

Chapter 6 Multiply by One-Digit Numbers

Using place-value models is not the only way to multiply a two-digit number by a one-digit number.

EXAMPLE

Multiply with Regrouping

1 Find 6 × 38. Estimate 6 × 38

One Way: To review the Distributive Property of Multiplication, see Lesson 4-6 (p. 166).

6 × 40 = 240

Distributive Property

6 × 38 = (6 × 30) + (6 × 8) = 180 + 48 = 228

Another Way: 38 ×6 −−− 48 + 180 −−−− 228

Partial Products

Multiply 6 × 8.

6

30

8

180

48

Multiply 6 × 30. Add the partial products.

Another Way:

Paper and Pencil

Multiply the ones.

Step 1

4

38 ×6 −−− 8

180 + 48 = 228

Step 2

Multiply the tens. 4

6 × 8 = 48 Regroup 48 ones as 4 tens and 8 ones.

38 ×6 −−− 228

6 × 3 = 18 Add the regrouped tens, 4.

Check for Reasonableness The product, 228, is close to the estimate, 240.



Multiply. Check for reasonableness. See Example 1 (p. 247) 1.

23 × 2 −−−

2.

3. 8 × $98

42 × 2 −−−

4. Haley can fit 25 books on each of 5 shelves. How many books will fit in all?

5.

Explain how to find 6 × 37.

Lesson 6-4 Multiply Two-Digit Numbers

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Multiply. Check for reasonableness. See Example 1 (p. 247) 6.

7. $24 × 2 −−−

33 × 2 −−−

8.

9.

11 × 7 −−−

13 × 3 −−−

10. 2 × $27

11. 4 × 29

12. 5 × 18

13. 7 × $36

14. 6 × 52

15. 8 × 75

16. 4 × $83

17. 9 × 99

19. Suppose the sales tax is 7 cents for each dollar that is spent on any item. How much sales tax is charged for a badminton set that costs $35?

18. Will makes $4 an hour shampooing dogs at a pet shop. Last month he worked 26 hours. How much money did Will earn?

Crystal Cave Park is located in Kutztown, Pennsylvania. 20. The Diaz family has 2 adults and 3 children. How much would it cost for the family to go on a walking tour?

Walking Tour Adults . . . . . . . . $18 Children . . . . . . . $15 Gemstone Panning per person . . . . . . $12

21. Can the Diaz family pan for gemstones for $75? Explain. 22. Find the total cost for the Diaz family to take the walking tour and pan for gemstones.

Source: Crystal Cave Co., Inc.

.

23. OPEN ENDED Write two problems that result in a product of 120. 24. WHICH ONE DOESN’T BELONG? Which multiplication problem does not belong with the other three? Explain.

12 ×8 −− 25.

22 ×4 −−

52 ×2 −−

How do you use partial products to find 6 × 42?

248

33 ×3 −−

Chapter 6 Multiply by One-Digit Numbers

CH

APTER

6

Mid-Chapter Check Lessons 6-1 through 6-4

Multiply. Use basic facts and patterns. (Lesson 6-1)

1. 3 3 3 3

× × × ×

4 40 400 4,000

2. 12 12 12 12

× × × ×

5 50 500 5,000

3. A Triceratops weighs 2 × 7,000 pounds. How much does a Triceratops weigh? 4. Kyra needs 292 toothpicks for a project. A box holds 150 toothpicks. Is it reasonable to buy 2 boxes? Explain. (Lesson 6-2)

5. Mara and Billy have 6 bags of 12 balloons. Is it reasonable to say they have more than 75 balloons? (Lesson 6-2)

9. Juan plans to read 264 pages a month to complete his book in 6 months. About how many pages are in his book? (Lesson 6-3) 10. Measurement Each gallon of paint covers about 350 square feet. Ann estimated that 3 gallons of paint would be enough to cover 1,400 square feet. Will Ann have enough paint? Explain. (Lesson 6-3)

Multiply. Check for reasonableness. (Lesson 6-4)

11. 43 × 2 −−−

12. $51 × 3 −−−

13. 9 × 62

14. 8 × 47

15. MULTIPLE CHOICE There are 27 boxes of markers in the art room. If each box holds 8 markers, how many markers are in the art room? (Lesson 6-4)

Estimate each product. (Lesson 6-3) 6. 3 × 252

7. 5 × 7,493

8. MULTIPLE CHOICE Jada pays $1,875 a year in car payments. About how much money will she pay in 5 years? (Lesson 6-3) A $5,000

C $9,375

B $7,500

D $10,000

16.

F 106

H 216

G 166

J 226

Cassie got the following problem wrong on her math test. Explain what she did wrong. (Lesson 6-4) 5

47 × 8 −−− 326 Formative Assessment

249

6-5

Problem-Solving Investigation MAIN IDEA I will choose the best strategy to solve a problem.



ISABEL: I am making punch for a party. One bowl of punch serves 35 guests. I am going to make four bowls of punch. YOUR MISSION: Find how many guests four bowls of punch serve.

Understand

One bowl of punch serves 35 guests. Isabel is making four bowls of punch. Find how many guests will be served by four bowls of punch.

Plan

Use the four-step plan and write a number sentence. Multiply the number of guests served by one bowl of punch by the number of bowls being made.

Solve

You need to find 35 × 4 = . 35 × 4 −−− 20 Multiply 4 × 5. +120 −−−− Multiply 4 × 30. 140 Add.

4

30

5

120

20

120 + 20 = 140

So, four bowls of punch will serve 140 guests.

Check

Look back. You can use repeated addition to check your answer. 35 + 35 + 35 + 35 = 140. So, the answer is correct.

250

Chapter 6 Multiply by One-Digit Numbers

EXTRA 0 2 ! # 4 )# % See page R16.

Use any strategy shown below to solve. Tell what strategy you used.

ING STRATEGIES PROBLEM-SOLV • Make a table.

5. There are 18 stickers on each sheet. There are five sheets in one pack. How many stickers are in one pack? 6. Algebra Copy and complete the pattern below. Describe the pattern. 100, 200, 400, , 1,600, , 6,400 7. Geometry If this pattern is repeated, identify the 18th shape in the pattern.

1. Algebra There are 12 members in each scout troop. Make a table to find out how many members will attend a meeting if there are 10, 11, 12, or 13 scout troops attending. 2. Nate is trying to choose 3 items from the menu below. What are 3 possible combinations Nate could choose?

8. A wall has an animal poster to the right of a car poster. A space poster is last. A music poster is to the left of the space poster. What is the order of the 4 posters? 9. Emma now has $32. She earned $12 babysitting and she received $5 for her allowance. How much money did she have originally? 10. The Turner family played miniature golf. What is the total cost if 2 adults and 3 children played 18 holes of golf?

3. Kishi is choosing an outfit to wear to school. She has 3 shirts, 2 pairs of pants, and 3 pairs of shoes to choose from. How many different outfits does she have to choose from? 4. While on a class field trip, Hally learned that four bears eat 2,000 ants per day. How many ants will 2 bears eat in one day?

11.

Look at Exercise 9. Identify the strategy you used. Explain how you used this strategy to solve the problem.

Lesson 6-5 Problem-Solving Investigation: Choose a Strategy

251

6-6

MAIN IDEA I will multiply a multi-digit number by a one-digit number.

Multiply Multi-Digit Numbers Today is Laura’s birthday, and she is nine years old. Except for leap years, there are 365 days in one year. How many days old is Laura?

Math Online macmillanmh.com • Extra Examples • Personal Tutor • Self-Check Quiz

You multiply multi-digit numbers the same way you multiply a two-digit number by a one-digit number.

Real-World EXAMPLE

Partial Products

1 TIME How many days old is Laura? To find how old Laura is in days, multiply the number of days in a year by the number of years. That is, find 365 × 9. You can use partial products. Estimate 9 × 365 365 × 9 −−− 45 540 + 2,700 −−−−−− 3,285

Multiply 9 × 5. Multiply 9 × 60. Multiply 9 × 300. Add the partial products.

300 9

9 × 400 = 3,600

+

2,700

60 + 5 540

45

2,700 540 + 45 −−−−− 3,285

So, Laura is 3,285 days old. Check for Reasonableness The product, 3,285, is close to the estimate, 3,600. 

252

Chapter 6 Multiply by One-Digit Numbers

You can also use paper and pencil to multiply.

EXAMPLE

Multiply Money

2 Find 3 × $1,175. Step 1 Multiply the ones. 1

Always check for reasonableness. 3 × $1,175 ↓ 3 × $1,000 = $3,000 Since $3,525 is close to $3,000, the answer

$1,175 × 3 5

3 × 5 ones = 15 Regroup 15 ones as 1 ten and 5 ones.

Step 2 Multiply the tens. 21

3 × 7 tens = 21 tens Add the regrouped tens. 21 tens + 1 ten = 22 tens

$1,175 × 3 −−−− 25

is reasonable.

Regroup 22 tens as 2 hundreds and 2 tens.

Step 3 Multiply the hundreds. 21

$1,175 × 3 −−−− 525

3 × 1 hundred = 3 hundreds Add the regrouped hundreds. 3 hundreds + 2 hundreds = 5 hundreds

Step 4 Multiply the thousands. 21

$1,175 × −−−3 $3,525 $1,000 3

$3,000

3 × 1 thousand = 3 thousands

+

$100 + $70 + $5 $300

$210 $15

$3,000 $300 $210 + $15 −−−−−− $3,525

Multiply. Check for reasonableness. See Examples 1 and 2 (pp. 252–253) 1. 135 × 2 −−−

2. 532 × 6 −−−

5. A vacation costs $1,389 for one person. What is the total cost of this vacation for a family of four?

3. 2 × $2,957

6.

4. 7 × 7,832

Explain why it is a good idea to estimate answers to multiplication problems.

Lesson 6-6 Multiply Multi-Digit Numbers

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Multiply. Check for reasonableness. See Examples 1 and 2 (pp. 252–253) 7. $168 × 2 −−−

8. 313 × 3 −−−

9. 252 × 2 −−−

10. $338 × 3 −−−

11. 238 × 4 −−−

12. 819 × 5 −−−

13. $781 × 5 −−−

14. 340 × 6 −−−

15. 7 × $4,160

16. 7 × 5,611

17. 8 × 6,328

18. 9 × $5,679

19. 8 × 7,338

20. 7 × 8,469

21. 9 × $9,927

22. 9 × 8,586

Algebra Find the value of each expression if n = 8. 23. n × 295

24. 737 × n

25. n × $2,735

26. 7,372 × n

Compare. Replace each  with >,

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