Name Daily Spiral Review 7-1 - Wikispaces - owlsharenestgrade+topic+7.pdfMar 18, 2008 · Daily Spiral Review 7-1 1. Dr . ... Daily Spiral Review 7Ð1 12 6 14 18 6 10 ... Daily Spiral

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Daily Spiral Review

7-1

1. Dr. Gallo’s waiting room has a total of 18 magazines, including 3 fashion magazines. There are 5 more cooking magazines than there are decorating magazines. How many decorating magazines are there? You can use cubes to act out the problem.A 5B 6C 10D 15

2. Gisela is putting her 35 CDs into categories. She has 11 that are pop music, and she has 3 times as many rock CDs as she has classical. How many rock CDs does Gisela have? You can use cubes to act out the problem.A 24B 20C 18D 6

3. An order comes in to Extreme Skate Co. for 56 pairs of its most popular skate shoes, including 14 pairs of grey. The order calls for 4 times as many hot pink pairs as red pairs, and 3 more pairs of black than grey. How many pairs of hot pink shoes were ordered? A 5 C 20B 17 D 42

4. Arturo’s Nursery has 48 tree seedlings ready to sell. There are 16 magnolia seedlings. There are 2 times as many dogwood seedlings as oak seedlings. There are 2 more magnolia seedlings than pine seedlings. How many of each type of seedling is ready to sell? Use the table.

Seedling Number Ready to Sell

Magnolia 16

Dogwood

Oak

Pine

5. Mr. Canela’s 42 students voted on a class mascot. The gorilla received 8 votes. The python received 3 times as many votes as the giraffe, and the crocodile received 2 more votes than the gorilla. How many votes did each animal receive? Use the table.

Mascot Number of Votes

Gorilla 8

Python

Giraffe

Crocodile

Daily Spiral Review

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Topic 7 25

Daily Spiral Review

7-1

1. Dr. Gallo’s waiting room has a total of 18 magazines, including 3 fashion magazines. There are 5 more cooking magazines than there are decorating magazines. How many decorating magazines are there? You can use cubes to act out the problem.A 5B 6C 10D 15

2. Gisela is putting her 35 CDs into categories. She has 11 that are pop music, and she has 3 times as many rock CDs as she has classical. How many rock CDs does Gisela have? You can use cubes to act out the problem.A 24B 20C 18D 6

3. An order comes in to Extreme Skate Co. for 56 pairs of its most popular skate shoes, including 14 pairs of grey. The order calls for 4 times as many hot pink pairs as red pairs, and 3 more pairs of black than grey. How many pairs of hot pink shoes were ordered? A 5 C 20B 17 D 42

4. Arturo’s Nursery has 48 tree seedlings ready to sell. There are 16 magnolia seedlings. There are 2 times as many dogwood seedlings as oak seedlings. There are 2 more magnolia seedlings than pine seedlings. How many of each type of seedling is ready to sell? Use the table.

Seedling Number Ready to Sell

Magnolia 16

Dogwood

Oak

Pine

5. Mr. Canela’s 42 students voted on a class mascot. The gorilla received 8 votes. The python received 3 times as many votes as the giraffe, and the crocodile received 2 more votes than the gorilla. How many votes did each animal receive? Use the table.

Mascot Number of Votes

Gorilla 8

Python

Giraffe

Crocodile

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Topic 7

7-1Problem of the DayProblem

of the Day

7-1

Which two numbers share a greatest common factor of 6 and a least common multiple of 60?

Problem of the Day 7-1

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Topic 7 27

Interactive Learning Recording Sheet

13

Interactive Learning Recording Sheet 1

3

Multiplying Decimals by 10, 100, or 1,000Nickels

Number of Nickels 1 2 3 4 5 10 100 1,000

Value

Dimes

Number of Dimes 1 2 3 4 5 10 100 1,000

Value

Quarters

Number of Quarters 1 2 3 4 5 10 100 1,000

Value

1. How can you multiply a decimal by 10?

2. How can you multiply a decimal by 100?

3. How can you multiply a decimal by 1,000?

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28 Topic 7

Quick Check

7-1Q

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1. Use mental math to find the product 12.56 ! 100.

A 12.5600B 125.6C 1,256D 12,560

2. Mark counts all the coins he has saved in his coin jar. What is the total amount of his savings?

1,000 100 10 10

A $18.50B $27.50C $72.50D $117.50

3. A manufacturer sells bolts in packages of 1,000 bolts. If a particular type of bolt weighs 4.23 grams, how much does a package of 1,000 bolts weigh?A 423,000 gramsB 4,230 gramsC 423 gramsD 4.23000 grams

4. Writing to Explain A printing company needs to send several items to a customer. The maximum weight that can be shipped in a single box is 50 pounds. Based on their sizes, the following number of items can be packed in a box. Determine whether each box can be shipped or whether it is too heavy.

Item Weight per item Number per box

booklets 0.67 pounds 100

flyers 0.035 pounds 1,000

textbooks 4.8 pounds 10

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Quick Check

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1. Use mental math to find the product 12.56 ! 100.

A 12.5600B 125.6C 1,256D 12,560

2. Mark counts all the coins he has saved in his coin jar. What is the total amount of his savings?

1,000 100 10 10

A $18.50B $27.50C $72.50D $117.50

3. A manufacturer sells bolts in packages of 1,000 bolts. If a particular type of bolt weighs 4.23 grams, how much does a package of 1,000 bolts weigh?A 423,000 gramsB 4,230 gramsC 423 gramsD 4.23000 grams

4. Writing to Explain A printing company needs to send several items to a customer. The maximum weight that can be shipped in a single box is 50 pounds. Based on their sizes, the following number of items can be packed in a box. Determine whether each box can be shipped or whether it is too heavy.

Item Weight per item Number per box

booklets 0.67 pounds 100

flyers 0.035 pounds 1,000

textbooks 4.8 pounds 10

See student samples at the right.

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Topic 7 29

Reteaching

7-1Multiplying Decimals by 10, 100, or 1,000You can use patterns to multiply decimals mentally by 10, 100, and 1,000.

Andrew starts selling his baseball cards for $0.10 each. After selling 10 cards, he has made $1.00. After selling 100 cards, he has made $10.00.

When you multiply by Move the decimal point 10 1 place to the right 100 2 places to the right 1,000 3 places to the rightIf Andrew sold 1,000 cards, how much money would he make?

For questions 1 through 4, find the product using mental math.

1. 6.1 ! 10 2. 100 ! 37.98

3. 92.3 ! 1,000 4. 0.418 ! 100

5. Myla has an antique flower vase that she bought for $15.75 many years ago. The vase’s value is now 1,000 times as great. What is the value of the vase?

6. Raul can hit a golf ball 26.4 yards. A.J. can hit a golf ball 10 times as far. How far can A.J. hit the ball?

7. Reasonableness Is 0.018 a reasonable answer for 1.8 ! 100?

$.0.10 $.0.10 ! 10 " $1.00 $0.10 ! 100 " $10.00

Reteaching 7-1

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Topic 7 29

Reteaching

7-1Multiplying Decimals by 10, 100, or 1,000You can use patterns to multiply decimals mentally by 10, 100, and 1,000.

Andrew starts selling his baseball cards for $0.10 each. After selling 10 cards, he has made $1.00. After selling 100 cards, he has made $10.00.

When you multiply by Move the decimal point 10 1 place to the right 100 2 places to the right 1,000 3 places to the rightIf Andrew sold 1,000 cards, how much money would he make?

For questions 1 through 4, find the product using mental math.

1. 6.1 ! 10 2. 100 ! 37.98

3. 92.3 ! 1,000 4. 0.418 ! 100

5. Myla has an antique flower vase that she bought for $15.75 many years ago. The vase’s value is now 1,000 times as great. What is the value of the vase?

6. Raul can hit a golf ball 26.4 yards. A.J. can hit a golf ball 10 times as far. How far can A.J. hit the ball?

7. Reasonableness Is 0.018 a reasonable answer for 1.8 ! 100?

$.0.10 $.0.10 ! 10 " $1.00 $0.10 ! 100 " $10.00

Reteaching 7-1

61 3,79892,300 41.8

$15,750

264 yards

No. The answer cannot be a smaller number than the factors unless at least one factor is between 0 and 1. The answer should be 180.

$100.00

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30 Topic 7

Practice

7-1Multiplying Decimals by 10, 100, or 1,000Use mental math to find each product.

1. 53.7 ! 10 2. 74.3 ! 100

3. 66.37 ! 1,000 4. 1.03 ! 10

5. 92.5 ! 10 6. 0.8352 ! 100

7. 0.567 ! 100 8. 572.6 ! 1,000

9. 5.8 ! 100 10. 0.21 ! 1,000

11. 6.2 ! 1,000 12. 1.02 ! 10

13. 0.003 ! 1,000 14. 0.002 ! 10

15. 7.03 ! 10 16. 4.06 ! 100

17. Algebra Kendra bought 10 gallons of gasoline at $3.26 per gallon. How much did she pay for the gasoline?

A $326.00 B $32.60 C $1.26 D $0.26

18. Strategy Practice Freddy is helping buy ingredients for salads for the school spaghetti dinner. He bought 10 pounds of onions at $0.69 per pound, 100 pounds of tomatoes at $0.99 pound, 1,000 pounds of bread crumbs at $0.09 per pound, and 100 pounds of lettuce at $0.69 per pound. Which of the items he bought cost the most?

A tomatoes B lettuce C bread crumbs D onions

19. Explain It Marco and Suzi each multiplied 0.721 ! 100. Marco got 7.21 for his product. Suzi got 72.1 for her product. Which student multiplied correctly? How do you know?

Prac

tice 7-1

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30 Topic 7

Practice

7-1Multiplying Decimals by 10, 100, or 1,000Use mental math to find each product.

1. 53.7 ! 10 2. 74.3 ! 100

3. 66.37 ! 1,000 4. 1.03 ! 10

5. 92.5 ! 10 6. 0.8352 ! 100

7. 0.567 ! 100 8. 572.6 ! 1,000

9. 5.8 ! 100 10. 0.21 ! 1,000

11. 6.2 ! 1,000 12. 1.02 ! 10

13. 0.003 ! 1,000 14. 0.002 ! 10

15. 7.03 ! 10 16. 4.06 ! 100

17. Algebra Kendra bought 10 gallons of gasoline at $3.26 per gallon. How much did she pay for the gasoline?

A $326.00 B $32.60 C $1.26 D $0.26

18. Strategy Practice Freddy is helping buy ingredients for salads for the school spaghetti dinner. He bought 10 pounds of onions at $0.69 per pound, 100 pounds of tomatoes at $0.99 pound, 1,000 pounds of bread crumbs at $0.09 per pound, and 100 pounds of lettuce at $0.69 per pound. Which of the items he bought cost the most?

A tomatoes B lettuce C bread crumbs D onions

19. Explain It Marco and Suzi each multiplied 0.721 ! 100. Marco got 7.21 for his product. Suzi got 72.1 for her product. Which student multiplied correctly? How do you know?

Prac

tice 7-1

53766,370 10.3

925 83.5256.7 572,600

5806,200

21010.2

3 .0270.3 406

Suzi’s answer was correct. She moved the decimal the correct number of spaces to the right.

7,430

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Topic 7 31

Enrichment

7-1

Mental Math

Decimal Patterns1. Jennifer sets her binoculars to enlarge objects

10 times their actual size. If the length of an ant is 0.52 inches, what is its length as seen through her binoculars?

2. A store has a contest to guess the weight of 1,000 black jellybeans on display in its window. If each of the jellybeans weighs 0.072 ounces, what is the total weight of all the jellybeans?

3. Jason saved $0.02 each day for 10,000 days. How much did he save in all?

4. Jefferson uses a microscope to observe a specimen in biology class. If his microscope enlarges objects 100 times their actual size and the specimen measures 0.009 inches, what is the size seen in the microscope?

5. Anya needs to buy 100 pounds of chocolate to make her holiday truffles. If chocolate sells for $0.49 per pound, how much will Anya spend?

6. Tim planted a tree that was 0.017 feet tall. After 10 years, the tree was 1,000 times as tall as when he planted it. What is the height of the tree after 10 years?

Enrichment 7

-1

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Topic 7 31

Enrichment

7-1

Mental Math

Decimal Patterns1. Jennifer sets her binoculars to enlarge objects

10 times their actual size. If the length of an ant is 0.52 inches, what is its length as seen through her binoculars?

2. A store has a contest to guess the weight of 1,000 black jellybeans on display in its window. If each of the jellybeans weighs 0.072 ounces, what is the total weight of all the jellybeans?

3. Jason saved $0.02 each day for 10,000 days. How much did he save in all?

4. Jefferson uses a microscope to observe a specimen in biology class. If his microscope enlarges objects 100 times their actual size and the specimen measures 0.009 inches, what is the size seen in the microscope?

5. Anya needs to buy 100 pounds of chocolate to make her holiday truffles. If chocolate sells for $0.49 per pound, how much will Anya spend?

6. Tim planted a tree that was 0.017 feet tall. After 10 years, the tree was 1,000 times as tall as when he planted it. What is the height of the tree after 10 years?

Enrichment 7

-1

5.2 inches

72 ounces

$200

0.9 inches

$49

17 feet

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32 Topic 7

1. Use mental math to ! nd the product.

9.3 ! 100

A 0.093B 93C 930D 9,300

2. Saul earns $25.75 each time he takes care of the Norman family’s pets over a long weekend. If he takes care of the Normans’ pets for 10 long weekends this year, how much money will he have earned?

A $2,575.00B $257.50C $35.75D $2.575

3. Find the difference.

54.59 " 26.61

A 81.20B 38.98C 32.18D 27.98

4. Kelvin rides the bus 7.78 miles to school each day. After 100 days of riding the bus, how many miles has he spent on the bus on the way to school?

5. Use mental math to ! nd each product.

0.07 ! 10

4.41 ! 100

0.058 ! 1,000

12.77 ! 100

0.26 ! 1,000

0.003 ! 10

Daily Spiral Review

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32 Topic 7

1. Use mental math to ! nd the product.

9.3 ! 100

A 0.093B 93C 930D 9,300

2. Saul earns $25.75 each time he takes care of the Norman family’s pets over a long weekend. If he takes care of the Normans’ pets for 10 long weekends this year, how much money will he have earned?

A $2,575.00B $257.50C $35.75D $2.575

3. Find the difference.

54.59 " 26.61

A 81.20B 38.98C 32.18D 27.98

4. Kelvin rides the bus 7.78 miles to school each day. After 100 days of riding the bus, how many miles has he spent on the bus on the way to school?

5. Use mental math to ! nd each product.

0.07 ! 10

4.41 ! 100

0.058 ! 1,000

12.77 ! 100

0.26 ! 1,000

0.003 ! 10

Daily Spiral Review

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Kelvin has spent 7.78 ! 100 " 778 miles on the bus.

0.7441581,2772600.03

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Topic 7 3

3


Alex swims 1.25 miles every other day. How many miles does she swim every 2 weeks?

Problem of the Day

7-2

7-2Problem of the Day

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14Multiplying a Whole Number and a Decimal Distances Traveled

Car 1 minute 3 minutes 5 minutes

1 1.3 km

2 0.75 km

3 2.15 km

4 1.8 km

Explain your solution.

34 Topic 7

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Topic 7 35

Quick Check

7-2

1. Calculate the product: 42.6 ! 15.

A 63.9B 639C 693D 6,390

2. Leslie and her friend eat lunch at a restaurant. To determine how much money to leave as a tip, she multiplies the bill by 0.18. How much money should she leave as a tip if the bill is $25?

A $6.25B $5.00C $4.50D $3.70

3. If the sales tax rate is 7.5%, the sales tax on a purchase can be calculated by multiplying the purchase price by 0.075. How much sales tax will you pay on a $112 purchase?

A $0.84B $4.80C $8.40D $84.00

4. Writing to Explain For a band fundraiser, the band boosters decide to sponsor a spaghetti dinner. They make a table of the items needed to prepare the dinner and the costs of each package on the table shown below. Calculate the total amount of money required to buy the food neededin the kitchen.

Product Packages needed Cost of each package

Pasta 45 $0.75

Sauce 52 $1.42

Prepared meatballs 8 $3.25

Quick C

heck 7-2

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Topic 7 35

Quick Check

7-2

1. Calculate the product: 42.6 ! 15.

A 63.9B 639C 693D 6,390

2. Leslie and her friend eat lunch at a restaurant. To determine how much money to leave as a tip, she multiplies the bill by 0.18. How much money should she leave as a tip if the bill is $25?

A $6.25B $5.00C $4.50D $3.70

3. If the sales tax rate is 7.5%, the sales tax on a purchase can be calculated by multiplying the purchase price by 0.075. How much sales tax will you pay on a $112 purchase?

A $0.84B $4.80C $8.40D $84.00

4. Writing to Explain For a band fundraiser, the band boosters decide to sponsor a spaghetti dinner. They make a table of the items needed to prepare the dinner and the costs of each package on the table shown below. Calculate the total amount of money required to buy the food neededin the kitchen.

Product Packages needed Cost of each package

Pasta 45 $0.75

Sauce 52 $1.42

Prepared meatballs 8 $3.25

Quick C

heck 7-2


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Rete

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Step 1. Multiply as with whole numbers.

2.6 ! 18 208 " 260 468

Step 2. Count the total decimal places in both factors.

2.6 1 decimal place

18 0 decimal places

Step 3. Since there is a total of 1 decimal place in the factors, there is 1 decimal place in the product.

46.8

Multiplying a Decimal by a Whole NumberTravis can read a book chapter in 2.6 hours. The book has 18 chapters. How long will it take Travis to read the book?

It will take Travis 46.8 hours to read the book.

For questions 1 through 3, find the product.

1. 2.3 2. 71.7 3. 0.894! 6 ! 12 ! 21

4. Sara is multiplying two factors, one with one decimal place and one with two decimal places. She says that the product should have two decimal places. Is this correct? Explain.

5. Critical Thinking Light bulbs usually cost $2. They are on sale for 0.50 of the regular price. What is the sale price? Is this a better price than if the sale price were 0.35 of the regular price?

Reteaching

7-2

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Rete

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Step 1. Multiply as with whole numbers.

2.6 ! 18 208 " 260 468

Step 2. Count the total decimal places in both factors.

2.6 1 decimal place

18 0 decimal places

Step 3. Since there is a total of 1 decimal place in the factors, there is 1 decimal place in the product.

46.8

Multiplying a Decimal by a Whole NumberTravis can read a book chapter in 2.6 hours. The book has 18 chapters. How long will it take Travis to read the book?

It will take Travis 46.8 hours to read the book.

For questions 1 through 3, find the product.

1. 2.3 2. 71.7 3. 0.894! 6 ! 12 ! 21

4. Sara is multiplying two factors, one with one decimal place and one with two decimal places. She says that the product should have two decimal places. Is this correct? Explain.

5. Critical Thinking Light bulbs usually cost $2. They are on sale for 0.50 of the regular price. What is the sale price? Is this a better price than if the sale price were 0.35 of the regular price?

Reteaching

7-2

13.8 860.4 18.774

This is incorrect. The factors have a total of three decimal places, so the product should have three decimal places.

$1; No, 0.35 is a smaller fraction than 0.50; the second price would be better.

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Topic 7 37

Practice

7-2Multiplying a Decimal by a Whole NumberFind each product.

1. 5.4 2. 3.8 3. 0.55 4. 8.19 ! 3 ! 4 ! 8 ! 5

Insert a decimal point in each answer to make the equation true.

5. 5 ! 6.3 " 315

6. 3.001 ! 9 " 27009

Use the table at the right for Exercises 7–9.

7. Which desert accumulates the least amount of rain in August?

8. If each month in Reno had the same average rainfall as in August, what would the total number of millimeters be after 12 months?

9. Explain It In December, the average total rainfall in all of the deserts together is 0.89 mm. Explain how to use the figures from the table to write a comparison of the total desert rainfall in August and December.

10. Algebra If 4n " 3.60, which is the value of n?

A 0.09 B 0.9 C 9 D 90

Average Desert Rainfall in August

Desert Average Rainfall

Reno 0.19 mm

Sahara 0.17 mm

Mojave 0.1 mm

Tempe 0.24 mm

Practice 7-2

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Topic 7 37

Practice

7-2Multiplying a Decimal by a Whole NumberFind each product.

1. 5.4 2. 3.8 3. 0.55 4. 8.19 ! 3 ! 4 ! 8 ! 5

Insert a decimal point in each answer to make the equation true.

5. 5 ! 6.3 " 315

6. 3.001 ! 9 " 27009

Use the table at the right for Exercises 7–9.

7. Which desert accumulates the least amount of rain in August?

8. If each month in Reno had the same average rainfall as in August, what would the total number of millimeters be after 12 months?

9. Explain It In December, the average total rainfall in all of the deserts together is 0.89 mm. Explain how to use the figures from the table to write a comparison of the total desert rainfall in August and December.

10. Algebra If 4n " 3.60, which is the value of n?

A 0.09 B 0.9 C 9 D 90

Average Desert Rainfall in August

Desert Average Rainfall

Reno 0.19 mm

Sahara 0.17 mm

Mojave 0.1 mm

Tempe 0.24 mm

Practice 7-2

16.2 15.2 4.4 40.95

31.527.009

Mojave

2.28 mm

In December, the average rainfall is greater than in August, because 0.89 mm > 0.7 mm.

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38 Topic 7

Enric

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How Much Faster?Ryan’s Deli makes a sandwich in 1 min. The chart at the right indicates how long it takes other delis to make a sandwich in comparison to Ryan’s. For example, Werner’s Deli takes 2.2 times as long to make a sandwich as Ryan’s. For the exercises below, determine if the statement is reasonable or unreasonable. Explain your answer.

1. In 10 min, Ryan’s Deli will make more than twice as many sandwiches as Werner’s Deli.

2. In 30 min, Main Street Deli will make more than twice as many sandwiches as Ryan’s Deli.

3. It takes the Two Star Deli under 38 min to make 10 sandwiches.

Reasonableness

Deli Time Factor

Werner’s 2.2

Main Street 0.6

Two Star 3.74

Enrichment

7-2

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38 Topic 7

Enric

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How Much Faster?Ryan’s Deli makes a sandwich in 1 min. The chart at the right indicates how long it takes other delis to make a sandwich in comparison to Ryan’s. For example, Werner’s Deli takes 2.2 times as long to make a sandwich as Ryan’s. For the exercises below, determine if the statement is reasonable or unreasonable. Explain your answer.

1. In 10 min, Ryan’s Deli will make more than twice as many sandwiches as Werner’s Deli.

2. In 30 min, Main Street Deli will make more than twice as many sandwiches as Ryan’s Deli.

3. It takes the Two Star Deli under 38 min to make 10 sandwiches.

Reasonableness

Deli Time Factor

Werner’s 2.2

Main Street 0.6

Two Star 3.74

Enrichment

7-2

Reasonable; it takes Werner’s more than twice as long to make a sandwich as Ryan’s.

Unreasonable; it takes the Main Street Deli more than half as long to make a sandwich as Ryan’s.

Reasonable; it takes the Two Star Deli 3.74 min to make 1 sandwich. So, it would take the Two Star Deli 10 ! 3.74, or 37.4 min, to make 10 sandwiches.

30428_T07_035_038_38 38 3/18/08 2:17:41 PM

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Topic 7 39

1. Find the product.

6.5 ! 5

A 33.5B 32.5C 32.0D 30.5

2. Zoe plants a sun! ower seed and tracks its growth. The seedling measures 3.71 inches after the " rst month. If Zoe’s plant grows 3.71 inches each month for 12 months, how many inches tall will it be at the end of one year?A 10.13 inchesB 34.52 inchesC 43.52 inchesD 44.52 inches

3. Find the sum.

68.47 " 121.35

A 52.88B 63.98C 189.72D 189.82

4. Maria Elena is planning to paint a horizontal stripe around the middle of her bedroom. Each of her 4 walls measures 168.2 inches. How many inches long will the stripe be?

5. Find each product.

7.1 ! 4

0.33 ! 9

18.2 ! 7

0.078 ! 2

42.6 ! 3

23 ! 0.05

380 ! 0.006

6,400 ! 0.2

Daily Spiral Review

7-3Daily Spiral Review

7-3

30468_T07_39 39 1/16/08 6:02:48 PM

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Topic 7 39

1. Find the product.

6.5 ! 5

A 33.5B 32.5C 32.0D 30.5

2. Zoe plants a sun! ower seed and tracks its growth. The seedling measures 3.71 inches after the " rst month. If Zoe’s plant grows 3.71 inches each month for 12 months, how many inches tall will it be at the end of one year?A 10.13 inchesB 34.52 inchesC 43.52 inchesD 44.52 inches

3. Find the sum.

68.47 " 121.35

A 52.88B 63.98C 189.72D 189.82

4. Maria Elena is planning to paint a horizontal stripe around the middle of her bedroom. Each of her 4 walls measures 168.2 inches. How many inches long will the stripe be?

5. Find each product.

7.1 ! 4

0.33 ! 9

18.2 ! 7

0.078 ! 2

42.6 ! 3

23 ! 0.05

380 ! 0.006

6,400 ! 0.2

Daily Spiral Review

7-3Daily Spiral Review

7-3

168.2 ! 4 # 672.8 inches

28.42.97127.40.156

127.81.15

2.281,280

30428_T07_039_040_39 39 3/18/08 2:17:52 PM


40

Topic 7

7-3Problem of the DayClarissa had 116 trading cards. She gave 10 cards to Lou. Then she gave 1 _ 2 of the remaining cards to Pia. How many cards does she have left?

Problem of the Day

7-3


30468_T07_40 40

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Topic 7 41


15


5

Estimating the Product of a Decimal and a Whole Number Mrs. Cash’s Grocery List

Item Price Amount needed Estimated Cost

Actual Cost

Bread $2.39 per loaf 4 loaves

Chopped Meat $3.89 per pound 3 pounds

Eggs $2.10 per dozen 2 dozen

Cheese $4.70 per package 3 packages

Milk $2.90 per gallon 2 gallons

Total cost:

1. How did you estimate?

2. If Mrs. Cash brings $50 with her, will she have enough money to buy everything on her list? Explain.

30468_T07_41 41 1/16/08 6:03:02 PM

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42 Topic 7

1. Which of the following is the best estimate of the product: 79.87 ! 15?

A about 850B about 1,200C about 1,600D about 12,000

2. The circumference of a circle is equal to ! times its diameter. Estimate the circumference of a round swimming pool that has a diameter of 24 feet. Use ! " 3.14.A about 720 feetB about 120 feetC about 72 feetD about 65 feet

3. Your family takes a taxi from the airport to your hotel. The total charge for the ride is $38.55. How much should you give the cab driver as a tip if you want the tip to be about 15%?A $3.00B $4.00C $5.00D $6.00

4. Writing to Explain An engineer needs to determine the amount of stone to order for a road construction project. The table shows the amount of stone needed for each meter of the highway. Estimate the amount of each type of stone needed for a 290-meter section of the road. Estimate each value to the nearest 1,000 tons. Show your work.

Quick Check

7-3

Type of stone Tons per meterLarge rock 10.13

Large gravel 29.62

Fine gravel 7.35

Qui

ck C

heck

7-3

30468_T07_42 42 1/16/08 6:03:08 PM

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42 Topic 7

1. Which of the following is the best estimate of the product: 79.87 ! 15?

A about 850B about 1,200C about 1,600D about 12,000

2. The circumference of a circle is equal to ! times its diameter. Estimate the circumference of a round swimming pool that has a diameter of 24 feet. Use ! " 3.14.A about 720 feetB about 120 feetC about 72 feetD about 65 feet

3. Your family takes a taxi from the airport to your hotel. The total charge for the ride is $38.55. How much should you give the cab driver as a tip if you want the tip to be about 15%?A $3.00B $4.00C $5.00D $6.00

4. Writing to Explain An engineer needs to determine the amount of stone to order for a road construction project. The table shows the amount of stone needed for each meter of the highway. Estimate the amount of each type of stone needed for a 290-meter section of the road. Estimate each value to the nearest 1,000 tons. Show your work.

Quick Check

7-3

Type of stone Tons per meterLarge rock 10.13

Large gravel 29.62

Fine gravel 7.35

Qui

ck C

heck

7-3


30428_T07_042_047_42 42 3/18/08 2:18:15 PM

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Topic 7 43

Estimating the Product of a Decimal and a Whole NumberYou can estimate when you are multiplying a decimal by a whole number to check the reasonableness of your product.

Zane needs to buy 27 lb of roast beef for the company party. The roast beef costs $2.98 per pound. About how much will the roast beef cost?

There are two ways to estimate.

Round both numbers Adjust your factors to compatible numbers you can multiply mentally.

$2.98 ! 27 $2.98 ! 27

$3 ! 30 " $90 $3 ! 25 " $75

The roast beef will cost about $90. The roast beef will cost about $75.

Estimate each product.

1. 0.8 ! 22 2. 19.3 ! 6

3. 345 ! 5.79 4. 966 ! 0.46

Number Sense Use the chart to answer questions 5 through 7.

5. About how much would it cost for Angelina and her 4 sisters to get a shampoo and a haircut?

6. Could 3 of the sisters get their hair colored for less than $100?

7. Angelina gets 9 haircuts per year. About how much does she spend on haircuts for the year?

Treatment CostShampoo $7.95

Haircut $12.95

Coloring $18.25

Perm $22.45

Reteaching

7-3Reteaching 7

-3

30468_T07_43 43 1/16/08 6:03:09 PM

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Topic 7 43

Estimating the Product of a Decimal and a Whole NumberYou can estimate when you are multiplying a decimal by a whole number to check the reasonableness of your product.

Zane needs to buy 27 lb of roast beef for the company party. The roast beef costs $2.98 per pound. About how much will the roast beef cost?

There are two ways to estimate.

Round both numbers Adjust your factors to compatible numbers you can multiply mentally.

$2.98 ! 27 $2.98 ! 27

$3 ! 30 " $90 $3 ! 25 " $75

The roast beef will cost about $90. The roast beef will cost about $75.

Estimate each product.

1. 0.8 ! 22 2. 19.3 ! 6

3. 345 ! 5.79 4. 966 ! 0.46

Number Sense Use the chart to answer questions 5 through 7.

5. About how much would it cost for Angelina and her 4 sisters to get a shampoo and a haircut?

6. Could 3 of the sisters get their hair colored for less than $100?

7. Angelina gets 9 haircuts per year. About how much does she spend on haircuts for the year?

Treatment CostShampoo $7.95

Haircut $12.95

Coloring $18.25

Perm $22.45

Reteaching

7-3

Reteaching 7-3

20 1001,800 500

(5 ! $8) " (5 ! $13) #

about $105

Yes; $20 ! 3 # $60.

10 ! $13 # about $130

Sample answers are given.

30428_T07_042_047_43 43 3/18/08 2:18:17 PM

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44 Topic 7

Estimating the Product of a Decimal and a Whole NumberEstimate each product using rounding or compatible numbers.

1. 0.97 ! 312

5. 0.33 ! 104

9. 0.13 ! 7

2. 8.02 ! 70

6. 0.83 ! 12

10. 45.1 ! 5

3. 31.04 ! 300

7. 0.89 ! 51

11. 99.3 ! 92

4. 0.56 ! 48

8. 4.05 ! 11

12. 47.2 ! 93

Practice

7-3Pr

actic

e 7-3

13. Critical Thinking Mr. Webster works 4 days a week at his office and 1 day a week at home. The distance to Mr. Webster’s office is 23.7 miles. He takes a different route home, which is 21.8 miles. When Mr. Webster works at home, he drives to the post office once a day, which is 2.3 miles from his house. Which piece of information is not important in figuring out how many miles Mr. Webster drives per week to his office?

A the number of days at the of! ceB the distance to his of! ceC the distance to the post of! ceD the distance from his of! ce

14. Strategy Practice Mrs. Smith bought her three children new snowsuits for winter. Each snowsuit cost $25.99. How much did Mrs. Smith pay in all?

A $259.90 B $77.97 C $51.98 D $25.99

15. Explain It How can estimating be helpful before finding an actual product?

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44 Topic 7

Estimating the Product of a Decimal and a Whole NumberEstimate each product using rounding or compatible numbers.

1. 0.97 ! 312

5. 0.33 ! 104

9. 0.13 ! 7

2. 8.02 ! 70

6. 0.83 ! 12

10. 45.1 ! 5

3. 31.04 ! 300

7. 0.89 ! 51

11. 99.3 ! 92

4. 0.56 ! 48

8. 4.05 ! 11

12. 47.2 ! 93

Practice

7-3Pr

actic

e 7-3

13. Critical Thinking Mr. Webster works 4 days a week at his office and 1 day a week at home. The distance to Mr. Webster’s office is 23.7 miles. He takes a different route home, which is 21.8 miles. When Mr. Webster works at home, he drives to the post office once a day, which is 2.3 miles from his house. Which piece of information is not important in figuring out how many miles Mr. Webster drives per week to his office?

A the number of days at the of! ceB the distance to his of! ceC the distance to the post of! ceD the distance from his of! ce

14. Strategy Practice Mrs. Smith bought her three children new snowsuits for winter. Each snowsuit cost $25.99. How much did Mrs. Smith pay in all?

A $259.90 B $77.97 C $51.98 D $25.99

15. Explain It How can estimating be helpful before finding an actual product?

300

30

560 9,000 25

10 50 44

0.7 225 9,000 4,500

If your estimate is very different fromyour actual product, you know that youneed to check your work.

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Topic 7 45

Mental Math

Decimal Estimates1. Georgia rollerskates 0.43 miles around her block

each day. If she rollerskated 279 days in 2006, about how many miles did she rollerskate?

2. Juan needs to buy 6.74 pounds of shrimp that sells for $9.68 per pound. Find an underestimate and an overestimate for the cost of the shrimp.

3. Lana got a tip of 16%, or 0.16, for delivering pizza. If the pizza tab came to $38.19, about how much tip did she receive?

4. Jerome needs to buy 26.9 yards of fabric to make bandannas for the Humane Society’s dog parade. The fabric he chose costs $7.65 per yard. Find an underestimate and an overestimate for the cost of the fabric.

5. Marcy picked 18.8 pounds of peaches at the pick-your-own orchard. Each pound of peaches costs $1.28. About how much will her peaches cost?

6. Bruce jogs from his house to the library to tutor students and back again, a round trip of 0.56 miles. If Bruce tutored at the library 328 days in 2006, about how many miles did he jog?

Enrichment

7-3Enrichm

ent 7-3

30468_T07_45 45 1/16/08 6:03:13 PM

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Topic 7 45

Mental Math

Decimal Estimates1. Georgia rollerskates 0.43 miles around her block

each day. If she rollerskated 279 days in 2006, about how many miles did she rollerskate?

2. Juan needs to buy 6.74 pounds of shrimp that sells for $9.68 per pound. Find an underestimate and an overestimate for the cost of the shrimp.

3. Lana got a tip of 16%, or 0.16, for delivering pizza. If the pizza tab came to $38.19, about how much tip did she receive?

4. Jerome needs to buy 26.9 yards of fabric to make bandannas for the Humane Society’s dog parade. The fabric he chose costs $7.65 per yard. Find an underestimate and an overestimate for the cost of the fabric.

5. Marcy picked 18.8 pounds of peaches at the pick-your-own orchard. Each pound of peaches costs $1.28. About how much will her peaches cost?

6. Bruce jogs from his house to the library to tutor students and back again, a round trip of 0.56 miles. If Bruce tutored at the library 328 days in 2006, about how many miles did he jog?

Enrichment

7-3Enrichm

ent 7-3

About 120 miles

Underestimate: $54; overestimate: $70

About $6

Underestimate: $175; overestimate: $240

About $26

About 180 miles

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46 Topic 7

1. Ms. MacDowell is buying her class of 27 students end-of-year gifts. Each gift costs $3.39, including tax. About how much is Ms. MacDowell spending on gifts for her students? Use the rounding strategy.

A about $60B about $80C about $90D about $100

2. Estimate the product using compatible numbers.

0.67 ! 623

A about 420B about 360C about 42D about 36

3. Find the difference: 73.92 " 49.63.

A 34.39B 34.29C 24.39D 24.29

4. Estimate each product using rounding or compatible numbers.

0.67 ! 322

3.12 ! 71

18.88 ! 23

207 ! 0.51

0.165 ! 44

0.42 ! 25

1.91 ! 787

5. For math class, Boone is using his shoe to measure one of his classroom walls. He ! nds that the wall is 27 shoes long. His shoe measures 9.8 inches long. Use compatible numbers to ! nd about how many inches long the wall is.

Daily Spiral Review

7-4Da

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7-4

30468_T07_46 46 1/16/08 6:03:14 PM

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46 Topic 7

1. Ms. MacDowell is buying her class of 27 students end-of-year gifts. Each gift costs $3.39, including tax. About how much is Ms. MacDowell spending on gifts for her students? Use the rounding strategy.

A about $60B about $80C about $90D about $100

2. Estimate the product using compatible numbers.

0.67 ! 623


3. Find the difference: 73.92 " 49.63.

A 34.39B 34.29C 24.39D 24.29

4. Estimate each product using rounding or compatible numbers.

0.67 ! 322

3.12 ! 71

18.88 ! 23

207 ! 0.51

0.165 ! 44

0.42 ! 25

1.91 ! 787

5. For math class, Boone is using his shoe to measure one of his classroom walls. He ! nds that the wall is 27 shoes long. His shoe measures 9.8 inches long. Use compatible numbers to ! nd about how many inches long the wall is.

Daily Spiral Review

7-4Da

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iew

7-4

210210

27 ! 10 " about 270 inches long

4001008

101,600

30428_T07_042_047_46 46 3/18/08 2:18:24 PM


Topic 7 4

7

The lockers at Claremont School are numbered from 1 to 250. On how many lockers does the digit 9 appear at least once?

Problem of the Day

7-4



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16Multiplying Two Decimals

Here are the prices and amounts for the fruit salad:

Item Price per Pound

Number of pounds

Estimated Costs

Exact Costs

Practical Answers

Apples $2.29 3.2

Pears $1.89 4.1

Bananas $0.89 4.9

Strawberries $2.99 2.3

1. How did you estimate the factors?

2. Is your estimate close to the exact product? Why or why not?

3. How is multiplying two decimals like multiplying a whole number and a decimal?

SUPERMARKET PRODUCE PRICES

ApplesPearsBananas

Strawberries

Item

$2.29$1.89$0.89$2.99

Price perPound

48 Topic 7

30468_T07_48 48 1/16/08 6:03:22 PM

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Topic 7 49

1. How many decimal places will there be in the product shown below?

23.589 ! 14.2 " ?

A oneB twoC threeD four

2. Find the product: 24.56 ! 12.3.A 30.2088B 302.088C 3,020.88D 302,088

3. The cost of a piece of fabric is $1.32 per yard. How much does a 3.5-yard piece of fabric cost?A $1.62B $3.76C $3.84D $4.62

4. Your classroom is 11.4 meters long and 8.4 meters wide. What is the ! oor area of the classroom in square meters? Use the formula area " length ! width.A 957.60 m2

B 198.34 m2

C 95.76 m2

D 92.86 m2

5. Writing to Explain Estimate the product of the numbers 2.16 and 7.96. Then multiply to " nd the exact answer. Show your work.

Quick Check

7-4Q

uick Check 7

-4

30468_T07_49 49 1/16/08 6:03:27 PM

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Topic 7 49

1. How many decimal places will there be in the product shown below?

23.589 ! 14.2 " ?

A oneB twoC threeD four

2. Find the product: 24.56 ! 12.3.A 30.2088B 302.088C 3,020.88D 302,088

3. The cost of a piece of fabric is $1.32 per yard. How much does a 3.5-yard piece of fabric cost?A $1.62B $3.76C $3.84D $4.62

4. Your classroom is 11.4 meters long and 8.4 meters wide. What is the ! oor area of the classroom in square meters? Use the formula area " length ! width.A 957.60 m2

B 198.34 m2

C 95.76 m2

D 92.86 m2

5. Writing to Explain Estimate the product of the numbers 2.16 and 7.96. Then multiply to " nd the exact answer. Show your work.

Quick Check

7-4Q

uick Check 7

-4


30428_T07_049-052_49 49 3/18/08 2:18:48 PM

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50 Topic 7

Multiplying Two DecimalsCaroline earns $2.40 per hour for babysitting her brother. She babysat last night for 3.25 hours. How much did she earn?

First, estimate your product so you can check for reasonableness.

$2.40 ! 3.25

$2 ! 3 " 6 Caroline earned about $6.00.

Step 1: Multiply as with whole numbers.

3.25 ! 2.40 000 13,000 #65,000 78,000

Step 2: Count the total number of decimal places in both factors.

3.25 2 decimal places


So, 4 decimal places total.

Step 3: Place the decimal point in the product with the correct total number of decimal places following it.

7.8000 " $7.80

Caroline earned $7.80 last night. Because $7.80 is close to your estimate of $6, your answer is reasonable.

Find each product. Check by estimating.

1. 0.2 ! 4.6 2. 3.98 ! 7.1 3. 8.54 ! 0.14

4. 0.532 ! 6.4 5. 9.3 ! 5.86 6. 0.37 ! 4.4

7. Critical Thinking Jackie wants to buy a new CD player. It costs $32.95. She has saved $26 and has a coupon for 30% off the price. Does Jackie have enough money to buy the CD player?

Reteaching

7-4Re

teac

hing

7-4

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50 Topic 7

Multiplying Two DecimalsCaroline earns $2.40 per hour for babysitting her brother. She babysat last night for 3.25 hours. How much did she earn?

First, estimate your product so you can check for reasonableness.

$2.40 ! 3.25

$2 ! 3 " 6 Caroline earned about $6.00.

Step 1: Multiply as with whole numbers.

3.25 ! 2.40 000 13,000 #65,000 78,000

Step 2: Count the total number of decimal places in both factors.



So, 4 decimal places total.

Step 3: Place the decimal point in the product with the correct total number of decimal places following it.

7.8000 " $7.80

Caroline earned $7.80 last night. Because $7.80 is close to your estimate of $6, your answer is reasonable.

Find each product. Check by estimating.

1. 0.2 ! 4.6 2. 3.98 ! 7.1 3. 8.54 ! 0.14

4. 0.532 ! 6.4 5. 9.3 ! 5.86 6. 0.37 ! 4.4

7. Critical Thinking Jackie wants to buy a new CD player. It costs $32.95. She has saved $26 and has a coupon for 30% off the price. Does Jackie have enough money to buy the CD player?

Reteaching

7-4Re

teac

hing

7-4

0.92 28.258 1.19563.4048 54.498 1.628

Yes. The coupon reduces the price of the CD player to $23.07.

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Topic 7 51

Multiplying Two DecimalsFind each product.

1. 3.7! 0.3

2. 4.4 ! 0.2

3. 0.61 ! 6.8

4. 1.9 ! 0.005

5. 0.79 ! 4.3 " 6. 0.79 ! 0.005 "

7. Number Sense The product of 4.7 and 6.5 equals 30.55. What is the product of 4.7 and 0.65? 4.7 and 65?

8. What would be the gravity in relation to Earth of a planet with 3.4 times the gravity of Mercury?

9. The gravity of Venus is 0.35 times that of Jupiter. What is the gravity of Venus in relation to Earth’s gravity?

10. How many decimal places are in the product of a number with decimal places to the thousandths multiplied by a number with decimal places to the hundredths?

A 2 B 3 C 4 D 5

11. Explain It Explain how you know the number of decimal places that should be in the product when you multiply two decimal numbers together.

Planet Gravity Mercury 0.39 Neptune 1.22 Jupiter 2.6

Relative (to Earth) Surface Gravity

Practice

7-4Practice 7

-4

30468_T07_51 51 1/16/08 6:03:30 PM

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Topic 7 51

Multiplying Two DecimalsFind each product.

1. 3.7! 0.3

2. 4.4 ! 0.2

3. 0.61 ! 6.8

4. 1.9 ! 0.005

5. 0.79 ! 4.3 " 6. 0.79 ! 0.005 "

7. Number Sense The product of 4.7 and 6.5 equals 30.55. What is the product of 4.7 and 0.65? 4.7 and 65?

8. What would be the gravity in relation to Earth of a planet with 3.4 times the gravity of Mercury?

9. The gravity of Venus is 0.35 times that of Jupiter. What is the gravity of Venus in relation to Earth’s gravity?

10. How many decimal places are in the product of a number with decimal places to the thousandths multiplied by a number with decimal places to the hundredths?

A 2 B 3 C 4 D 5

11. Explain It Explain how you know the number of decimal places that should be in the product when you multiply two decimal numbers together.

Planet Gravity Mercury 0.39 Neptune 1.22 Jupiter 2.6

Relative (to Earth) Surface Gravity

Practice

7-4

Practice 7-4

0.00395 1.11 0.88 4.148 0.0095

3.397

3.055, 305.5

1.326

0.91

The total number of decimal places in the numbers being multiplied is the number of decimal places in the product.

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52 Topic 7

Decimal Dinners 1. Gina wants to bake pumpkin pies for a Thanksgiving

potluck dinner. She needs 8.8 pounds of pumpkins that sell for $0.93 per pound. How much will she spend? Round to the nearest cent.

2. Tony is making his sweet-potato side dish for the potluck. Sweet potatoes are on sale at the market for $0.67 per pound. If Tony needs 9.3 pounds of sweet potatoes, how much will he spend? Round the cost to the nearest cent.

3. Reba is making a tablecloth for the dessert table. She needs to decide between the autumn-leaf fabric that sells for $4.99 per yard and the turkey-print fabric that sells for $5.75 per yard. If Reba needs 3.6 yards, how much will she spend for each of the fabrics? Round the cost to the nearest cent.

4. Jack is mixing hot apple-cider punch for the potluck. His recipe calls for 12.4 quarts of apple cider. If apple cider sells for $1.82 per quart, how much will Jack spend? Round the cost to the nearest cent.

5. Lindsay is in charge of buying turkeys for Thanksgiving dinner. The turkeys she has selected weigh a total of 49.5 pounds. If turkey is on sale for $2.17 per pound, how much will Lindsay spend? Round the cost to the nearest cent.

6. Wayne is making a string-bean casserole for the potluck. He needs 3.8 pounds of string beans, which sell for $0.82 per pound. How much will Wayne spend on string beans? Round the cost to the nearest cent.

Enrichment

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Number Sense

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52 Topic 7

Decimal Dinners 1. Gina wants to bake pumpkin pies for a Thanksgiving

potluck dinner. She needs 8.8 pounds of pumpkins that sell for $0.93 per pound. How much will she spend? Round to the nearest cent.

2. Tony is making his sweet-potato side dish for the potluck. Sweet potatoes are on sale at the market for $0.67 per pound. If Tony needs 9.3 pounds of sweet potatoes, how much will he spend? Round the cost to the nearest cent.

3. Reba is making a tablecloth for the dessert table. She needs to decide between the autumn-leaf fabric that sells for $4.99 per yard and the turkey-print fabric that sells for $5.75 per yard. If Reba needs 3.6 yards, how much will she spend for each of the fabrics? Round the cost to the nearest cent.

4. Jack is mixing hot apple-cider punch for the potluck. His recipe calls for 12.4 quarts of apple cider. If apple cider sells for $1.82 per quart, how much will Jack spend? Round the cost to the nearest cent.

5. Lindsay is in charge of buying turkeys for Thanksgiving dinner. The turkeys she has selected weigh a total of 49.5 pounds. If turkey is on sale for $2.17 per pound, how much will Lindsay spend? Round the cost to the nearest cent.

6. Wayne is making a string-bean casserole for the potluck. He needs 3.8 pounds of string beans, which sell for $0.82 per pound. How much will Wayne spend on string beans? Round the cost to the nearest cent.

Enrichment

7-4En

richm

ent 7

-4

Number Sense

$8.18

$6.23

$17.96 for the autumn-leaf fabric; $20.70 for the turkey-print fabric

$22.57

$107.42

$3.12

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School Election

StudentAmelia Jared Fred

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1. A computer can load 1,247 megabytes in 40 seconds. Which best describes the loading speed of the computer?A Around 20 megabytes per

secondB Nearly 28 megabytes

per second C Close to 31 megabytes per

second D More than 40 megabytes per

second

2. The table shows the number of square feet painted by three house painters.

Painter Square Feet Painted

Days Worked

Megan 604 5John 521 4Cathy 460 3

Which best describes John’s average painting speed?

A Almost 120 square feet per day B Almost 130 square feet per day C Almost 140 square feet per day D Almost 150 square feet per day

3. A model of 1-foot cubes is shown below.

What is the volume of this model?

A 50 cubic feetB 44 cubic feetC 40 cubic feet D 34 cubic feet

4. List the painters in Question 2 in order from slowest to fastest average painting speed.

5. A business earns $63,745 in March and $81,239 in April. How much money did the business earn during these two months?

6. The graph shows the number of votes for each person in a school election.

Which student won the election?

Topic 7 53

Daily Spiral Review 7-5

Daily Spiral Review

7-5

30468_T07_53 53 1/16/08 6:03:38 PM

Num

ber

of V

otes

504540353025201510

50

School Election

StudentAmelia Jared Fred

Name©

Pea

rson

Edu

catio

n, In

c. 5

1. A computer can load 1,247 megabytes in 40 seconds. Which best describes the loading speed of the computer?A Around 20 megabytes per

secondB Nearly 28 megabytes

per second C Close to 31 megabytes per

second D More than 40 megabytes per

second

2. The table shows the number of square feet painted by three house painters.

Painter Square Feet Painted

Days Worked

Megan 604 5John 521 4Cathy 460 3

Which best describes John’s average painting speed?

A Almost 120 square feet per day B Almost 130 square feet per day C Almost 140 square feet per day D Almost 150 square feet per day

3. A model of 1-foot cubes is shown below.

What is the volume of this model?

A 50 cubic feetB 44 cubic feetC 40 cubic feet D 34 cubic feet

4. List the painters in Question 2 in order from slowest to fastest average painting speed.

5. A business earns $63,745 in March and $81,239 in April. How much money did the business earn during these two months?

6. The graph shows the number of votes for each person in a school election.

Which student won the election?

Topic 7 53

Daily Spiral Review 7-5

Daily Spiral Review

7-5

Megan, John, Cathy

$144,984

Amelia

30428_T07_053_53 53 3/18/08 2:19:07 PM


54

Topic 7



of the Day

7-5

Henry is saving for a new game system. During the first week, he saved $4. In the second week, he saved $8, and in the third week, he saved $16. If Henry continues to save in this manner, how much will he have saved by the sixth week?

30468_T07_54 54

1/16/08 6:03:44 PM

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uick Check 7

-5

1. Use mental math to find the quotient: 567.8 ! 100.

A 0.05678

B 0.5678

C 5.678

D 56.78

3. Tickets for rides at a carnival cost $0.80 each, but you can buy a book of 10 tickets for $6.50. What is the cost of each ticket in the book of tickets?

A $0.80

B $0.68

C $0.65

D $0.55

2. Use mental math to find the quotient: 0.233 ! 1,000.

A 0.233

B 0.0233

C 0.00233

D 0.000233

4. A kilometer is 3,280.8 feet. How many feet long is a meter?

A 0.32808 feet

B 3.2808 feet

C 32.808 feet

D 328.08 feet

5. Writing to Explain For a fundraising drive, a charity asks people to contribute their saved pennies. The drive collects 8,342,540 pennies. How many dollars were collected? Explain how you calculated your answer.

30468_T07_55 55 1/16/08 6:03:50 PM

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7-5Q

uick Check 7

-5

1. Use mental math to find the quotient: 567.8 ! 100.

A 0.05678

B 0.5678

C 5.678

D 56.78

3. Tickets for rides at a carnival cost $0.80 each, but you can buy a book of 10 tickets for $6.50. What is the cost of each ticket in the book of tickets?

A $0.80

B $0.68

C $0.65

D $0.55

2. Use mental math to find the quotient: 0.233 ! 1,000.

A 0.233

B 0.0233

C 0.00233

D 0.000233

4. A kilometer is 3,280.8 feet. How many feet long is a meter?

A 0.32808 feet

B 3.2808 feet

C 32.808 feet

D 328.08 feet

5. Writing to Explain For a fundraising drive, a charity asks people to contribute their saved pennies. The drive collects 8,342,540 pennies. How many dollars were collected? Explain how you calculated your answer.


30428_T07_055_55 55 3/18/08 2:19:27 PM

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56 Topic 7

Reteaching

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teac

hing

7-5

Dividing Decimals by 10, 100, or 1,000You can use place-value patterns when you divide a decimal by 10, 100, or 1,000.

Sanjai has 27.5 lb of clay. If he uses the clay to make 10 bowls, how much clay will he use for each bowl? What if he makes 100 bowls from the clay? What if he makes 1,000 bowls?

Dividing a number by 10 moves the decimal point one place to the left.

27.5 ! 10 " 2.75

Dividing a number by 100 moves the decimal point two places to the left.

27.5 ! 100 " 0.275

Dividing a number by 1,000 moves the decimal point three places to the left.

27.5 ! 1,000 " 0.0275

Sanjai will use 2.75 lb for each of 10 bowls, 0.275 lb for each of 100 bowls, and 0.0275 lb for each of 1,000 bowls.

Remember: When you divide a number by 10, 100, or 1,000, your quotient will be smaller than that number.

For questions 1 through 6, find the quotient. Use mental math.

1. 16.4 ! 10 2. 38.92 ! 100 3. 297.1 ! 100

4. 540.9 ÷ 10 5. 41.628 ! 1,000 6. 0.33 ! 10

7. The city has a section of land 3,694.7 ft long. The city wants to make 100 equal-sized gardens with this land. How long will each garden be?

8. Reasonableness Connor divided 143.89 by 100. He said his answer was 14.389. Is this a reasonable answer?

30468_T07_56 56 1/16/08 6:03:56 PM

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56 Topic 7

Reteaching

7-5Re

teac

hing

7-5

Dividing Decimals by 10, 100, or 1,000You can use place-value patterns when you divide a decimal by 10, 100, or 1,000.

Sanjai has 27.5 lb of clay. If he uses the clay to make 10 bowls, how much clay will he use for each bowl? What if he makes 100 bowls from the clay? What if he makes 1,000 bowls?

Dividing a number by 10 moves the decimal point one place to the left.

27.5 ! 10 " 2.75

Dividing a number by 100 moves the decimal point two places to the left.

27.5 ! 100 " 0.275

Dividing a number by 1,000 moves the decimal point three places to the left.

27.5 ! 1,000 " 0.0275

Sanjai will use 2.75 lb for each of 10 bowls, 0.275 lb for each of 100 bowls, and 0.0275 lb for each of 1,000 bowls.

Remember: When you divide a number by 10, 100, or 1,000, your quotient will be smaller than that number.

For questions 1 through 6, find the quotient. Use mental math.

1. 16.4 ! 10 2. 38.92 ! 100 3. 297.1 ! 100

4. 540.9 ÷ 10 5. 41.628 ! 1,000 6. 0.33 ! 10

7. The city has a section of land 3,694.7 ft long. The city wants to make 100 equal-sized gardens with this land. How long will each garden be?

8. Reasonableness Connor divided 143.89 by 100. He said his answer was 14.389. Is this a reasonable answer?

No. Connor moved the decimal point only one place to the left. He should have moved it two places to the left.

1.64

36.947 ft

2.9710.03354.09 0.3892

0.041628

30428_T07_056-058_56 56 3/18/08 2:19:40 PM

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Topic 7 57

Practice

7-5Practice 7

-5

Dividing Decimals by 10, 100, or 1,000Find each quotient. Use mental math.

1. 86.6 ! 10 " 2. 192.5 ! 100 "

3. 1.99 ! 100 " 4. 0.87 ! 10 "

5. 228.55 ! 1,000 " 6. 0.834 ! 100 "

7. 943.35 ! 1,000 " 8. 1.25 ! 10 "

Algebra Write 10, 100, or 1,000 for each n.

9. 78.34 ! n " 0.7834 10. 0.32 ! n " 0.032 11. (75.34 # 25.34) ! n " 5

12. There are 145 children taking swimming lessons at the pool. If 10 children will be assigned to each instructor, how many instructors need to be hired?

13. Ronald ran 534.3 mi in 100 days. If he ran an equal distance each day, how many miles did he run per day?

A 5 B 5.13 C 5.343 D 6.201

14. Explain It Carlos says that 17.43 ! 100 is the same as 174.3 $ 0.01. Is he correct? Explain.

30468_T07_57 57 1/16/08 6:03:58 PM

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Topic 7 57

Practice

7-5Practice 7

-5

Dividing Decimals by 10, 100, or 1,000Find each quotient. Use mental math.

1. 86.6 ! 10 " 2. 192.5 ! 100 "

3. 1.99 ! 100 " 4. 0.87 ! 10 "

5. 228.55 ! 1,000 " 6. 0.834 ! 100 "

7. 943.35 ! 1,000 " 8. 1.25 ! 10 "

Algebra Write 10, 100, or 1,000 for each n.

9. 78.34 ! n " 0.7834 10. 0.32 ! n " 0.032 11. (75.34 # 25.34) ! n " 5

12. There are 145 children taking swimming lessons at the pool. If 10 children will be assigned to each instructor, how many instructors need to be hired?

13. Ronald ran 534.3 mi in 100 days. If he ran an equal distance each day, how many miles did he run per day?

A 5 B 5.13 C 5.343 D 6.201

14. Explain It Carlos says that 17.43 ! 100 is the same as 174.3 $ 0.01. Is he correct? Explain.

8.660.0199

0.228550.94335

1.9250.087

0.008340.125

n ! 100 n ! 10 n ! 10

15 instructors

No, he is not correct. 17.43 " 100 is 0.1743 and 174.3 # 0.01 is 1.743.

30428_T07_056-058_57 57 3/18/08 2:19:42 PM

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58 Topic 7

Enrichment

7-5

Mental Math

Enric

hmen

t 7-5

Dividing DecimalsFind each quotient. Use mental math.

1. 783.9 ! 10

2. 35.6 ! 100

3. 591.72 ! 1,000

4. 54.8 ! 10

5. 2.17 ! 100

6. 92.5 ! 1,000

7. 6.36 ! 10

8. 475.1 ! 100

9. 81.3 ! 1,000

10. 0.076 ! 10

11. 793 ! 100

12. 8,324 ! 1,000

30468_T07_58 58 1/16/08 6:04:00 PM

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58 Topic 7

Enrichment

7-5

Mental Math

Enric

hmen

t 7-5

Dividing DecimalsFind each quotient. Use mental math.

1. 783.9 ! 10

2. 35.6 ! 100

3. 591.72 ! 1,000

4. 54.8 ! 10

5. 2.17 ! 100

6. 92.5 ! 1,000

7. 6.36 ! 10

8. 475.1 ! 100

9. 81.3 ! 1,000

10. 0.076 ! 10

11. 793 ! 100

12. 8,324 ! 1,000

78.390.356

0.591725.48

0.02170.09250.6364.7510.08130.00767.93

8.324

30428_T07_056-058_58 58 3/18/08 2:19:46 PM

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Topic 7 59

Daily Spiral Review

7-6

1. Which shows the correct quotient?

56.78 ! 100

A 0.05678B 0.5678C 5.678D 567.8

2. Ma’Kayla’s project group earns 989.25 points out of 1,000 on their Communities project. The points are to be divided evenly among the 10 people in her group. How many points will each member of the group receive?A 9,892.5B 98.925C 9.8925D 0.98925

3. Find 123.63 " 98.71.

A 24.92B 35.12C 35.92D 222.34

4. Lam wants to earn enough money to buy a robot. The robot he wants costs $289.95. He decides to try to earn the money in 100 days. How much money will Lam need to earn each day in order to have the full amount in 100 days? Round your answer to the nearest cent.

5. Find the quotients.

35.86 ! 10

9.55 ! 1,000

257.16 ! 100

1.805 ! 1,000

710.5 ! 10

0.742 ! 1,000

9.3 ! 100

Daily Spiral Review

7–6

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Topic 7 59

Daily Spiral Review

7-6

1. Which shows the correct quotient?

56.78 ! 100

A 0.05678B 0.5678C 5.678D 567.8

2. Ma’Kayla’s project group earns 989.25 points out of 1,000 on their Communities project. The points are to be divided evenly among the 10 people in her group. How many points will each member of the group receive?A 9,892.5B 98.925C 9.8925D 0.98925

3. Find 123.63 " 98.71.

A 24.92B 35.12C 35.92D 222.34

4. Lam wants to earn enough money to buy a robot. The robot he wants costs $289.95. He decides to try to earn the money in 100 days. How much money will Lam need to earn each day in order to have the full amount in 100 days? Round your answer to the nearest cent.

5. Find the quotients.

35.86 ! 10

9.55 ! 1,000

257.16 ! 100

1.805 ! 1,000

710.5 ! 10

0.742 ! 1,000

9.3 ! 100

Daily Spiral Review

7–6

3.5860.009552.57160.00180571.050.0007420.093

$289.95 ! 100 " $2.8995, $2.90 per day.

30428_T07_059_59 59 3/18/08 2:19:56 PM


60

Topic 7



of the Day

7-6

Max has 7 coins that total $0.66. What are the coins?

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-6

3. At the grocery store, bags of frozen vegetables are on sale. You can buy 5 packages for $6.45. What is the cost of each package at that rate?

A $1.19

B $1.29

C $1.90

D $2.09

4. An industrial machine produces complicated parts used in the structure of a bridge. If it produces 15 parts in 6.75 hours, what is the production time for one part?

A 0.90 hour

B 0.75 hour

C 0.45 hour

D 0.35 hour

1. Find the quotient: 4.2 ! 7.

A 0.06

B 0.6

C 1.7

D 6


A 11.55

B 1.55

C 1.5

D 0.155

5. Writing to Explain Three of Amy’s friends decided to buy her a birthday present together and share the cost equally. The total cost of the present was $24.56. What was the cost for each person? Use long division to find the quotient to the thousandths place and then round to the nearest cent. Show your work.

30468_T07_61 61 1/16/08 6:04:17 PM

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5Quick Check

7-6Q

uick Check 7

-6

3. At the grocery store, bags of frozen vegetables are on sale. You can buy 5 packages for $6.45. What is the cost of each package at that rate?

A $1.19

B $1.29

C $1.90

D $2.09

4. An industrial machine produces complicated parts used in the structure of a bridge. If it produces 15 parts in 6.75 hours, what is the production time for one part?

A 0.90 hour

B 0.75 hour

C 0.45 hour

D 0.35 hour


A 0.06

B 0.6

C 1.7

D 6


A 11.55

B 1.55

C 1.5

D 0.155

5. Writing to Explain Three of Amy’s friends decided to buy her a birthday present together and share the cost equally. The total cost of the present was $24.56. What was the cost for each person? Use long division to find the quotient to the thousandths place and then round to the nearest cent. Show your work.


30428_T07_061_61 61 3/18/08 2:20:19 PM

0 0.5 1.0 1.5

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62 Topic 7

Rete

achi

ng 7-6

Dividing a Decimal by a Whole NumberJia needs to cut a board into 3 equal pieces to make bookshelves. The board is 1.5 yd long. How long will each bookshelf be?

Laying a measuring tape next to the board, Jia sees that her board can be cut into 3 pieces that are each 0.5 yd long. Jia also writes out her problem to make sure her answer is correct.

Step 1. Write a decimal point in the quotient directly above the decimal point in the dividend.

Step 2. Divide as you would with whole numbers.

0.5 3 !"" 1.5 !15 0

Step 3. Check your quotient by multiplying.

0.5 " 3 # 1.5

Sometimes you will need to add a zero to the right of the dividend so that you can continue dividing. Example: 8.1 $ 18

0.45 18 !""" 8.10 !72 90 !90 0

Since the quotient matches the measurement that Jia saw on her measuring tape, she knows that her answer is correct.

For 1 through 6, find each quotient. Check by multiplying.

1. 14 !"" 6.3 2. 77 !""" 2.31 3. 89 !""" 2.492

4. 123.08 $ 34 5. 0.57 $ 30 6. 562.86 $ 59

7. A family of five people attends a theme park. They purchase 2 adult tickets for $27.50 each and 3 student tickets for $12.50 each. If the 5 tickets are purchased with a $100 bill, how much change do they receive?

Reteaching

7-6

30468_T07_62 62 1/16/08 6:04:23 PM

0 0.5 1.0 1.5

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62 Topic 7

Rete

achi

ng 7-6

Dividing a Decimal by a Whole NumberJia needs to cut a board into 3 equal pieces to make bookshelves. The board is 1.5 yd long. How long will each bookshelf be?

Laying a measuring tape next to the board, Jia sees that her board can be cut into 3 pieces that are each 0.5 yd long. Jia also writes out her problem to make sure her answer is correct.

Step 1. Write a decimal point in the quotient directly above the decimal point in the dividend.

Step 2. Divide as you would with whole numbers.

0.5 3 !"" 1.5 !15 0

Step 3. Check your quotient by multiplying.

0.5 " 3 # 1.5

Sometimes you will need to add a zero to the right of the dividend so that you can continue dividing. Example: 8.1 $ 18

0.45 18 !""" 8.10 !72 90 !90 0

Since the quotient matches the measurement that Jia saw on her measuring tape, she knows that her answer is correct.

For 1 through 6, find each quotient. Check by multiplying.

1. 14 !"" 6.3 2. 77 !""" 2.31 3. 89 !""" 2.492

4. 123.08 $ 34 5. 0.57 $ 30 6. 562.86 $ 59

7. A family of five people attends a theme park. They purchase 2 adult tickets for $27.50 each and 3 student tickets for $12.50 each. If the 5 tickets are purchased with a $100 bill, how much change do they receive?

Reteaching

7-6

0.028

$7.50

3.62 0.0190.03

9.540.45

30428_T07_062-064_62 62 3/18/08 2:20:27 PM

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Topic 7 63

Practice 7-6

Dividing a Decimal by a Whole NumberFind each quotient.

1. 13 !""" 68.9 2. 35 !""" 412.3 3. 90 !""" 14.4 4. 60 !""" 53.4

5. 123.08 ! 34 " 6. 0.57 ! 30 "

7. 562.86 ! 59 " 8. 24.4 ! 80 "

9. John paid $7.99 for 3 boxes of cereal. The tax was $1.69. Excluding tax, how much did John pay for each box of cereal if they all were the same price?

10. If a package of granola bars with 12 bars costs $3.48, how much does each granola bar cost?

A 29¢ B 31¢ C 44¢ D $1.00

11. Estimation 64.82 ! 11 is

A a little more than 6. C a little less than 6.

B a little more than 60. D a little less than 60.

12. Explain It Explain how to divide 0.12 by 8.

Practice

7-6

30468_T07_63 63 1/16/08 6:04:25 PM

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Topic 7 63

Practice 7-6

Dividing a Decimal by a Whole NumberFind each quotient.

1. 13 !""" 68.9 2. 35 !""" 412.3 3. 90 !""" 14.4 4. 60 !""" 53.4

5. 123.08 ! 34 " 6. 0.57 ! 30 "

7. 562.86 ! 59 " 8. 24.4 ! 80 "

9. John paid $7.99 for 3 boxes of cereal. The tax was $1.69. Excluding tax, how much did John pay for each box of cereal if they all were the same price?

10. If a package of granola bars with 12 bars costs $3.48, how much does each granola bar cost?

A 29¢ B 31¢ C 44¢ D $1.00

11. Estimation 64.82 ! 11 is

A a little more than 6. C a little less than 6.

B a little more than 60. D a little less than 60.

12. Explain It Explain how to divide 0.12 by 8.

Practice

7-6

3.629.54

0.0190.305

Sample answer: Write zeros in the onesand tenths places in the quotient. Annex a zero in the dividend and continue dividing. The quotient is 0.015.

5.3 11.78 0.16 0.89

$2.10

30428_T07_062-064_63 63 3/18/08 2:20:30 PM

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64 Topic 7

Number Sense

Enric

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t 7-6

Division with a Point 1. Maria opened a bank account to save for college.

She deposited an equal amount of money into her account each month. At the end of 9 months, she had saved $551.25. How much money did Maria deposit into her account each month?

2. The 5th-grade bowling league went out for ice cream sundaes to celebrate their victory. The bill at the ice cream shop came to $92.82. If all 26 bowling league members shared the bill equally, how much did each pay?

3. The 8 children in the Garcia family bought a necklace for their mother’s birthday. If the necklace cost $237.68 and each child put in an equal share, how much did each spend on the necklace?

4. Kevin bought a case of granola bars for $41.58. If there are 42 granola bars in a case, how much did Kevin pay per bar?

5. Ramon is buying a telescope for $865.32 and paying in 12 equal monthly installments. How much will he pay each month?

6. The 33 students in Mr. Wong’s piano class are buying him a pocket watch for his retirement. If the pocket watch costs $650.76, how much will each student pay?

7. Bagels cost $5.40 for a dozen at the Uptown Café and $4.16 for 8 at the Downtown Coffee Bar. Which bagels are cheaper?

Enrichment

7-6

30468_T07_64 64 1/16/08 6:04:27 PM

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64 Topic 7

Number Sense

Enric

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t 7-6

Division with a Point 1. Maria opened a bank account to save for college.

She deposited an equal amount of money into her account each month. At the end of 9 months, she had saved $551.25. How much money did Maria deposit into her account each month?

2. The 5th-grade bowling league went out for ice cream sundaes to celebrate their victory. The bill at the ice cream shop came to $92.82. If all 26 bowling league members shared the bill equally, how much did each pay?

3. The 8 children in the Garcia family bought a necklace for their mother’s birthday. If the necklace cost $237.68 and each child put in an equal share, how much did each spend on the necklace?

4. Kevin bought a case of granola bars for $41.58. If there are 42 granola bars in a case, how much did Kevin pay per bar?

5. Ramon is buying a telescope for $865.32 and paying in 12 equal monthly installments. How much will he pay each month?

6. The 33 students in Mr. Wong’s piano class are buying him a pocket watch for his retirement. If the pocket watch costs $650.76, how much will each student pay?

7. Bagels cost $5.40 for a dozen at the Uptown Café and $4.16 for 8 at the Downtown Coffee Bar. Which bagels are cheaper?

Enrichment

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$61.25

$3.57

$29.71

$0.99

$72.11

$19.72

The Uptown Café’s bagels are $0.45 apiece; the others cost $0.52.

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Daily Spiral Review

7-7

1. Which answer shows the correct quotient?70 !"" 3.5 A 5B 0.5C 0.05D 0.005

2. Mrs. Mistry’s subscription to the newspaper costs $26.75 for 5 months. How much money is she paying each month?A $0.53B $0.54C $5.35D $5.37

3. Round each number to the nearest whole number, then ! nd the difference.

23.89 ! 19.12 " ?


4. Four of Carolina’s friends are throwing her a surprise birthday party. The total cost of the cake, the decorations, and the present is $94.28. How much will each of the four friends have to pay?

5. For each of the following problems, ! nd the quotient.

12 !"" 2.4

80 !""" 4.8

6 !""" 72.6

30 !"" 1.2

80 !""" 46.68

20 !"""" 232.62

Daily Spiral Review

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Topic 7 65

Daily Spiral Review

7-7

1. Which answer shows the correct quotient?70 !"" 3.5 A 5B 0.5C 0.05D 0.005

2. Mrs. Mistry’s subscription to the newspaper costs $26.75 for 5 months. How much money is she paying each month?A $0.53B $0.54C $5.35D $5.37

3. Round each number to the nearest whole number, then ! nd the difference.

23.89 ! 19.12 " ?


4. Four of Carolina’s friends are throwing her a surprise birthday party. The total cost of the cake, the decorations, and the present is $94.28. How much will each of the four friends have to pay?

5. For each of the following problems, ! nd the quotient.

12 !"" 2.4

80 !""" 4.8

6 !""" 72.6

30 !"" 1.2

80 !""" 46.68

20 !"""" 232.62

Daily Spiral Review

7-7

$94.28 ! 4 " $23.57 each

0.20.0612.10.04

0.583511.631

30428_T07_065_65 65 3/18/08 2:20:44 PM


66

Topic 7



of the Day

7-7

Julio runs 3.1 miles in 0.5 hours. If he keeps up at that rate, how far can he run in 2 hours and 30 minutes?

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Topic 7 67

Approximate Driving Distances (in miles) Between California Locations

San Francisco

San Diego San Jose Santa

BarbaraSanta Cruz Yosemite

Los Angeles 387.3 127.4 347.6 90.7 356.3 359.4

Monterey 114.3 450.6 69.2 242.4 42.4 202.8

Napa 46.4 527.2 85.1 360.4 107.1 231.2

Palm Springs 492.7 137.2 454.3 205.2 452.1 468.4

Sacramento 89.9 508.9 125.8 379.3 144.2 196.2

Example 1 Example 2

From Locations:

To Total miles:

Total miles

Estimate the time it takes to drive the Estimate the time it takes to drive the distance driving 58 miles per hour. distance driving 47 miles per hour.


17


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Topic 7 67

Approximate Driving Distances (in miles) Between California Locations

San Francisco

San Diego San Jose Santa

BarbaraSanta Cruz Yosemite

Los Angeles 387.3 127.4 347.6 90.7 356.3 359.4

Monterey 114.3 450.6 69.2 242.4 42.4 202.8

Napa 46.4 527.2 85.1 360.4 107.1 231.2

Palm Springs 492.7 137.2 454.3 205.2 452.1 468.4

Sacramento 89.9 508.9 125.8 379.3 144.2 196.2

Example 1 Example 2

From Locations:

To Total miles:

Total miles

Estimate the time it takes to drive the Estimate the time it takes to drive the distance driving 58 miles per hour. distance driving 47 miles per hour.


17


7

San JoseLos Angeles347.6 miles

Sample answer:Monterey to San DiegoSample answer: 450.6

Sample answer: Estimate 300 ! 60.It will take about 5hours.

Sample answer: Estimate 450.6 ! 47.Use compatible whole numbers to estimate.450 ! 50 " 9So, it will take about 9 hours.

30428_T07_067-067_67 67 3/18/08 2:21:06 PM

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1. Which of these numbers is a good estimate of the quotient: 78.23 ! 19?

A 3

B 4

C 6

D 7

3. Mark deposited $200 in a savings account. After one year, his account, with interest, had a balance of $211. About how much interest did he earn each week?

A $1.10

B $0.80

C $0.50

D $0.20

2. Estimate the quotient: 621.49 ! 51.

A 30

B 15

C 12

D 8

4. Angela has a part-time job. One week, she worked 11 hours and her pay for the week was $84.81. About how much is Angela paid per hour?

A $6.00

B $8.00

C $10.00

D $12.00

Quick Check

7-7

5. Writing to Explain On a long trip, you record the distance that the car travels and the amount of driving time. If you went 378.9 miles in 8 hours, estimate your average speed. Then find the actual average speed. Show your work. Was your estimate reasonable? Explain why or why not.

30468_T07_68 68 1/16/08 6:04:51 PM

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1. Which of these numbers is a good estimate of the quotient: 78.23 ! 19?

A 3

B 4

C 6

D 7

3. Mark deposited $200 in a savings account. After one year, his account, with interest, had a balance of $211. About how much interest did he earn each week?

A $1.10

B $0.80

C $0.50

D $0.20


A 30

B 15

C 12

D 8

4. Angela has a part-time job. One week, she worked 11 hours and her pay for the week was $84.81. About how much is Angela paid per hour?

A $6.00

B $8.00

C $10.00

D $12.00

Quick Check

7-7

5. Writing to Explain On a long trip, you record the distance that the car travels and the amount of driving time. If you went 378.9 miles in 8 hours, estimate your average speed. Then find the actual average speed. Show your work. Was your estimate reasonable? Explain why or why not.


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Topic 7 69

Reteaching 7-7

Estimation: Decimals Divided by Whole NumbersThe merry-go-round in the Smithson Town Park took in $795.60 in the last six months. The ticket taker says that 442 people rode the merry-go-round during that time. About how much does it cost to ride?

You can estimate to find the quotient of $795.60 ! 442 either by rounding or using compatible numbers and mental math.

To round your numbers, cover the digit in the hundreds place with your hand. Look at the number next to your hand. Since 9 " 5, you round $795.60 up to $800. Since 4 # 5, you round 442 down to 400.

800 ! 400 $ 2 It costs about $2 to ride.

Or you can use compatible numbers and mental math.


Estimate each quotient.

1. 81.2 ! 19 2. 376.44 ! 22 3. 62.91 ! 16

4. 763.85 ! 82 5. 550.8 ! 9 6. 486.5 ! 3

7. Number Sense Explain how you would know an error had been made if you find the quotient for 231.68 ! 16 to be 144.8.

8. Reasonableness Is 61.5 ! 15 a little less than 4, a little more than 4, a little less than 40, or a little more than 40?

Reteaching

7-7

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Topic 7 69

Reteaching 7-7

Estimation: Decimals Divided by Whole NumbersThe merry-go-round in the Smithson Town Park took in $795.60 in the last six months. The ticket taker says that 442 people rode the merry-go-round during that time. About how much does it cost to ride?

You can estimate to find the quotient of $795.60 ! 442 either by rounding or using compatible numbers and mental math.

To round your numbers, cover the digit in the hundreds place with your hand. Look at the number next to your hand. Since 9 " 5, you round $795.60 up to $800. Since 4 # 5, you round 442 down to 400.


Or you can use compatible numbers and mental math.


Estimate each quotient.

1. 81.2 ! 19 2. 376.44 ! 22 3. 62.91 ! 16

4. 763.85 ! 82 5. 550.8 ! 9 6. 486.5 ! 3

7. Number Sense Explain how you would know an error had been made if you find the quotient for 231.68 ! 16 to be 144.8.

8. Reasonableness Is 61.5 ! 15 a little less than 4, a little more than 4, a little less than 40, or a little more than 40?

Reteaching

7-7

a little more than 4

Possible answer: by estimating the division as 200 ! 20 " 10, which is not close to 144.8

Sample answers are given.4 42010 60 150

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Estimation: Decimals Divided by Whole NumbersEstimate each quotient.

1. 73.5 ! 10 2. 246.78 ! 83 3. 185.7 ! 3

4. 535.6 ! 35 5. 553.9 ! 90 6. 366.6 ! 12

7. 35.6 ! 7 8. 86.4 ! 4 9. 270.53 ! 3

10. 839.7 ! 90 11. 93.26 ! 3 12. 77.3 ! 11

13. Joseph is saving $23 a week to buy a graphing calculator that costs $275.53. About how many weeks will it take before he can buy the calculator?

14. Juan works at a health food store two hours a day, three days a week. His weekly pay is $73.50. About how much does Juan make per hour?

15. Reasonableness Which of the following is a reasonable estimate for the operation 566.3 ! 63?

A about 16 B about 9 C about 4 D about 6

16. Explain It When would you estimate a quotient instead of finding the exact quotient?

Practice

7-7

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Estimation: Decimals Divided by Whole NumbersEstimate each quotient.

1. 73.5 ! 10 2. 246.78 ! 83 3. 185.7 ! 3

4. 535.6 ! 35 5. 553.9 ! 90 6. 366.6 ! 12

7. 35.6 ! 7 8. 86.4 ! 4 9. 270.53 ! 3

10. 839.7 ! 90 11. 93.26 ! 3 12. 77.3 ! 11

13. Joseph is saving $23 a week to buy a graphing calculator that costs $275.53. About how many weeks will it take before he can buy the calculator?

14. Juan works at a health food store two hours a day, three days a week. His weekly pay is $73.50. About how much does Juan make per hour?

15. Reasonableness Which of the following is a reasonable estimate for the operation 566.3 ! 63?

A about 16 B about 9 C about 4 D about 6

16. Explain It When would you estimate a quotient instead of finding the exact quotient?

Practice

7-7

about 12 weeks

Sample answer: Estimating a quotient could help you quickly figure out how many items you can buy with yourmoney or how long a trip will take.

about $12 per hour

7 3 60

15 6 305 20 90

9 30 7

Sample answers are given.

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Topic 7 71

Number Sense

Enrichment 7

-7

Estimating Costs 1. Penelope bought a 24-ounce bottle of maple syrup

that cost $13.25. About how much does one ounce cost?

2. Armand bought 4 pounds of beeswax to make candles. If he paid $22.79, about how much does one pound cost?

3. There are 890.5 calories in each 6-cup package of nutty granola. About how many calories would be in one cup?

4. Ginger bought 32.7 pounds of rabbit chow for $59.03. About how much does one pound cost?

5. Tom bought a 62-ounce bottle of apple cider for $8.61. About how much does one ounce cost?

6. Rita pet-sits for Mr. Monroe’s three dogs while he is on vacation. She earned $615.86 after pet-sitting for two weeks. About how much did Rita earn each day?

7. Sam bought 7 pounds of chocolate truffles for $65.59. About how much did he pay per pound?

Enrichment

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Topic 7 71

Number Sense

Enrichment 7

-7

Estimating Costs 1. Penelope bought a 24-ounce bottle of maple syrup

that cost $13.25. About how much does one ounce cost?

2. Armand bought 4 pounds of beeswax to make candles. If he paid $22.79, about how much does one pound cost?

3. There are 890.5 calories in each 6-cup package of nutty granola. About how many calories would be in one cup?

4. Ginger bought 32.7 pounds of rabbit chow for $59.03. About how much does one pound cost?

5. Tom bought a 62-ounce bottle of apple cider for $8.61. About how much does one ounce cost?

6. Rita pet-sits for Mr. Monroe’s three dogs while he is on vacation. She earned $615.86 after pet-sitting for two weeks. About how much did Rita earn each day?

7. Sam bought 7 pounds of chocolate truffles for $65.59. About how much did he pay per pound?

Enrichment

7-7

about $0.50

about $6.00

about 150 calories

about $2.00

about $0.15

about $45.00 per day

about $9.00 per pound

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2. In the 6 months Angie has spent preparing to run a marathon, she has run 780.3 miles. About how many miles has Angie run each month?A about 200 milesB about 130 milesC about 80 milesD about 78 miles

3. Find 251.9 " 37.7.

A 214.2B 288.6C 289.6D 628.9

4. Ty’s 3 dogs eat 47.75 pounds of dog food each week all together. About how many pounds does each dog eat each week?

5. Estimate the quotients.

73.61 ! 2

399.7 ! 5

118.51 ! 4

39.74 ! 40

192.78 ! 45

6. Soledad has saved $36.25, which she uses to buy 4 nail polish sets at her favorite store. About how much did she spend on each nail set?

Daily Spiral Review

7-8

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2. In the 6 months Angie has spent preparing to run a marathon, she has run 780.3 miles. About how many miles has Angie run each month?A about 200 milesB about 130 milesC about 80 milesD about 78 miles

3. Find 251.9 " 37.7.

A 214.2B 288.6C 289.6D 628.9

4. Ty’s 3 dogs eat 47.75 pounds of dog food each week all together. About how many pounds does each dog eat each week?

5. Estimate the quotients.

73.61 ! 2

399.7 ! 5

118.51 ! 4

39.74 ! 40

192.78 ! 45

6. Soledad has saved $36.25, which she uses to buy 4 nail polish sets at her favorite store. About how much did she spend on each nail set?

Daily Spiral Review

7-8

35803014

about 16 pounds

about $9

30428_T07_072_72 72 3/18/08 2:21:46 PM



Topic 7 7

3

A certain number is greater than 30 but less than 50. It is a multiple of 6, and the sum of its digits is 6. What is the number?

Problem of the Day

7-8


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1. Find the quotient: 16.85 ! 0.5.

A 3.37

B 8.425

C 33.7

D 34.7

3. The winner of a snail race traveled 9.72 inches in 5.4 minutes. What was the snail’s average speed?

A 1.8 inches per minute

B 0.9 inches per minute

C 0.55 inches per minute

D 0.18 inches per minute

2. What is the value of the quotient: 4.5 !"""" 272.25 ?

A 6.05

B 60.5

C 65

D 605

4. Swiss cheese costs $5.70 per pound at the deli. You buy a package of cheese that costs $6.27. How much cheese is in the package?

A 1.9 pounds

B 1.7 pounds

C 1.1 pounds

D 0.9 pounds

Quick Check

7-8

5. Writing to Explain A freight company charges 45 cents per pound to ship a box. If the total shipping charge for your box is $22.59, how much does it weigh? Calculate the weight to the nearest tenth of a pound. Use long division and show your work.

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1. Find the quotient: 16.85 ! 0.5.

A 3.37

B 8.425

C 33.7

D 34.7

3. The winner of a snail race traveled 9.72 inches in 5.4 minutes. What was the snail’s average speed?

A 1.8 inches per minute

B 0.9 inches per minute

C 0.55 inches per minute

D 0.18 inches per minute

2. What is the value of the quotient: 4.5 !"""" 272.25 ?

A 6.05

B 60.5

C 65

D 605

4. Swiss cheese costs $5.70 per pound at the deli. You buy a package of cheese that costs $6.27. How much cheese is in the package?

A 1.9 pounds

B 1.7 pounds

C 1.1 pounds

D 0.9 pounds

Quick Check

7-8

5. Writing to Explain A freight company charges 45 cents per pound to ship a box. If the total shipping charge for your box is $22.59, how much does it weigh? Calculate the weight to the nearest tenth of a pound. Use long division and show your work.


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Topic 7 75

Reteaching 7-8

Dividing a Decimal by a DecimalSebastian is shipping a box to his cousin. The box weighs 23.6 lb. The cost to ship the box is $88.50. How much does it cost per pound to ship the box?

To divide a decimal by a decimal, you need to change the problem into a simpler type of problem that you already know how to solve.

Step 1: To change this problem, you multiply the divisor by a power of 10 until it becomes a whole number. 23.6 ! 10 " 236

Step 2: You must also multiply the dividend by the same power of 10. Sometimes, you may have to add zeros as placeholders. 88.50 ! 10 " 885.0

Step 3: Place a decimal point in the quotient and divide as you would with whole numbers.

The box costs $3.75 per pound to ship.

For questions 1 through 6, find each quotient.

1. 0.104 ÷ 0.08 2. 5.49 ÷ 0.9 3. 50.4 ÷ 1.2

4. 0.427 ÷ 61 5. 0.8449 ÷ 0.71 6. 9.483 ÷ 8.7

7. Miriam needs to buy new notebooks for school. The notebooks cost $0.98 each including tax. Miriam’s mother gave her $6.45 and told her to buy 8 notebooks. Did her mother give her enough money?

8. Miriam finds a coupon in the store that reduces the price of notebooks to $0.75 each including tax. How many notebooks can Miriam buy now?

Reteaching

7-8

3.75 236 !"""" 885.00 #708 1770 #1652 1180 #1180 0

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Topic 7 75

Reteaching 7-8

Dividing a Decimal by a DecimalSebastian is shipping a box to his cousin. The box weighs 23.6 lb. The cost to ship the box is $88.50. How much does it cost per pound to ship the box?

To divide a decimal by a decimal, you need to change the problem into a simpler type of problem that you already know how to solve.

Step 1: To change this problem, you multiply the divisor by a power of 10 until it becomes a whole number. 23.6 ! 10 " 236

Step 2: You must also multiply the dividend by the same power of 10. Sometimes, you may have to add zeros as placeholders. 88.50 ! 10 " 885.0

Step 3: Place a decimal point in the quotient and divide as you would with whole numbers.

The box costs $3.75 per pound to ship.

For questions 1 through 6, find each quotient.

1. 0.104 ÷ 0.08 2. 5.49 ÷ 0.9 3. 50.4 ÷ 1.2

4. 0.427 ÷ 61 5. 0.8449 ÷ 0.71 6. 9.483 ÷ 8.7

7. Miriam needs to buy new notebooks for school. The notebooks cost $0.98 each including tax. Miriam’s mother gave her $6.45 and told her to buy 8 notebooks. Did her mother give her enough money?

8. Miriam finds a coupon in the store that reduces the price of notebooks to $0.75 each including tax. How many notebooks can Miriam buy now?

Reteaching

7-8

3.75 236 !"""" 885.00 #708 1770 #1652 1180 #1180 0

No. She can only buy 6 notebooks with $6.45.

She can buy 8 notebooks.

1.3 6.1 420.007 1.19 1.09

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Dividing a Decimal by a DecimalFind each quotient.

1. 0.8 !""" 1.84 2. 0.9 !"" 2.7 3. 2.5 !""" 4.75 4. 1.1 !""" 1.21

5. 7.1 !""" 6.39 6. 0.8 !""" 0.648 7. 1.3 !"""" 10.725 8. 0.2 !""" 0.51

9. 0.07 !""" 0.77 10. 4.8 !""" 4.32 11. 0.7 !"" 8.4 12. 2.3 !"" 6.9

13. Chan paid $4.75 for trail mix that costs $2.50 a pound. How many pounds of trail mix did he buy?

14. Max’s family car has a gas tank that holds 12.5 gallons of gas. It cost $40.62 to completely fill the tank yesterday. What was the price of gas per gallon?

15. Strategy Practice Strawberries cost $5.99 per pound, and bananas cost $0.59 per pound. How many pounds of bananas could you buy for the cost of one pound of strawberries?

A 101.5 pounds B 10.15 pounds C 5.99 pounds D .59 pounds

16. Explain It When dividing a decimal by a decimal, why is it sometimes necessary to add a zero to the right of the decimal point in the quotient?

Practice

7-8

30468_T07_76 76 1/16/08 6:05:27 PM

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Dividing a Decimal by a DecimalFind each quotient.

1. 0.8 !""" 1.84 2. 0.9 !"" 2.7 3. 2.5 !""" 4.75 4. 1.1 !""" 1.21

5. 7.1 !""" 6.39 6. 0.8 !""" 0.648 7. 1.3 !"""" 10.725 8. 0.2 !""" 0.51

9. 0.07 !""" 0.77 10. 4.8 !""" 4.32 11. 0.7 !"" 8.4 12. 2.3 !"" 6.9

13. Chan paid $4.75 for trail mix that costs $2.50 a pound. How many pounds of trail mix did he buy?

14. Max’s family car has a gas tank that holds 12.5 gallons of gas. It cost $40.62 to completely fill the tank yesterday. What was the price of gas per gallon?

15. Strategy Practice Strawberries cost $5.99 per pound, and bananas cost $0.59 per pound. How many pounds of bananas could you buy for the cost of one pound of strawberries?

A 101.5 pounds B 10.15 pounds C 5.99 pounds D .59 pounds

16. Explain It When dividing a decimal by a decimal, why is it sometimes necessary to add a zero to the right of the decimal point in the quotient?

Practice

7-8

1.9 pounds

Sample answer: Often, after moving decimal points to make the numbers ready for division, you must add a zero so that a smaller number can be divided by a larger number.

$3.25

0.9 0.81 8.25 2.55

2.3 3 1.9 1.1

11 0.9 12 3

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Topic 7 77

Number Sense

Enrichment 7

-8

Splitting DecimalsThe Chocolate Shop listed its prices on the chart below.

Chocolate-Covered Treats

Price per pound

Cherries $3.25Peanuts $3.04Pretzels $2.61Raisins $1.98Popcorn $0.76

1. How many pounds of chocolate-covered cherries could you buy for $22.10?

2. How much would 1 _ 2 pound of chocolate covered raisins cost?

3. The price of a pound of chocolate-covered peanuts is how many times the price of a pound of chocolate-covered popcorn?

4. If you bought three pounds of chocolate-covered pretzels and paid with $10, how much money would you get back?

5. If you bought 5.5 pounds of chocolate-covered popcorn, how much would you spend?

6. How many pounds of chocolate-covered peanuts could you buy for $45.60?

Enrichment

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Topic 7 77

Number Sense

Enrichment 7

-8

Splitting DecimalsThe Chocolate Shop listed its prices on the chart below.

Chocolate-Covered Treats

Price per pound

Cherries $3.25Peanuts $3.04Pretzels $2.61Raisins $1.98Popcorn $0.76

1. How many pounds of chocolate-covered cherries could you buy for $22.10?

2. How much would 1 _ 2 pound of chocolate covered raisins cost?

3. The price of a pound of chocolate-covered peanuts is how many times the price of a pound of chocolate-covered popcorn?

4. If you bought three pounds of chocolate-covered pretzels and paid with $10, how much money would you get back?

5. If you bought 5.5 pounds of chocolate-covered popcorn, how much would you spend?

6. How many pounds of chocolate-covered peanuts could you buy for $45.60?

Enrichment

7-8

6.8 pounds

$0.99

4 times

$2.17

$4.18

15 pounds

30428_T07_075-077_77 77 3/18/08 2:22:26 PM

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1. Find the quotient.2.7 ! 0.9

A 30B 3C 0.3D 0.03

2. Benjamin ! nished his triathlon in 12.44 hours. During the race, he drank 460.28 " uid ounces of liquid. How many " uid ounces did he drink per hour?

A 3.7 " ozB 3.788 " ozC 37 " ozD 37.88 " oz

3. Which answer is correct?347.14 " 58.71

A 311.63B 299.43C 298.43D 288.43

For 4 and 5, use the chart below.

Candy Price per PieceGumballs $0.08Sour Straws $0.04Jawbreakers $0.40Licorice Rope $0.16

4. Tania brings $8.32 to the candy store. She wants to buy 21 jawbreakers. Does she have enough money? Round your answer down to the nearest whole number.

5. Tania divides her money into two equal amounts. How many sour straws can she buy with half of her money? How many licorice ropes can she buy with the second half of her money?

Daily Spiral Review

7-9

30468_T07_78 78 1/16/08 6:05:34 PM

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1. Find the quotient.2.7 ! 0.9

A 30B 3C 0.3D 0.03

2. Benjamin ! nished his triathlon in 12.44 hours. During the race, he drank 460.28 " uid ounces of liquid. How many " uid ounces did he drink per hour?

A 3.7 " ozB 3.788 " ozC 37 " ozD 37.88 " oz

3. Which answer is correct?347.14 " 58.71

A 311.63B 299.43C 298.43D 288.43

For 4 and 5, use the chart below.

Candy Price per PieceGumballs $0.08Sour Straws $0.04Jawbreakers $0.40Licorice Rope $0.16

4. Tania brings $8.32 to the candy store. She wants to buy 21 jawbreakers. Does she have enough money? Round your answer down to the nearest whole number.

5. Tania divides her money into two equal amounts. How many sour straws can she buy with half of her money? How many licorice ropes can she buy with the second half of her money?

Daily Spiral Review

7-9

104 sour straws;26 licorice ropes

No; sample answer: $8.32 ! $0.40 " 20.8;Tania can buy only20 jawbreakers.

30428_T07_078_78 78 3/18/08 2:22:38 PM



Topic 7 7

9

Harley received $0.45 in change from a purchase. The cashier had only quarters, dimes, and nickels. How many ways could he receive the change?

Problem of the Day

7-9


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1. The homework assignment in Jim’s English class is to read a novel. The book has 202 pages. Jim read 45 pages on Monday, 18 pages on Tuesday, and 36 pages on Wednesday. What hidden question needs to be answered before you can find out how many pages he still has to read?

A When is the assignment due?

B How many pages can Jim read on Thursday?

C How many pages has he read so far?

D How many pages does the book have?

2. Jenna made money babysitting, and she also earned $20 cleaning her neighbor’s basement. During the week, her total earnings were $55. If she charges $5 per hour for babysitting, how many hours did she babysit?

A 11

B 7

C 5

D 4

3. The stage for a school play is 70 feet wide. A set for the play will be built in two sections, separated by 5 feet in the center. In addition, 3 feet must be left free on the left and on the right as space for the actors to stand offstage. What should be the width of each section of the set?

A 20 feet

B 25 1 _ 2 feet

C 29 1 _ 2 feet

D 59 feet

4. Writing to Explain You are allowed to spend $125 for new clothes. You find a sweater that costs $29.99, a jacket that costs $35.00, and 2 pairs of socks for $3.25 each. You want to know how many pairs of shoes you can buy for $22.50 per pair. Identify a hidden question that you need to answer to find how many pairs of shoes you can buy. Then calculate the number of pairs of shoes you can buy. Show your work.

Quick Check

7-9

30468_T07_80 80 1/16/08 6:05:46 PM

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1. The homework assignment in Jim’s English class is to read a novel. The book has 202 pages. Jim read 45 pages on Monday, 18 pages on Tuesday, and 36 pages on Wednesday. What hidden question needs to be answered before you can find out how many pages he still has to read?

A When is the assignment due?

B How many pages can Jim read on Thursday?

C How many pages has he read so far?

D How many pages does the book have?

2. Jenna made money babysitting, and she also earned $20 cleaning her neighbor’s basement. During the week, her total earnings were $55. If she charges $5 per hour for babysitting, how many hours did she babysit?

A 11

B 7

C 5

D 4

3. The stage for a school play is 70 feet wide. A set for the play will be built in two sections, separated by 5 feet in the center. In addition, 3 feet must be left free on the left and on the right as space for the actors to stand offstage. What should be the width of each section of the set?

A 20 feet

B 25 1 _ 2 feet

C 29 1 _ 2 feet

D 59 feet

4. Writing to Explain You are allowed to spend $125 for new clothes. You find a sweater that costs $29.99, a jacket that costs $35.00, and 2 pairs of socks for $3.25 each. You want to know how many pairs of shoes you can buy for $22.50 per pair. Identify a hidden question that you need to answer to find how many pairs of shoes you can buy. Then calculate the number of pairs of shoes you can buy. Show your work.

Quick Check

7-9


30428_T07_080_80 80 3/18/08 2:23:00 PM

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Topic 7 81

Reteaching 7-9

Problem Solving: Multiple-Step ProblemsA multiple-step problem is a problem where you may need more than one step to find your answer.

Marcie was in a 3-day charity walk. Her friend Gayle said she would give the charity $1.50 for each mile that Marcie walked. The first day, Marcie walked 26.42 miles. The second day, Marcie walked 32.37 miles. The third day, Marcie walked 28.93 miles. How much money did Gayle give?

Step 1. Read through the problem again and write a list of what you already know.

Marcie walked 26.42, 32.37, and 28.93 miles. Gayle gave $1.50 for each mile.

Step 2. Write a list of what you need to know.

Total amount Gayle gave

Step 3. Write a list of the steps to solve the problem.

Find the total number of miles Marcie walked. Find the amount Gayle gave.

Step 4. Solve the problem one step at a time.

26.42 ! 32.37 ! 28.93 " 87.72 total number of miles Marcie walked

87.72 # $1.50 " $131.58 total amount Gayle gave

Use the information above to answer Exercise 1.

1. Marcie’s brother Tom was also in the charity walk. He only walked 0.8 as far as Marcie on the first day, 0.7 as far on the second day, and 0.9 as far on the third day. How many miles did Tom walk, rounded to the nearest hundredth of a mile?

2. Diego is buying fruit at the store. Which costs less: 1 pound of each fruit or 4 pounds of peaches?

Fruit Cost per pound

Apples $0.89Oranges $1.29Peaches $0.99Grapes $1.09

Reteaching

7-9

30468_T07_81 81 1/16/08 6:05:52 PM

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Topic 7 81

Reteaching 7-9

Problem Solving: Multiple-Step ProblemsA multiple-step problem is a problem where you may need more than one step to find your answer.

Marcie was in a 3-day charity walk. Her friend Gayle said she would give the charity $1.50 for each mile that Marcie walked. The first day, Marcie walked 26.42 miles. The second day, Marcie walked 32.37 miles. The third day, Marcie walked 28.93 miles. How much money did Gayle give?

Step 1. Read through the problem again and write a list of what you already know.

Marcie walked 26.42, 32.37, and 28.93 miles. Gayle gave $1.50 for each mile.

Step 2. Write a list of what you need to know.

Total amount Gayle gave

Step 3. Write a list of the steps to solve the problem.

Find the total number of miles Marcie walked. Find the amount Gayle gave.

Step 4. Solve the problem one step at a time.

26.42 ! 32.37 ! 28.93 " 87.72 total number of miles Marcie walked

87.72 # $1.50 " $131.58 total amount Gayle gave

Use the information above to answer Exercise 1.

1. Marcie’s brother Tom was also in the charity walk. He only walked 0.8 as far as Marcie on the first day, 0.7 as far on the second day, and 0.9 as far on the third day. How many miles did Tom walk, rounded to the nearest hundredth of a mile?

2. Diego is buying fruit at the store. Which costs less: 1 pound of each fruit or 4 pounds of peaches?

Fruit Cost per pound

Apples $0.89Oranges $1.29Peaches $0.99Grapes $1.09

Reteaching

7-9

69.83 miles

4 pounds of peaches

30428_T07_081-083_81 81 3/18/08 2:23:12 PM

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Prac

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Problem Solving: Multiple-Step Problems Write and answer the hidden question or questions in each problem and then solve the problem. Write your answer in a complete sentence.

1. Sue bought 2 pairs of jeans and a belt that cost $6.95. The tax on the items was $5.85. Sue paid the cashier $70.00. How much money did Sue receive in change?

2. A recreation department purchased 12 T-shirts for day camp. The department does not have to pay sales tax. It paid with a $100.00 bill. How much change did it receive?

3. When Mrs. Johnson saw the sale, she decided to get clothes for each child in her family. She bought each of her 6 children a pair of jeans and a T-shirt. She paid $14.35 in sales tax. How much was Mrs. Johnson’s total bill?

A $94.35 B $119.70 C $229.35 D $253.35

4. Write a Problem Write a two-step problem that contains a hidden question about buying something at the mall. Tell what the hidden question is and solve your problem. Use $8.95 somewhere in your equation. Write your answer in a complete sentence.

5. Explain It What are hidden questions and why are they important when solving multiple-step problems?

Practice

7-9

Jeans $29.95 for 1 pair OR 2 pairs for $55.00

T-shirts $9.95 for 1 OR 3 T-shirts for $25.00

Storewide Sale

30468_T07_82 82 1/16/08 6:05:54 PM

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82 Topic 7

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tice 7-9

Problem Solving: Multiple-Step Problems Write and answer the hidden question or questions in each problem and then solve the problem. Write your answer in a complete sentence.

1. Sue bought 2 pairs of jeans and a belt that cost $6.95. The tax on the items was $5.85. Sue paid the cashier $70.00. How much money did Sue receive in change?

2. A recreation department purchased 12 T-shirts for day camp. The department does not have to pay sales tax. It paid with a $100.00 bill. How much change did it receive?

3. When Mrs. Johnson saw the sale, she decided to get clothes for each child in her family. She bought each of her 6 children a pair of jeans and a T-shirt. She paid $14.35 in sales tax. How much was Mrs. Johnson’s total bill?

A $94.35 B $119.70 C $229.35 D $253.35

4. Write a Problem Write a two-step problem that contains a hidden question about buying something at the mall. Tell what the hidden question is and solve your problem. Use $8.95 somewhere in your equation. Write your answer in a complete sentence.

5. Explain It What are hidden questions and why are they important when solving multiple-step problems?

Practice

7-9

Check students’ problems.

Sample answer: Hidden questions are not directly stated in the problem. The answers to the hidden questions give information needed to solve the problem.

What was the total cost of Sue’s items? $67.80; Sue received $2.20 in change.

What was the cost for 12 T-shirts? $100.00; The department received no change, because it paid the exact amount.

Jeans $29.95 for 1 pair OR 2 pairs for $55.00

T-shirts $9.95 for 1 OR 3 T-shirts for $25.00

Storewide Sale

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Topic 7 83

Enrichment 7

-9

Decision Making

Smart ShoppersMr. Murphy owns a fruit stand in the city. People buy fruit all day long as they pass by. Help the customers spend their money wisely.

1. One customer bought two 2-lb bunches of grapes. How much did she save by buying these instead of four 1-lb bunches?

2. Another customer bought 6 bananas, 9 apples, and 1 pound of grapes. Based on the money he spent, identify an example of how he could purchase more fruit for less money.

3. You have $10.00 to spend at Murphy’s Fruit Stand. Give one example of how you could get the best value for the money. Tell what you would buy and how much money you would have left over.

Enrichment

7-9

Murphy’s Fruit Stand

Fruit

Bananas

Apples

Grapes

Price

$ 0.40 each or $1.98for a bunch of 8

$0.50 each or $3.99for a bag of 10

$1.99 for 1 lb or$3.49 for 2 lb

30468_T07_83 83 1/16/08 6:05:56 PM

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Topic 7 83

Enrichment 7

-9

Decision Making

Smart ShoppersMr. Murphy owns a fruit stand in the city. People buy fruit all day long as they pass by. Help the customers spend their money wisely.

1. One customer bought two 2-lb bunches of grapes. How much did she save by buying these instead of four 1-lb bunches?

2. Another customer bought 6 bananas, 9 apples, and 1 pound of grapes. Based on the money he spent, identify an example of how he could purchase more fruit for less money.

3. You have $10.00 to spend at Murphy’s Fruit Stand. Give one example of how you could get the best value for the money. Tell what you would buy and how much money you would have left over.

Enrichment

7-9

$0.98

Sample answer: I could buy a bunch of 8 bananas, a bag of 10 apples, and 2 lb of grapes. I would spend $9.46 and have $0.54 left over, or I could buy 1 more banana and have $0.14 left.

Sample answer: The customer spent $8.89. For that amount, he could buy a bag of 10 apples, a pound of grapes, and a bunch of 8 bananas as well as 1 more apple and 1 more banana or 2 bananas.

Murphy’s Fruit Stand

Fruit

Bananas

Apples

Grapes

Price

$ 0.40 each or $1.98for a bunch of 8

$0.50 each or $3.99for a bag of 10

$1.99 for 1 lb or$3.49 for 2 lb

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1. Ms. Martina filled her truck’s gas tank with 28.7 gallons of gas. If she drove 100 miles on the same tank of gas, how much gas did she use per mile? (7-5)

A 2.87 gallons

B 0.287 gallons

C 0.0287 gallons

D 0.00287 gallons

2. Kim made $5.35 on the first day she set up her lemonade stand. If she makes the same amount each day for six days, how much money will she have? (7-2)

A $42.80

B $37.30

C $32.10

D $28.70

3. The table shows the amount of different produce Mrs. Ramirez bought, and the total price she paid for each. What is the price per pound she paid for apples? (7-8)

A $0.09

B $0.80

C $0.84

D $0.90

4. A pizza shop bought 28 pounds of tomatoes for $23.80. How much did the shop pay for 1 pound of tomatoes? (7-6)

A $0.85

B $0.99

C $1.10

D $2.45

5. An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees? (7-4)

A 3.345

B 2.577

C 2.49

D 1.098

Mark the best answer.

Topic 7 Multiple-Choice Test

84 Topic 7

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Produce Pounds Total Price

Apples 3.6 $3.24

Bananas 2.5 $2.23

Grapes 4.8 $4.08

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1. Ms. Martina filled her truck’s gas tank with 28.7 gallons of gas. If she drove 100 miles on the same tank of gas, how much gas did she use per mile? (7-5)

A 2.87 gallons

B 0.287 gallons

C 0.0287 gallons

D 0.00287 gallons

2. Kim made $5.35 on the first day she set up her lemonade stand. If she makes the same amount each day for six days, how much money will she have? (7-2)

A $42.80

B $37.30

C $32.10

D $28.70

3. The table shows the amount of different produce Mrs. Ramirez bought, and the total price she paid for each. What is the price per pound she paid for apples? (7-8)

A $0.09

B $0.80

C $0.84

D $0.90

4. A pizza shop bought 28 pounds of tomatoes for $23.80. How much did the shop pay for 1 pound of tomatoes? (7-6)

A $0.85

B $0.99

C $1.10

D $2.45

5. An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees? (7-4)

A 3.345

B 2.577

C 2.49

D 1.098

Mark the best answer.

Topic 7 Multiple-Choice Test

84 Topic 7

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Produce Pounds Total Price

Apples 3.6 $3.24

Bananas 2.5 $2.23

Grapes 4.8 $4.08

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Topic 7Free-Response Test


Use mental math to find each product.

1. 54.6 ! 1,000

2. 0.65 ! 100

3. 7.03 ! 10

4. 88.6 ! 100

Find each product.

5. 0.2 ! 33

6. 130 ! 0.007

7. 50 ! 0.22

8. 313 ! 0.6

Estimate by rounding or using compatible numbers.

9. 55.1 ! 4

10. 0.5 ! 181

11. 99.7 ! 84

12. 64 " 0.48

13. 18.3 " 0.31

14. 5.4 " 0.21

15. 11.9 " 0.82

16. 71 " 0.214

17. 9.6 " 0.53

18. 43.1 " 0.792

19. 5.7 " 0.32

20. 4.13 " 0.802

21. Phoenix, Arizona, is one of the driest cities in the United States. It receives just 7.66 inches of rain each year. If Phoenix receives the same amount of rain each month, how much rain will it get in 1.5 years?

22. Duluth, Minnesota, has a mean yearly precipitation of 30 inches. San Diego, California, has a mean yearly precipitation that is 0.33 of Duluth’s. What is San Diego’s mean yearly precipitation?

23. If you multiply 0.73 by 2.52, how many decimal places will be in the product? How do you know?

24. Offensive linemen in the National Football League often weigh 0.16 of a ton. If you weigh 0.25 of a lineman’s weight, what part of a ton do you weigh?

Topic 7 87

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Use mental math to find each product.

1. 54.6 ! 1,000

2. 0.65 ! 100

3. 7.03 ! 10

4. 88.6 ! 100

Find each product.

5. 0.2 ! 33

6. 130 ! 0.007

7. 50 ! 0.22

8. 313 ! 0.6

Estimate by rounding or using compatible numbers.

9. 55.1 ! 4

10. 0.5 ! 181

11. 99.7 ! 84

12. 64 " 0.48

13. 18.3 " 0.31

14. 5.4 " 0.21

15. 11.9 " 0.82

16. 71 " 0.214

17. 9.6 " 0.53

18. 43.1 " 0.792

19. 5.7 " 0.32

20. 4.13 " 0.802

21. Phoenix, Arizona, is one of the driest cities in the United States. It receives just 7.66 inches of rain each year. If Phoenix receives the same amount of rain each month, how much rain will it get in 1.5 years?

22. Duluth, Minnesota, has a mean yearly precipitation of 30 inches. San Diego, California, has a mean yearly precipitation that is 0.33 of Duluth’s. What is San Diego’s mean yearly precipitation?

23. If you multiply 0.73 by 2.52, how many decimal places will be in the product? How do you know?

24. Offensive linemen in the National Football League often weigh 0.16 of a ton. If you weigh 0.25 of a lineman’s weight, what part of a ton do you weigh?

Topic 7 87

54,60065

0.91

70.38,860

220

6.6

11

8,400

187.8

90

1286025123502050

205

11.49 inches

9.9 inches

4; each factor has 2 decimal places, and 2 ! 2 " 4

0.04 ton

30428_T07_087-088_87 Sec187 3/18/08 2:23:44 PM

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Performance Assessment

Topic 7

Performance Assessm

ent

1. Use the foreign currency exchange rate table below to create a list of expenses for an international trip. Write an amount in a different foreign currency for each of these 5 items: One-way train ticket between two cities, hotel room per night, dinner for two, sightseeing excursion, and museum entrance fee.

For example, choose an appropriate price for anight in a hotel. Then choose a country and multiply to convert the U.S. dollar amount into that country’s currency.

U.S. 124.50 ! 42.65 rupees " 5,309.93

Use a different currency for each of the 5 items and write only the numerical amounts. Trade lists with a partner. Divide by various exchange rates to find the original prices in U.S. dollars.

2. Use the business pages of a newspaper or other research materials to find the exchange rate for 5 other countries of your choice. Round each exchange rate to the nearest hundredth with your partner. Repeat the conversion process for the 5 items using the new currencies.

3. If you were planning an actual trip to a foreign country, how would you go about budgeting your expenses?

U.S. $1.00 !

1.13 Canadian dollars

1.21 Australian dollars

7.72 Chinese yuan

42.65 Indian rupees

119.03 Japanese yen

68.40 Kenyan shillings

11.00 Mexican pesos

30468_T07_89 89 1/16/08 6:06:18 PM

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Performance Assessment

Topic 7

Performance Assessm

ent

1. Use the foreign currency exchange rate table below to create a list of expenses for an international trip. Write an amount in a different foreign currency for each of these 5 items: One-way train ticket between two cities, hotel room per night, dinner for two, sightseeing excursion, and museum entrance fee.

For example, choose an appropriate price for anight in a hotel. Then choose a country and multiply to convert the U.S. dollar amount into that country’s currency.

U.S. 124.50 ! 42.65 rupees " 5,309.93

Use a different currency for each of the 5 items and write only the numerical amounts. Trade lists with a partner. Divide by various exchange rates to find the original prices in U.S. dollars.

2. Use the business pages of a newspaper or other research materials to find the exchange rate for 5 other countries of your choice. Round each exchange rate to the nearest hundredth with your partner. Repeat the conversion process for the 5 items using the new currencies.

3. If you were planning an actual trip to a foreign country, how would you go about budgeting your expenses?

U.S. $1.00 !

1.13 Canadian dollars

1.21 Australian dollars

7.72 Chinese yuan

42.65 Indian rupees

119.03 Japanese yen

68.40 Kenyan shillings

11.00 Mexican pesos

If prices were in the other currency, Iwould divide by the exchange rate tofind the cost in dollars.

See below.

See below.

30428_T07_089-089_89 89 3/18/08 2:23:56 PM

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