lesson 10 - amazon s3...i can write each decimal as an improper fraction and multiply. the...

$: Lesson 10 - Amazon S3...I can write each decimal as an improper fraction and multiply. The denominator of the fraction product will tell me how many decimal places the product will$
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Practice Lesson 10 Multiply and D

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©Curriculum Associates, LLC Copying is not permitted. 99Lesson 10 Multiply and Divide Decimals

Name: Multiply and Divide Decimals

Lesson 10

Prerequisite: Multiply Decimals to Hundredths

Study the example showing how to multiply a decimal by a decimal. Then solve problems 1–7.

1 Explain why the factor 1 5 is broken into two numbers in the model

2 What does each small square in the model represent?

3 How would the area model change if the factor 0 4 were changed to 1 4?

Example

Find 1 5 3 0 4

You can use an area model to multiply tenths by tenths

0.4

1.5 3 0.4 5 0.4 1 0.2 5 0.6

1 1 3 0.4 5 0.4

0.5 3 0.4 5 0.20 5 0.20.5

9999

Possible explanation: 1.5 has both ones and tenths.

Possible answer: There would be 10 more columns of 15 small squares each.

one hundredth

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©Curriculum Associates, LLC Copying is not permitted.100 Lesson 10 Multiply and Divide Decimals

Solve.

Use the situation below to solve problems 4–5.

Lisa walks at a speed of 3 25 miles per hour for 1 5 hours How many miles does she walk in all?

4 Complete the area model that represents 1 5 3 3 25

5 Explain how you can use the area model to fi nd the number of miles that Lisa walks

6 Moira multiplies 1 8 by 2 4 and writes the product as 0 432 Tom says that her product is incorrect How could Tom know this without multiplying the two numbers?

7 Andrew lives 1 7 kilometers from the soccer fi eld He rode his bike 0 9 of the distance to the fi eld How much farther does Andrew need to ride to reach the soccer fi eld? Include an area model in your answer

Show your work.

Solution:

3 0 25

1 1 3 5 3 1 3 5

0 5 3 3 5 1 5 3 5

100

1 0.7

0.9 0.9 0.63

1.7 3 0.9 5 0.9 1 0.63 5 1.531.7 2 1.53 5 0.17

Andrew needs to ride 0.17 kilometer farther.

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I can add the partial products. 3 1 1.5 1 0.25 1 0.125 5 4.875 miles

Possible answer: Tom estimated the answer as 2 times 2, or 4.

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3

0.5

0.250.25

0.1250.250.5

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Unit 2 Th

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Name: Lesson 10

Multiply Decimals to Thousandths

Study the example problem showing how to multiply decimals to thousandths. Then solve problems 1–7.

1 How does your estimate help you place the decimal point in the product?

2 How can you use fractions to place the decimal point in the product?

3 How does the number of decimal places in the factors relate to the number of decimal places in the product of the example?

Example

A scientist used 4 317 liters of a chemical for one experiment She uses 1 75 times that amount for another experiment How much of the chemical does the scientist use for the second experiment?

First, estimate Because 4 317 is about 4 and 1 75 is about 2, the product will be about 4(2) 5 8

The scientist uses 7 55475 liters of the chemical for the second experiment

4 3173 1 75

21585

302190

1 431700

7 55475

Multiply decimals as you would multiply whole numbers Remember to place the decimal point in the product

101

The answer is around 8, so I can place the decimal point so that the product is around 8.

I can write each decimal as an improper fraction and multiply. The denominator of the

fraction product will tell me how many decimal places the product will have.

There are 3 decimal places in the first factor, 2 decimal places in the second factor, and

5 decimal places in the product. The number of decimal places in the product equals

the sum of the number of decimal places in the factors.

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B

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Solve.

4 Without multiplying, tell whether the product 0 644 3 0 25 will be greater than 1 or less than 1? Explain how you know Then fi nd the product

5 Selena drove at an average speed of 50 55 miles per hour for 1 75 hours She stopped at a rest stop and then drove at an average speed of 45 2 miles per hour for 2 25 hours Did Selena drive more miles before or after the rest stop? How many more miles?

Show your work.

Solution:

6 Estimate the product of 23 725 3 6 25 Then fi nd the product Why is it a good idea to estimate fi rst?

7 Ellen walks dogs on weekends She gets paid $8 50 per hour Each day she works 5 hours and 45 minutes Does she earn more or less than $85 in one weekend? How much more or less? Explain

102

Possible explanation: the product will be less than 1 because 0.644 and 0.25 are both

less than 1; The product of 0.644 3 0.25 is 0.16100, which is equal to 0.161.

Selena drove 13.2375 more miles after the rest stop.

Possible estimate: 144; product: 148.28125; Because it helps me place the decimal

point.

Ellen works more than 10 hours in one weekend, so she earns more than $85, or $8.50 3

10. She works 1.5 hours more, so she earns $8.50 3 1.5, or $12.75, more than $85.

Possible student work:

101.7 2 88.4625 5 13.2375

50.553 1.75

25275

35385

1 5055

88.4625

45.23 2.25

2260

904

1 904

101.700

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Unit 2 Th

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Unit 2


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Solve.

5 Emma made a mistake when she divided 6 4 by 0 02 Describe her mistake and show the correct division

6 Aaron paid $9 75 for markers that cost $0 75 each He bought 4 times as many pencils for $0 35 each How much did Aaron pay for the pencils?

Show your work.

Solution:

7 Mei spent $66 buying fabric that costs $7 50 per yard How many yards of fabric did Mei buy? How do you know that your answer is reasonable?

0 02 q ······ 6 4 32

2 q ······ 64 2 6

42 4

0

104

Possible explanation: She multiplied the

dividend by 10. She should have multiplied the

dividend by 100, as she did with the divisor.


First, I need to divide 9.75 by 0.75, which is 975 4 75.

Aaron paid $18.20 for the pencils.

8.8 yards; Using estimation, $66 4 $7.50 is about $64 4 $8 5 8. So 8.8 yards

is reasonable.

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He bought 13 markers, which means that he bought 52 pencils. So I can multiply $0.35 by 52.

1375 q ······ 975 2 75

2252 225

0

0.353 52

070

1 175

18.20

3202 q ······ 640 2 6

402 40

0


Name: Lesson 10

Divide by Decimals

Study the example problem showing how to divide by decimals. Then solve problems 1–7.

1 Why was the divisor changed to a whole number?

2 How do you change 0 35 to a whole number?

3 Why must you multiply the dividend by the same power of 10 that you multiplied the divisor by to write it as a whole number?

4 Complete the equation to show that 4 2 4 0 35 is equivalent to 420 4 35

4 2 4 0 35 5 ———––– 3 ———––– 5 ———––– 5 420 4 35

Example

Jamie has 4 2 pounds of dried fruit to put into bags She puts 0 35 pound of fruit in each bag How many bags of dried fruit does she have?

First, estimate Because 4 2 is about 4 and 0 35 is about 0 4, the quotient is about 4 divided by 4 tenths, or 10

Next, write the divisor as a whole number by multiplying it by a power of 10 Multiply the dividend by that same power Then divide as you would with whole numbers

Jamie has 12 bags of dried fruit

0 35 q ······ 4 20 12

35 q ······ 420 2 35

702 70

0

103

Possible answer: It is easier to divide by a whole number than by a decimal.

multiply by 100; to keep the relationship between the numbers equivalent to the one

in the problem

multiply by 100

B

B

B

B

4.2 100 420

0.35 100 35

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Solving

Unit 2 Th

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ber System U

nit 2Practice Lesson 10 M

ultiply and Divide D

ecimals


Name:

Divide Decimals

Study the example problem showing how to divide decimals by using an algorithm. Then solve problems 1–6.

1 In the example, the dividend and divisor were multiplied by what power of 10? Explain why they were multiplied by this power of 10

2 Complete the equation to show that 19 625 4 2 5 is equivalent to 196 25 4 25

3 Would the quotient be the same if you multiplied the numerator and the denominator by 100? Explain

Example

Tanisha rode her bike 19 625 miles in 2 5 hours What was her average speed?

First, estimate Because 19 625 is about 20, the quotient is about 20 divided by 2 5, or 8 Next divide 19 625 by 2 5

Tanisha’s average speed was 7 85 miles per hour

Lesson 10

2 5 q ······ 19 625 7 85

25 q ······ 196 25 2 175

2122 200

1252 125

0

19 625 4 2 5 5 ————– 3 ————– 5 ————– 5 196 25 4 25

105

They were both multiplied by 10 so that the divisor 2.5 became a whole number.

Yes; Possible explanation: Dividing 1962.5 by 250 is equivalent to dividing

196.25 by 25.

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19.625 10 196.25

2.5 10 25


Solve.

Use the information below to solve problems 4–5.

Jake bought 14 5 pounds of dried navy beans for $25 52

4 Explain how to estimate the price per pound

5 What is the price per pound of the beans? Explain how you know that your answer is reasonable

Show your work.

Solution:

6 Jeff is training for a walkathon He walked 8 84 miles at an average speed of 3 4 miles per hour Then he walked for an additional 1 6 hours at the same speed How many hours did Jeff walk in all?

Show your work.

Solution:

106

Possible explanation: I know that 14.5 is close to 15 and $25.52 is close to $30.

Because 30 4 15 5 2, a reasonable estimate is $2 per pound.

Possible student work:25.52 4 14.5 5 255.2 4 145

The price per pound is $1.76. Possible explanation: The answer is reasonable

because it is close to $2, the estimated price per pound.

Jeff walked for a total of 2.6 1 1.6 5 4.2 hours.

1.76145 q ······ 255.20

2 145

11022 1015

8702 870

0

Possible student work:For the first part, the number of hours Jeff walked is 8.84 4 3.4 5 88.4 4 34.

2.6 1 1.6 5 4.2 hours

2.634 q ······ 88.4 2 68

2042 204

0

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©C

urricu

lum

Associates, L

LC

C

opying is n

ot permitted.

Practice and Prob

lem Solvin

gU

nit 2 The N

umb

er System

Unit 2


ivide Decim

als


5 Hillary earned $17 92 weeding gardens for 3 2 hours She was paid the same hourly rate to mow lawns Hillary mowed lawns for 2 75 hours How much did Hillary earn mowing lawns?

Show your work.

Solution:

Solve.

3 Is each expression equivalent to 23 6 4 4 02? Select Yes or No

a. 2 36 4 40 2 u Yes u No

b. 2360 4 402 u Yes u No

c. 2 36 4 0 402 u Yes u No

d. 236 4 4020 u Yes u No

4 Isabel’s car gets 33 5 miles per gallon Her gas tank holds 15 1 gallons of gas How many miles can Isabel drive on a full tank of gas?

A 2 22 miles C 505 85 miles

B 22 2 miles D 5,058 5 miles

John chose D as the correct answer How did he get that answer?

How can you use estimation to determine whether your answer makes sense?

Do you multiply or divide to find the hourly rate?

How can you tell whether each quotient is equivalent to the original problem?

108

333

3


17.92 4 3.2 5 179.2 4 32

5.632 q ······ 179.2 2 160

192 2 192

0

2.753 5.6

1650

1 1375

15.400

Hillary earned $15.40 mowing lawns.

He multiplied correctly, but he did not place the

decimal point correctly.

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Name: Lesson 10

Multiply and Divide Decimals

Solve the problems.

2 Which expressions represent the model? Select all that apply

A 0 84

B 0 6 1 0 4

C 0 6 1 0 24

D 1 4 3 0 6

1 A total of 6 825 inches of snow fell during a storm The snow fell at an average rate of 1 3 inches per hour For how many hours did the snow fall?

Show your work.

Solution:

How many decimal places are in the divisor?

What does each small square in the model represent?0.6

1

0.4

107

6.825 4 1.3 5 68.25 4 13

The snow fell for 5.25 hours.

B

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5.2513 q ······ 68.25 2 65

322 26

652 65

0

lesson 10 - amazon s3...i can write each decimal as an improper fraction and multiply. the...

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