Dividing Decimals By Decimals

3-7 Dividing by Decimals

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpDivide.

1. 4.8 ÷ 2

2. 16.1 ÷ 7

3. 0.36 ÷ 3

4. 25.28 ÷ 4

2.42.3

0.12

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6.32

Problem of the Day

In the following magic square, 3.375 is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers.

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4.5 0.25

0.5

3

1 1.5 2.25

0.75 9

Learn to divide whole numbers and decimals by decimals.

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Multiplying the divisor and the dividend by the same number does not change the quotient.

42 ÷ 6 = 7

10 10

420 ÷ 60 = 7

10 10

4,200 ÷ 600 = 7

Helpful Hint

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Additional Example 1A: Dividing a Decimal by a Decimal

Find the quotient.

5.2 ÷ 1.3

1.3 5.2 Multiply the divisor and dividend by the same power of ten.

There is one decimal place in the divisor. Multiply by 101, or 10.

Think: 1.3 x 10 = 13 5.2 x 10 = 52

Divide.

13 524

–520

5.2 ÷ 1.3 = 4

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Additional Example 1B: Dividing a Decimal by a Decimal

61.3 ÷ 0.36

0.36 61.30

Think: 0.36 x 100 = 36 61.3 x 100 = 6,130

Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.

36 6,130.000

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Additional Example 1B Continued

Place the decimal point in the quotient. Divide.

36 6,130.0007

-36

1

253-252

10 -0

0

100

.2

-72

-252

7

280-252

280

7

28 61.3 ÷ 0.36 = 170.27

__

When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

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Check It Out: Example 1A

Find the quotient.

6.6 ÷ 1.1

1.1 6.6 Multiply the divisor and dividend by the same power of ten.

There is one decimal place in the divisor. Multiply by 10 , or 10.

Think: 1.1 x 10 = 11 6.6 x 10 = 66

1

Divide.

11 666

-660

6.6 ÷ 1.1 = 6

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Check It Out: Example 1B

51.2 ÷ 0.24

0.24 51.2

Think: 0.24 x 100 = 24 51.2 x 100 = 5,120

Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.

24 5120.00

0

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Check It Out: Example 1B Continued

Divide. 24 5,120.00

1

-48

2

32 -24

80-72

3

80

.3

-72

-72 80

3

51.2 ÷ 0.24 = 213.33__

When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.

8

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Additional Example 2: Problem Solving Application

After driving 216.3 miles, the York’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas?

11 Understand the Problem

The answer will be the average number of miles per gallon.

List the important information:

They drove 216.3 miles. They used 10.5 gallons of gas.

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22 Make a Plan

Solve a simpler problem by replacing the decimals in the problem with whole numbers.

If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem.

Solve33

First estimate the answer. You can use compatible numbers.

216.3 ÷ 10.5 200 ÷ 10 = 20

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The York family averaged 20.6 miles per gallon.

105 2163.0-210

2

63 -0630

-630

0

0

.6

Solve Continued33

10.5 216.3Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163


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Look Back44

The answer is reasonable since 20.6 is close to the estimate of 20.

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Check It Out: Example 2

After driving 191.1 miles, the Chang’s filled up with 10.5 gallons of gas. On average, how many miles did they drive per gallon of gas?

11 Understand the Problem

The answer will be the average number of miles per gallon.

List the important information:

They drove 191.1 miles. They used 10.5 gallons of gas.

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22 Make a Plan

Solve a simpler problem by replacing the decimals in the problem with whole numbers.

If they drove 10 miles using 2 gallons of gas, they averaged 5 miles per gallon. You need to divide miles by gallons to solve the problem.

Solve33

First estimate the answer. You can use compatible numbers.

191.1 ÷ 10.5 190 ÷ 10 = 19

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105 1911.0-105

1

861-840

210-210

8

0

.2

The Chang family averaged 18.2 miles per gallon.

Solve Continued33

10.5 191.1Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911


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Look Back44

The answer is reasonable since 18.2 is close to the estimate of 19.

Lesson Quiz

Find each quotient.

1. 49 ÷ 0.7

2. 21.63 ÷ 2.1

3. 38.43 ÷ 6.1

4. 16.9 ÷ 5.2

5. John spent $13.44 renting 4 videos for the

weekend. What was the cost per video?

10.3

70

Insert Lesson Title Here

6.3

3.25

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$3.36

Education

Dividing Decimals By Decimals