3-8 Dividing by Decimals

Course 1

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

5. 6.25 ÷ 5

2.42.3

0.12

Course 1

3-8 Dividing by Decimals

6.32

1.25

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.

Course 1

3-8 Dividing by Decimals

4.5 0.25

0.5

3

1 1.5 2.25

0.75 9

Learn to divide whole numbers and decimals by decimals.

Course 1

3-8 Dividing by Decimals

Course 1

3-8 Dividing by Decimals

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

Course 1

3-8 Dividing by Decimals

Additional Example 1A: Dividing a Decimal by a Decimal

Find each quotient.

A. 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

Course 1

3-8 Dividing by Decimals

Additional Example 1B: Dividing a Decimal by a Decimal

B. 61.3 ÷ 0.36

0.36 61.3

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

Course 1

3-8 Dividing by Decimals

Additional Example 1B Continued

Divide. 36 6,130.000

7

-36

1

253252

10 -0

0

100

.2

-72

-252

7

280-252

280

7

28

170.277… = 170.27__

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

Course 1

3-8 Dividing by Decimals

Try This: Example 1A

Find each quotient.

A. 4.8 ÷ 1.2

1.2 4.8 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: 1.2 x 10 = 12 4.8 x 10 = 48

1

Divide.

12 484

-480

Course 1

3-8 Dividing by Decimals

Try This: Example 1B

B. 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 5120.000

Course 1

3-8 Dividing by Decimals

Try This: Example 1B Continued

Divide. 24 5,120.00

1

-48

2

32 24

80-72

3

80

.3

-72

-72 80

3

213.33… = 213.33__

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

8

Course 1

3-8 Dividing by Decimals

Additional Example 2: Problem Solving Application

After driving 216.3 miles, the Yorks used 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.

Course 1

3-8 Dividing by Decimals

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

10.5 216.3

Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163 Place the decimal point in the quotient. Divide.

The York family averaged 20.6 miles per gallon.

Course 1

3-8 Dividing by Decimals

Look Back44

Use compatible numbers to estimate the quotient.

216.3 ÷ 10.5 220 ÷ 11 =20

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

Course 1

3-8 Dividing by Decimals

Try This: Example 2

After driving 191.1 miles, the Changs used 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.

Course 1

3-8 Dividing by Decimals

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

10.5 191.1

Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911 Place the decimal point in the quotient. Divide.

The York family averaged 18.2 miles per gallon.

Course 1

3-8 Dividing by Decimals

Look Back44

Use compatible numbers to estimate the quotient.

191.1 ÷ 10.5 190 ÷ 10 = 19

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

Course 1

3-8 Dividing by Decimals

$3.36