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Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Divide. 1. 4.8 ÷ 2 2. 16.1 ÷ 7 3. 0.36 ÷ 3 4. 25.28 ÷ 4. 2.4. 2.3. 0.12. 6.32. Problem of the Day

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Warm Up

Problem of the Day

Lesson Presentation

Lesson Quizzes

Warm Up

Divide.

1. 4.8 ÷ 2

2. 16.1 ÷ 7

3. 0.36 ÷ 3

4. 25.28 ÷ 4

2.4

2.3

0.12

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.

3

1

1.5

2.25

0.75

9

Helpful Hint

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

Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10.

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

Divide as with whole numbers.

Additional Example 1A: Dividing a Decimal by a Decimal

Find the quotient.

5.2 ÷ 1.3

1.3 5.2

4

13 52

–52

0

5.2 ÷ 1.3 = 4

Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.

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

36 6,130.000

Additional Example 1B: Dividing a Decimal by a Decimal

61.3 ÷ 0.36

0.36 61.30

Place the decimal point in the quotient. Divide as with whole numbers.

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

__

61.3 ÷ 0.36 = 170.27

Additional Example 1B Continued

0

.2

1

7

7

7

36 6,130.000

-36

253

-252

10

-0

100

-72

280

-252

280

-252

28

Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10.

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

Divide as with whole numbers.

Check It Out: Example 1A

Find the quotient.

6.6 ÷ 1.1

1.1 6.6

6

11 66

-66

0

6.6 ÷ 1.1 = 6

Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.

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

24 5120.00

Check It Out: Example 1B

51.2 ÷ 0.24

0.24 51.2

0

Place the decimal point in the quotient. Divide as with whole numbers.

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

__

51.2 ÷ 0.24 = 213.3

Check It Out: Example 1B Continued

2

.3

1

3

3

24 5,120.00

-48

32

-24

80

-72

80

-72

80

-72

8

1

Understand the Problem

Additional Example 2: Problem Solving Application

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

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.

2

Make a Plan

3

Solve

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.

First estimate the answer. You can use compatible numbers.

216.3 ÷ 10.5 200 ÷ 10 = 20

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 as with whole numbers.

Solve Continued

10.5 216.3

2

.6

0

105 2163.0

-210

63

-0

630

-630

0

The York family averaged 20.6 miles per gallon.

4

Look Back

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

1

Understand the Problem

Check It Out: Example 2

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

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.

2

Make a Plan

3

Solve

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.

First estimate the answer. You can use compatible numbers.

191.1 ÷ 10.5 190 ÷ 10 = 19

3

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 as with whole numbers.

Solve Continued

10.5 191.1

1

.2

8

105 1911.0

-105

861

-840

210

-210

0

The Chang family averaged 18.2 miles per gallon.

4

Look Back

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