Dividing Decimals by Decimals Divisor Quotient Remember! 0.15 0.75 5 Dividend Dividing Decimals by...

Module 1: DECIMALS

Lesson 10: Dividing Decimals by Decimals

Name: ___________________________________ Date: ____________

Dividing Decimals by Decimals

Divisor

Quotient

Remember!

0.150.755

Dividend


To divide decimals, first write the divisor as a whole number.

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

Remember!


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


Example: Dividing a Decimal by a Decimal

Find the quotient.

5.2 ÷ 1.3

1.3 5.2 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. 13 52

4

–520

5.2 ÷ 1.3 = 4


Example: 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

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

36 6,130.000


Example - Continued

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

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.


Check It Out

Find the quotient.

51.2 ÷ 0.25

0.25 51.2 25 5120.00204.8


Example: 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?

1 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.


2 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.

Solve3

First estimate the answer. You can use compatible numbers.

216.3 ÷ 10.5 200 ÷ 10 = 20


The York family averaged 20.6 miles per gallon.

105 2163.0-210

2

63 -0630

-630

0

0

.6

Solve Continued3

10.5 216.3Multiply 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.


Look Back4

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

Check It Out: Example 2

After driving 154.7 miles, the Changs filled up with 8.5 gallons of gas. On average, how many miles did they drive per gallon of gas?

1 Understand the Problem

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

List the important information:

They drove 154.7 miles. They used 8.5 gallons of gas.

2 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.

Solve3

8.5 154.7

The Chang family averaged 18.2 miles per gallon.

Look Back4

Use compatible numbers to estimate the quotient.

154.7 ÷ 8.5 → 160 ÷ 8 = 20

The answer is reasonable because 18.2 is close to the estimate of 20.


1. Identify the quotient.

72 0.9

A. 70

B. 79

C. 80

D. 90

Student Response Systems


2. Identify the quotient.

36.12 4.2

A. 8.6

B. 8.8

C. 9.5

D. 9.6



5. Dee bought 5 cups of iced tea for $4.85. What was the cost per cup?

A. $0.66

B. $0.69

C. $0.95

D. $0.97



Dividing Decimals by Decimals Divisor Quotient Remember! 0.15 0.75 5 Dividend Dividing Decimals by...

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