1. Learn to divide whole numbers and decimals by decimals.

2. Multiplying the divisor and the dividend by the same number does not change the quotient.
42 ÷ 6 = 7
  10
420 ÷ 60 = 7
  10
4,200 ÷ 600 = 7
Helpful Hint

3. Additional Example 1A: Dividing a Decimal by a Decimal
Find the quotient.
5.2 ÷ 1.3
Multiply the divisor and dividend by the same power of ten. 4
There is one decimal place in the divisor. Multiply by 101, or 10.
Think: 1.3 x 10 = x 10 = 52
13 52
–52
Divide.
5.2 ÷ 1.3 = 4

4. Additional Example 1B: Dividing a Decimal by a Decimal
61.3 ÷ 0.36
Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.
Think: 0.36 x 100 = x 100 = 6,130
36 6,

5. Additional Example 1B Continued7 .2 7 7
36 6,
Place the decimal point in the quotient. Divide.
-36
253
-252 10 -0
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.
100
-72
280
-252
280
61.3 ÷ 0.36 = __
-252 28

6. Multiply the divisor and dividend by the same power of ten. 1.1 6.6
Check It Out: Example 1A
Find the quotient.
6.6 ÷ 1.1
Multiply the divisor and dividend by the same power of ten. 6
There is one decimal place in the divisor. Multiply by 10 , or 10.
Think: 1.1 x 10 = x 10 = 66 1
11 66
-66
Divide.
6.6 ÷ 1.1 = 6

7. Check It Out: Example 1B
51.2 ÷ 0.24
Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.
Think: 0.24 x 100 = x 100 = 5,120

8. Check It Out: Example 1B Continued2 1 3 .3 3
24 5,120.00
Divide.
-48 32
-24 80
-72
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 80
-72 80
-72 8
51.2 ÷ 0.24 = 213.3 __

9. Understand the Problem
Additional Example 2: Problem Solving Application
After driving miles, the York’s 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 miles. They used gallons of gas.

10. 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.
Solve 3
First estimate the answer. You can use compatible numbers.
216.3 ÷ ÷ 10 = 20

11. 3
Solve Continued
Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 2,163 2 .6
Place the decimal point in the quotient. Divide.
-210 63 -0
630
-630
The York family averaged 20.6 miles per gallon.

12. Look Back 4
The answer is reasonable since 20.6 is close to the estimate of 20.

13. Understand the Problem
Check It Out: Example 2
After driving miles, the Chang’s 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 miles. They used gallons of gas.

14. 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.
Solve 3
First estimate the answer. You can use compatible numbers.
191.1 ÷ ÷ 10 = 19

15. 3
Solve Continued
Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 1,911 1 8 .2
Place the decimal point in the quotient. Divide.
-105
861
-840
210
-210
The Chang family averaged 18.2 miles per gallon.

16. Look Back 4
The answer is reasonable since 18.2 is close to the estimate of 19.