1. Learn to divide decimals.

2. When you divide two numbers, you can multiply
both numbers by the same power of ten without
changing the final answer.
Multiply both 0.6 and 0.3 by 10:
0.6 · 10 = 6
and
0.3 · 10 = 3
0.6 ÷ 0.3 = 2
and
6 ÷ 3 = 2
By multiplying both numbers by the same power of ten, you can make the divisor an integer. Dividing by an integer is much easier than dividing by a decimal.

3. When diving, the divisor must be a whole number.
To make the divisor a whole number, multiply by a power of ten to “move” the decimal point.
Remember: What you do to one number you must do to the other.

4. Additional Example 1A: Dividing Decimals by Decimals
Divide.
8.28 ÷ 4.6
Multiply both numbers by 10 to make the divisor an integer.
8.28 ÷ 4.6
= 82.8 ÷ 46 1. 8 46 )
82.8
Divide as with whole numbers. – 46 36 8
–36 8
Multiply both numbers by the least power of ten that will make the divisor an integer.
Helpful Hint

5. Additional Example 1B: Dividing Decimals by Decimals
Divide.
18.48 ÷ (–1.75)
18.48 ÷ (–1.75) =
1848 ÷ 175
Multiply both numbers by 100 to make the divisor an integer. 1 .5 6
Use zeros as placeholders
175 )
1848 . 00
–175
Divide as with whole
numbers. 9 8
–87 5
10 50
–10 50
18.48 ÷ (–1.75) = –10.56
The signs are different.

6. Check It Out: Example 1A Divide. 6.45 ÷ 0.5 6.45 ÷ 0.5 = 64.5 ÷ 5
Multiply both numbers by 10 to make the divisor an integer. 1 2 . 9 5 )
64.5
Divide as with whole numbers. – 5 14
–10 4 5
–4 5

7. Check It Out: Example 1B Divide. 16.48 ÷ (–2.06) 16.48 ÷ (–2.06) =
1648 ÷ (206)
Multiply both numbers by 100 to make the divisor an integer. 8
206 )
1,648
–1 648
Divide as with whole numbers.
16.48 ÷ (–2.06) = –8
The signs are different.

8. Additional Example 2A: Dividing Integers by Decimals
Divide. Estimate to check whether each answer is reasonable.
4 ÷ 1.25
4.00 ÷ 1.25 =
400 ÷ 125
Multiply both numbers by 100. 3 . 2
125 )
400 .0
Use zero as a placeholder.
–375
Divide as with whole numbers.
25 0
–25 0
Estimate
4 ÷ 1 = 4
The answer is reasonable.

9. Additional Example 2B: Dividing Integers by Decimals
Divide. Estimate to check whether each answer is Reasonable.
–24 ÷ (–2.5)
–24.0 ÷ (–2.5) =
–240 ÷ (–25)
Multiply both numbers by 10. 9 . 6 25 )
240 .
Divide as with whole numbers.
– 225 15
– 15 0
Estimate
–24 ÷ (–3) = 8
The answer is reasonable.

10. Divide. Estimate to check whether each answer is reasonable.
Check It Out: Example 2A
Divide. Estimate to check whether each answer is reasonable.
6 ÷ 1.25
6.00 ÷ 1.25 =
600 ÷ 125
Multiply both numbers by 100. 4 . 8
125 )
600 .0
Use zero as a placeholder.
–500
Divide as with whole numbers.
100 0
–100 0
Estimate
6 ÷ 1 = 6
The answer is reasonable.

11. Divide. Estimate to check whether each answer is Reasonable.
Check It Out: Example 2B
Divide. Estimate to check whether each answer is Reasonable.
–22 ÷ (–2.5)
–22.0 ÷ (–2.5) =
–220 ÷ (–25)
Multiply both numbers by 10. 8 . 8 25 )
220 .
Divide as with whole numbers.
–200 20
–20 0
Estimate
–21 ÷ (–3) = 7
The answer is reasonable.

12. Additional Example 3: Transportation Application
Eric paid $ to rent a car. The fee to rent the car was $32.75 per day. For how long did Eric rent the car?
÷ =
22,925 ÷ 3,275
Multiply both numbers
by 100. 7 )
3,275
22,975
Divide as with
whole numbers.
–22,975
Eric rented the car for 7 days.

13. Check It Out: Example 3
Jace took a trip in which he drove 350 miles. During the trip his truck used 12.5 gallons of gas. What was his truck’s gas mileage?
350.0 ÷ 12.5 =
3500 ÷ 125
Multiply both numbers by 10. 2 8
Divide as with whole numbers.
125 )
3500
–250
To calculate miles per gallon, divide the number of miles driven by the number of gallons of gas used.
Helpful Hint
100
–1000
Jace’s truck’s gas mileage was 28 miles per gallon.

14. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

15. Lesson Quiz
Divide. Estimate to check whether each answer is reasonable.
÷ 0.04
2. –9.72 ÷ 2.7
÷ 1.6
÷ 3.25
5. Jordan used gallons of gas to drive his van miles. How many miles did Jordan get per gallon?
1,995
–3.6
11.8 6 18

16. Lesson Quiz for Student Response Systems
1. Divide.
87.3 ÷ 0.09
A. 873
B. 970
C. 977
D. 1230

17. Lesson Quiz for Student Response Systems
2. Divide.
–14.72 ÷ (3.2)
A. –4.6
B. –5
C. –5.2
D. –5.6

18. Lesson Quiz for Student Response Systems
3. Divide.
19.98 ÷ 1.8
A. 11.4
B. 11.3
C. 11.2
D. 11.1

19. Lesson Quiz for Student Response Systems
4. Divide.
17.15 ÷ 2.45
A. 7
B. 8
C. 9
D. 10

20. Lesson Quiz for Student Response Systems
5. Chris drives at an average speed of miles per hour. How long does it take for him to travel a distance of miles?
A. 6 hours
B. 7 hours
C. 8 hours
D. 9 hours