1. Standards California Extension of NS2.3
Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
California
Standards

2. You can use a grid to model 0.6  0.3. Circle groups
of 0.3 and count the number of groups.
There are 2 groups of 0.3 in 0.6, so 0.6 ÷ 0.3 = 2.

3. 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.

4. 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 1. 8
Divide as with whole numbers. 46 )
82.8 – 46 36 8
–36 8
Multiply both numbers by the least power of ten that will make the divisor an integer.
Helpful Hint

5. Example 1B: Dividing Decimals by Decimals
Divide.
18.48 ÷ (–1.75)
18.48 ÷ (–1.75)
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 1B Divide. 16.48 ÷ (–2.06) 16.48 ÷ (–2.06)
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.

7. Example 2A: Dividing Integers by Decimals
Divide. Estimate to check whether each answer is reasonable.
4 ÷ 1.25
4.00 ÷ 1.25
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.

8. Example 2B: Dividing Integers by Decimals
Divide. Estimate to check whether each answer is reasonable.
–24 ÷ (–2.5)
–24.0 ÷ (–2.5)
Multiply both numbers by 10. 9 . 6 ) 25
240 .
Divide as with whole numbers.
– 225 15
– 15 0
–24 ÷ (–2.5) = 9.6
The signs are the same.
Estimate
–24 ÷ (–3) = 8
The answer is reasonable.

9. 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
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.

10. 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?
÷ 32.75
Multiply both numbers by 100 to make the divisor an integer. 7
3,275 )
22,925
Divide as with whole numbers.
–22,925
Eric rented the car for 7 days.

11. Check It Out! Example 1A Divide. 6.45 ÷ 0.5 6.45 ÷ 0.5
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

12. 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)
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.

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
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
The gas mileage was 28 miles per gallon.