Transcript Divide as with whole numbers.

4-8 Dividing Decimals
California
Standards
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.
Holt CA Course 1
4-8 Dividing Decimals
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.
Holt CA Course 1
4-8 Dividing Decimals
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.
Holt CA Course 1
4-8 Dividing Decimals
Example 1A: Dividing Decimals by Decimals
Divide.
8.28 ÷ 4.6
8.28 ÷ 4.6
1.8
46) 82.8
– 46
36 8
–36 8
Multiply both numbers by 10 to
make the divisor an integer.
Divide as with whole numbers.
0
Helpful Hint
Multiply both numbers by the least power of ten that will
make the divisor an integer.
Holt CA Course 1
4-8 Dividing Decimals
Example 1B: Dividing Decimals by Decimals
Divide.
18.48 ÷ (–1.75)
18.48 ÷ (–1.75)
1 0.5 6
175 ) 1848 . 00
–175
98 0
–87 5
10 50
–10 50
0
18.48 ÷ (–1.75) = –10.56
Holt CA Course 1
Multiply both numbers by 100
to make the divisor an integer.
Use zeros as placeholders.
Divide as with whole
numbers.
The signs are different.
4-8 Dividing Decimals
Example 2A: Dividing Integers by Decimals
Divide. Estimate to check whether each
answer is reasonable.
4 ÷ 1.25
4.00 ÷ 1.25
3. 2
125 )400 .0
–375
25 0
–25 0
0
Estimate
4÷1=4
Holt CA Course 1
Multiply both numbers by 100.
Use zero as a placeholder.
Divide as with whole numbers.
The answer is reasonable.
4-8 Dividing Decimals
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
Divide as with whole numbers.
25 ) 240 .0
– 225
15 0
– 15 0
0
–24 ÷ (–2.5) = 9.6
The signs are the same.
Estimate
–24 ÷ (–3) = 8
The answer is reasonable.
Holt CA Course 1
4-8 Dividing Decimals
Example 3: Transportation Application
Eric paid $229.25 to rent a car. The fee to rent
the car was $32.75 per day. For how long did
Eric rent the car?
229.25 ÷ 32.75
7
3,275 ) 22,925
–22,925
0
Multiply both numbers by 100 to
make the divisor an integer.
Divide as with whole numbers.
Eric rented the car for 7 days.
Holt CA Course 1
4-8 Dividing Decimals
Check It Out! Example 1A
Divide.
6.45 ÷ 0.5
6.45 ÷ 0.5
12 . 9
5 ) 64.5
–5
14
–10
45
–4 5
0
Holt CA Course 1
Multiply both numbers by 10 to
make the divisor an integer.
Divide as with whole numbers.
4-8 Dividing Decimals
Check It Out! Example 2B
Divide. Estimate to check whether each
answer is Reasonable.
–22 ÷ (–2.5)
–22.0 ÷ (–2.5)
8. 8
25 ) 220 .0
–200
20 0
–20 0
0
Estimate
–21 ÷ (–3) = 7
Holt CA Course 1
Multiply both numbers by 10.
Divide as with whole numbers.
The answer is reasonable.
4-8 Dividing Decimals
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
28
125) 3500
–250
1000
–1000
0
Multiply both numbers by 10.
Divide as with whole numbers.
Helpful Hint
To calculate miles per gallon, divide the
number of miles driven by the number
of gallons of gas used.
The gas mileage was 28 miles per gallon.
Holt CA Course 1