holt ca course 1 4-8 dividing decimals extension of ns2.3 solve addition, subtraction,...
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Holt CA Course 1
4-8 Dividing Decimals
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
Holt CA Course 1
4-8 Dividing Decimals
You can use a grid to model 0.6 0.3. Circle groupsof 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 withoutchanging 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
Divide.
Example 1A: Dividing Decimals by Decimals
8.28 ÷ 4.6
) 82.8461.
46–36 8
–36 8
Multiply both numbers by 10 to make the divisor an integer.
Divide as with whole numbers.
0
Multiply both numbers by the least power of ten that will make the divisor an integer.
Helpful Hint
8.28 ÷ 4.6
8
Holt CA Course 1
4-8 Dividing Decimals
Divide.
Example 1B: Dividing Decimals by Decimals
18.48 ÷ (–1.75)
18.48 ÷ (–1.75) Multiply both numbers by 100 to make the divisor an integer.
)175 1848 . 00 Use zeros as placeholders.Divide as with whole numbers.
1
–17598 0
0.5
–87 510 50
–10 50
0
18.48 ÷ (–1.75) = –10.56
6
The signs are different.
Holt CA Course 1
4-8 Dividing Decimals
Divide. Estimate to check whether each answer is reasonable.
Example 2A: Dividing Integers by Decimals
4 ÷ 1.25
4.00 ÷ 1.25 Multiply both numbers by 100.
)125 400 .0 Use zero as a placeholder.3
–37525 0
–25 0
0
Divide as with whole numbers.
Estimate4 ÷ 1 = 4 The answer is reasonable.
. 2
Holt CA Course 1
4-8 Dividing Decimals
Divide. Estimate to check whether each answer is reasonable.
Example 2B: Dividing Integers by Decimals
–24 ÷ (–2.5)
–24.0 ÷ (–2.5) Multiply both numbers by 10.
)25 2409
– 22515
.
.0
0
6
– 15 00
Estimate–24 ÷ (–3) = 8 The answer is reasonable.
Divide as with whole numbers.
–24 ÷ (–2.5) = 9.6 The signs are the same.
Holt CA Course 1
4-8 Dividing Decimals
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?
Example 3: Transportation Application
229.25 ÷ 32.75 Multiply both numbers by 100 to make the divisor an integer.
)3,275 22,925 Divide as with whole numbers.7
–22,9250
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
) 64.5 51
5–14
–10
6.45 ÷ 0.5
2
4 5
.9
–4 50
Multiply both numbers by 10 to make the divisor an integer.
Divide as with whole numbers.
Holt CA Course 1
4-8 Dividing Decimals
Divide. Estimate to check whether each answer is Reasonable.
Check It Out! Example 2B
–22 ÷ (–2.5)
–22.0 ÷ (–2.5) Multiply both numbers by 10.
)25 2208
–20020
.
.0
0
8
–20 00
Estimate–21 ÷ (–3) = 7 The answer is reasonable.
Divide as with whole numbers.
Holt CA Course 1
4-8 Dividing DecimalsCheck 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.
)125 3500Divide as with whole numbers.2
–250100
8
0–1000
0
The gas mileage was 28 miles per gallon.
To calculate miles per gallon, divide the number of miles driven by the number of gallons of gas used.
Helpful Hint