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3-3 Dividing Decimals
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
3-3 Dividing Decimals
Warm UpDivide.
1. 24.5 ÷ 7
2. 50.4 ÷ 6
3. 19.2 ÷ (–2)
4. 128.1 ÷ 21
3.5
8.4
–9.6
6.1
3-3 Dividing Decimals
Problem of the Day
Place 20 pennies in a row on a table. Replace every fourth coin with a nickel. Now replace every third coin with a dime. Then replace every sixth coin with a quarter. What is the value of the 20 coins now on the table?
$1.35
3-3 Dividing Decimals
Learn to divide decimals.
3-3 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.
3-3 Dividing Decimals
Divide.
Additional 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
= 82.8 ÷ 46
3-3 Dividing Decimals
Divide.
Additional Example 1B: Dividing Decimals by Decimals
18.48 ÷ (–1.75)
18.48 ÷ (–1.75) = 1848 ÷ 175 Multiply both numbers by 100 to make the divisor an integer.
)175 1848 . 00 Use zeros as placeholdersDivide 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.
3-3 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.
= 64.5 ÷ 5
3-3 Dividing Decimals
Divide.
16.48 ÷ (–2.06)
16.48 ÷ (–2.06) = 1648 ÷ (206)
)1,6482068
–1 648
16.48 ÷ (–2.06) = –8
Multiply both numbers by 100 to make the divisor an integer.
Divide as with whole numbers.0
Check It Out: Example 1B
The signs are different.
3-3 Dividing Decimals
Divide. Estimate to check whether each answer is reasonable.
Additional Example 2A: Dividing Integers by Decimals
4 ÷ 1.25
4.00 ÷ 1.25 = 400 ÷ 125 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
3-3 Dividing Decimals
Divide. Estimate to check whether each answer is Reasonable.
Additional Example 2B: Dividing Integers by Decimals
–24 ÷ (–2.5)
–24.0 ÷ (–2.5) = Multiply both numbers by 10.–240 ÷ (–25)
)25 2409
– 22515
.
.0
0
6
– 15 00
Estimate–24 ÷ (–3) = 8 The answer is reasonable.
Divide as with whole numbers.
3-3 Dividing Decimals
Divide. Estimate to check whether each answer is reasonable.
Check It Out: Example 2A
6 ÷ 1.25
6.00 ÷ 1.25 = 600 ÷ 125 Multiply both numbers by 100.
)125 600 .0 Use zero as a placeholder.4
–500100 0
–100 00
Divide as with whole numbers.
Estimate6 ÷ 1 = 6 The answer is reasonable.
.8
3-3 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.–220 ÷ (–25)
)25 2208
–20020
.
.0
0
8
–20 00
Estimate–21 ÷ (–3) = 7 The answer is reasonable.
Divide as with whole numbers.
3-3 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?
Additional Example 3: Transportation Application
229.25 ÷ 32.75 = 22,925 ÷ 3,275 Multiply both numbersby 100.
)3,275 22,975 Divide as with whole numbers.
7
–22,9750
Eric rented the car for 7 days.
3-3 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 = 3500 ÷ 125 Multiply both numbers by 10.
)125 3500Divide as with whole numbers.2
–250100
8
0–1000
0
Jace’s truck’s 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
3-3 Dividing Decimals
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
3-3 Dividing Decimals
Lesson Quiz
Divide. Estimate to check whether each answer is reasonable.
1. 78.2 ÷ 0.04
2. –9.72 ÷ 2.7
3. 18.88 ÷ 1.6
4. 19.5 ÷ 3.25
5. Jordan used 32.46 gallons of gas to drive his
van 584.28 miles. How many miles did Jordan get
per gallon?
–3.6
1,995
11.8
6
18
3-3 Dividing Decimals
1. Divide.
87.3 ÷ 0.09
A. 873
B. 970
C. 977
D. 1230
Lesson Quiz for Student Response Systems
3-3 Dividing Decimals
2. Divide.
–14.72 ÷ (3.2)
A. –4.6
B. –5
C. –5.2
D. –5.6
Lesson Quiz for Student Response Systems
3-3 Dividing Decimals
3. Divide.
19.98 ÷ 1.8
A. 11.4
B. 11.3
C. 11.2
D. 11.1
Lesson Quiz for Student Response Systems
3-3 Dividing Decimals
4. Divide.
17.15 ÷ 2.45
A. 7
B. 8
C. 9
D. 10
Lesson Quiz for Student Response Systems
3-3 Dividing Decimals
5. Chris drives at an average speed of 55.45 miles per hour. How long does it take for him to travel a distance of 388.15 miles?
A. 6 hours
B. 7 hours
C. 8 hours
D. 9 hours
Lesson Quiz for Student Response Systems
