This document provides a lesson on dividing decimals. It includes examples of dividing decimals by decimals through multiplying the divisor and dividend by powers of ten to move the decimals. It also includes word problems involving dividing decimals to find averages and unit rates. The lesson concludes with a quiz to assess understanding of dividing decimals.

1. 3-7 Dividing by Decimals
Warm Up
Problem of the Day
Lesson Presentation
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2. 3-7 Dividing by Decimals
Warm Up
Divide.
1. 4.8 ÷ 2 2.4
2. 16.1 ÷ 7 2.3
3. 0.36 ÷ 3 0.12
4. 25.28 ÷ 4 6.32
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3. 3-7 Dividing by Decimals
Problem of the Day
In the following magic square, 3.375 is
the product of the numbers in every
row, column, and diagonal. Fill in the
missing numbers.
4.5 0.25 3
1 1.5 2.25
0.75 9 0.5
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4. 3-7 Dividing by Decimals
Learn to divide whole numbers and
decimals by decimals.
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5. 3-7 Dividing by Decimals
Helpful Hint
Multiplying the divisor and the dividend by the
same number does not change the quotient.
42 ÷ 6 = 7
×10 × 10
420 ÷ 60 = 7
× 10 × 10
4,200 ÷ 600 = 7
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6. 3-7 Dividing by Decimals
Additional Example 1A: Dividing a Decimal by a
Decimal
Find the quotient.
5.2 ÷ 1.3
Multiply the divisor and dividend by
1.3 5.2
the same power of ten.
4 There is one decimal place in the
13 52 divisor. Multiply by 101, or 10.
–52
0 Think: 1.3 x 10 = 13 5.2 x 10 = 52
Divide.
5.2 ÷ 1.3 = 4
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7. 3-7 Dividing by Decimals
Additional Example 1B: Dividing a Decimal by a
Decimal
61.3 ÷ 0.36
Make the divisor a whole number
0.36 61.30 by multiplying the divisor and
dividend by 102, or 100.
Think: 0.36 x 100 = 36
36 6,130.000 61.3 x 100 = 6,130
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8. 3-7 Dividing by Decimals
Additional Example 1B Continued
1 70.2 77
36 6,130.000
-36 Place the decimal point in the
253 quotient. Divide.
-252
10
-0 When a repeating pattern
100 occurs, show three dots or
-72
draw a bar over the repeating
280
part of the quotient.
-252
280 __
-252 61.3 ÷ 0.36 = 170.27
28
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9. 3-7 Dividing by Decimals
Check It Out: Example 1A
Find the quotient.
6.6 ÷ 1.1
Multiply the divisor and dividend by
1.1 6.6
the same power of ten.
6 There is one decimal place in the
11 66 1
divisor. Multiply by 10 , or 10.
-66
0 Think: 1.1 x 10 = 11 6.6 x 10 = 66
Divide.
6.6 ÷ 1.1 = 6
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10. 3-7 Dividing by Decimals
Check It Out: Example 1B
51.2 ÷ 0.24
Make the divisor a whole number
0.24 51.2 0 by multiplying the divisor and
dividend by 102, or 100.
Think: 0.24 x 100 = 24
24 5120.00 51.2 x 100 = 5,120
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11. 3-7 Dividing by Decimals
Check It Out: Example 1B Continued
2 13.3 3
24 5,120.00
-48 Divide.
32
-24
80
-72 When a repeating pattern
80 occurs, show three dots or
-72
draw a bar over the repeating
80
part of the quotient.
-72
8 __
51.2 ÷ 0.24 = 213.33
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12. 3-7 Dividing by Decimals
Additional Example 2: Problem Solving
Application
After driving 216.3 miles, the York’s filled
up with 10.5 gallons of gas. On average,
how many miles did they drive per gallon
of gas?
1 Understand the Problem
The answer will be the average number of
miles per gallon.
List the important information:
They drove 216.3 miles. They used 10.5
gallons of gas.
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13. 3-7 Dividing by Decimals
2 Make a Plan
Solve a simpler problem by replacing the
decimals in the problem with whole numbers.
If they drove 10 miles using 2 gallons of gas,
they averaged 5 miles per gallon. You need to
divide miles by gallons to solve the problem.
3 Solve
First estimate the answer. You can use
compatible numbers.
216.3 ÷ 10.5 200 ÷ 10 = 20
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14. 3-7 Dividing by Decimals
3 Solve Continued
Multiply the divisor and dividend
10.5 216.3 by 10. Think: 10.5 x 10 = 105
216.3 x 10 = 2,163
2 0.6
105 2163.0 Place the decimal point in the
-210 quotient. Divide.
63
-0
630
-630
0
The York family averaged 20.6 miles per gallon.
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15. 3-7 Dividing by Decimals
4 Look Back
The answer is reasonable since 20.6 is close
to the estimate of 20.
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16. 3-7 Dividing by Decimals
Check It Out: Example 2
After driving 191.1 miles, the Chang’s
filled up with 10.5 gallons of gas. On
average, how many miles did they drive
per gallon of gas?
1 Understand the Problem
The answer will be the average number of
miles per gallon.
List the important information:
They drove 191.1 miles. They used 10.5
gallons of gas.
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17. 3-7 Dividing by Decimals
2 Make a Plan
Solve a simpler problem by replacing the
decimals in the problem with whole numbers.
If they drove 10 miles using 2 gallons of gas,
they averaged 5 miles per gallon. You need to
divide miles by gallons to solve the problem.
3 Solve
First estimate the answer. You can use
compatible numbers.
191.1 ÷ 10.5 190 ÷ 10 = 19
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18. 3-7 Dividing by Decimals
3 Solve Continued
Multiply the divisor and dividend
10.5 191.1 by 10. Think: 10.5 x 10 = 105
191.1 x 10 = 1,911
1 8.2
Place the decimal point in the
105 1911.0
quotient. Divide.
-105
861
-840
210
-210
0
The Chang family averaged 18.2 miles per gallon.
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19. 3-7 Dividing by Decimals
4 Look Back
The answer is reasonable since 18.2 is close
to the estimate of 19.
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20. 3-7 Dividing by Decimals
Insert Lesson Title Here
Lesson Quiz
Find each quotient.
1. 49 ÷ 0.7 70
2. 21.63 ÷ 2.1 10.3
3. 38.43 ÷ 6.1 6.3
4. 16.9 ÷ 5.2 3.25
5. John spent $13.44 renting 4 videos for the
weekend. What was the cost per video?
$3.36
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