3-7 Dividing by Decimals
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpDivide.
1. 4.8 ÷ 2
2. 16.1 ÷ 7
3. 0.36 ÷ 3
4. 25.28 ÷ 4
2.42.3
0.12
Course 1
3-7 Dividing by Decimals
6.32
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.
Course 1
3-7 Dividing by Decimals
4.5 0.25
0.5
3
1 1.5 2.25
0.75 9
Learn to divide whole numbers and decimals by decimals.
Course 1
3-7 Dividing by Decimals
TEKS 6.11.B: Underlying processes and mathematical tools: use a problem-solving model ...
Course 1
3-7 Dividing by Decimals
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
Helpful Hint
Course 1
3-7 Dividing by Decimals
Additional Example 1A: Dividing a Decimal by a Decimal
Find the quotient.
5.2 ÷ 1.3
1.3 5.2 Multiply the divisor and dividend by the same power of ten.
There is one decimal place in the divisor. Multiply by 101, or 10.
Think: 1.3 x 10 = 13 5.2 x 10 = 52
Divide.
13 524
–520
5.2 ÷ 1.3 = 4
Course 1
3-7 Dividing by Decimals
Additional Example 1B: Dividing a Decimal by a Decimal
61.3 ÷ 0.36
0.36 61.30
Think: 0.36 x 100 = 36 61.3 x 100 = 6,130
Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.
36 6,130.000
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3-7 Dividing by Decimals
Additional Example 1B Continued
Place the decimal point in the quotient. Divide.
36 6,130.0007
-36
1
253-252
10 -0
0
100
.2
-72
-252
7
280-252
280
7
28 61.3 ÷ 0.36 = 170.27
__
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.
Course 1
3-7 Dividing by Decimals
Check It Out: Example 1A
Find the quotient.
6.6 ÷ 1.1
1.1 6.6 Multiply the divisor and dividend by the same power of ten.
There is one decimal place in the divisor. Multiply by 10 , or 10.
Think: 1.1 x 10 = 11 6.6 x 10 = 66
1
Divide.
11 666
-660
6.6 ÷ 1.1 = 6
Course 1
3-7 Dividing by Decimals
Check It Out: Example 1B
51.2 ÷ 0.24
0.24 51.2
Think: 0.24 x 100 = 24 51.2 x 100 = 5,120
Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.
24 5120.00
0
Course 1
3-7 Dividing by Decimals
Check It Out: Example 1B Continued
Divide. 24 5,120.00
1
-48
2
32 -24
80-72
3
80
.3
-72
-72 80
3
51.2 ÷ 0.24 = 213.33__
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.
8
Course 1
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?
11 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.
Course 1
3-7 Dividing by Decimals
22 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.
Solve33
First estimate the answer. You can use compatible numbers.
216.3 ÷ 10.5 200 ÷ 10 = 20
Course 1
3-7 Dividing by Decimals
The York family averaged 20.6 miles per gallon.
105 2163.0-210
2
63 -0630
-630
0
0
.6
Solve Continued33
10.5 216.3Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 216.3 x 10 = 2,163
Place the decimal point in the quotient. Divide.
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3-7 Dividing by Decimals
Look Back44
The answer is reasonable since 20.6 is close to the estimate of 20.
Course 1
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?
11 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.
Course 1
3-7 Dividing by Decimals
22 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.
Solve33
First estimate the answer. You can use compatible numbers.
191.1 ÷ 10.5 190 ÷ 10 = 19
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3-7 Dividing by Decimals
105 1911.0-105
1
861-840
210-210
8
0
.2
The Chang family averaged 18.2 miles per gallon.
Solve Continued33
10.5 191.1Multiply the divisor and dividend by 10. Think: 10.5 x 10 = 105 191.1 x 10 = 1,911
Place the decimal point in the quotient. Divide.
Course 1
3-7 Dividing by Decimals
Look Back44
The answer is reasonable since 18.2 is close to the estimate of 19.
Lesson Quiz
Find each quotient.
1. 49 ÷ 0.7
2. 21.63 ÷ 2.1
3. 38.43 ÷ 6.1
4. 16.9 ÷ 5.2
5. John spent $13.44 renting 4 videos for the
weekend. What was the cost per video?
10.3
70
Insert Lesson Title Here
6.3
3.25
Course 1
3-7 Dividing by Decimals
$3.36