Download document 8461748

3-8 Dividing by Decimals
Warm Up
Problem of the Day
Lesson Presentation
Course 1
3-8 Dividing by Decimals
Warm Up
Divide.
1. 4.8 ÷ 2
2. 16.1 ÷ 7
3. 0.36 ÷ 3
2.4
2.3
4. 25.28 ÷ 4
0.12
6.32
5. 6.25 ÷ 5
1.25
Course 1
3-8 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.
Course 1
4.5
0.25
3
1
1.5
2.25
0.75
9
0.5
3-8 Dividing by Decimals
Learn to divide whole numbers and
decimals by decimals.
Course 1
3-8 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
Course 1
3-8 Dividing by Decimals
Additional Example 1A: Dividing a Decimal by a
Decimal
Find each quotient.
A. 5.2 ÷ 1.3
1.3 5.2
4
13 52
–52
0
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
Divide.
Course 1
5.2 x 10 = 52
3-8 Dividing by Decimals
Additional Example 1B: Dividing a Decimal by a
Decimal
B. 61.3 ÷ 0.36
0.36 61.3
36 6,130.000
Course 1
Make the divisor a whole number
by multiplying the divisor and
dividend by 102, or 100.
Think: 0.36 x 100 = 36
61.3 x 100 = 6,130
3-8 Dividing by Decimals
Additional Example 1B Continued
1 70.2 77
36 6,130.000
-36
253
252
10
-0
100
-72
280
-252
280
-252
28
Course 1
Divide.
__
170.277… = 170.27
When a repeating pattern
occurs, show three dots or
draw a bar over the repeating
part of the quotient.
3-8 Dividing by Decimals
Try This: Example 1A
Find each quotient.
A. 4.8 ÷ 1.2
1.2 4.8
4
12 48
-48
0
Multiply the divisor and dividend by
the same power of ten.
There is one decimal place in the
1
divisor. Multiply by 10 , or 10.
Think: 1.2 x 10 = 12
Divide.
Course 1
4.8 x 10 = 48
3-8 Dividing by Decimals
Try This: Example 1B
B. 51.2 ÷ 0.24
0.24 51.2
24 5120.000
Course 1
Make the divisor a whole number
by multiplying the divisor and
dividend by 102, or 100.
Think: 0.24 x 100 = 24
51.2 x 100 = 5,120
3-8 Dividing by Decimals
Try This: Example 1B Continued
2 13.3 3
24 5,120.00
-48
32
24
80
-72
80
-72
80
-72
8
Course 1
Divide.
__
213.33… = 213.33
When a repeating pattern
occurs, show three dots or
draw a bar over the repeating
part of the quotient.
3-8 Dividing by Decimals
Additional Example 2: Problem Solving Application
After driving 216.3 miles, the Yorks used 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.
Course 1
3-8 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
Multiply the divisor and dividend by
10. Think: 10.5 x 10 = 105
10.5 216.3 216.3 x 10 = 2,163
Place the decimal point in the
quotient. Divide.
The York family averaged 20.6 miles per gallon.
Course 1
3-8 Dividing by Decimals
4
Look Back
Use compatible numbers to estimate the
quotient.
216.3 ÷ 10.5
220 ÷ 11 =20
The answer is reasonable since 20.6 is close
to the estimate of 20.
Course 1
3-8 Dividing by Decimals
Try This: Example 2
After driving 191.1 miles, the Changs used 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.
Course 1
3-8 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
Multiply the divisor and dividend by
10. Think: 10.5 x 10 = 105
10.5 191.1 191.1 x 10 = 1,911
Place the decimal point in the
quotient. Divide.
The York family averaged 18.2 miles per gallon.
Course 1
3-8 Dividing by Decimals
4
Look Back
Use compatible numbers to estimate the
quotient.
191.1 ÷ 10.5
190 ÷ 10 = 19
The answer is reasonable since 18.2 is close
to the estimate of 19.
Course 1
3-8 Dividing
Insert Lesson
by Decimals
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
Course 1