1. 3-7 Dividing by Decimals Warm Up Problem of the Day
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. 3-7 Dividing by Decimals Warm Up Divide. 1. 4.8 ÷ 2 2. 16.1 ÷ 7
Course 1
3-7
Dividing by Decimals
Warm Up
Divide.
÷ 2
÷ 7
÷ 3
÷ 4
2.4
2.3
0.12
6.32

3. 3-7 Dividing by Decimals Problem of the Day
Course 1
3-7
Dividing by Decimals
Problem of the Day
In the following magic square, is the product of the numbers in every row, column, and diagonal. Fill in the missing numbers.
4.5
0.25
0.5 3 1
1.5
2.25
0.75 9

4. Course 1
3-7
Dividing by Decimals
Learn to divide whole numbers and decimals by decimals.

5. 3-7 Dividing by Decimals Helpful Hint
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
420 ÷ 60 = 7
  10
4,200 ÷ 600 = 7
Helpful Hint

6. Additional Example 1A: Dividing a Decimal by a Decimal
Course 1
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 the same power of ten. 4
There is one decimal place in the divisor. Multiply by 101, or 10.
Think: 1.3 x 10 = x 10 = 52
13 52
–52
Divide.
5.2 ÷ 1.3 = 4

7. Additional Example 1B: Dividing a Decimal by a Decimal
Course 1
3-7
Dividing by Decimals
Additional Example 1B: Dividing a Decimal by a Decimal
61.3 ÷ 0.36
Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.
Think: 0.36 x 100 = x 100 = 6,130
36 6,

8. Additional Example 1B Continued
Course 1
3-7
Dividing by Decimals
Additional Example 1B Continued 1 7 .2 7 7
36 6,
Place the decimal point in the quotient. Divide.
-36
253
-252 10 -0
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient.
100
-72
280
-252
280
61.3 ÷ 0.36 = __
-252 28

9. 3-7 Dividing by Decimals Check It Out: Example 1A Find the quotient.
Course 1
3-7
Dividing by Decimals
Check It Out: Example 1A
Find the quotient.
6.6 ÷ 1.1
Multiply the divisor and dividend by the same power of ten. 6
There is one decimal place in the divisor. Multiply by 10 , or 10.
Think: 1.1 x 10 = x 10 = 66 1
11 66
-66
Divide.
6.6 ÷ 1.1 = 6

10. 3-7 Dividing by Decimals Check It Out: Example 1B 51.2 ÷ 0.24
Course 1
3-7
Dividing by Decimals
Check It Out: Example 1B
51.2 ÷ 0.24
Make the divisor a whole number by multiplying the divisor and dividend by 102, or 100.
Think: 0.24 x 100 = x 100 = 5,120

11. Check It Out: Example 1B Continued
Course 1
3-7
Dividing by Decimals
Check It Out: Example 1B Continued 2 1 3 .3 3
24 5,120.00
Divide.
-48 32
-24 80
-72
When a repeating pattern occurs, show three dots or draw a bar over the repeating part of the quotient. 80
-72 80
-72 8
51.2 ÷ 0.24 = __

12. Understand the Problem
Course 1
3-7
Dividing by Decimals
Additional Example 2: Problem Solving Application
After driving 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 miles. They used 10.5 gallons of gas.

13. 3-7 Dividing by Decimals 2 Make a Plan
Course 1
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.
Solve 3
First estimate the answer. You can use compatible numbers.
216.3 ÷ ÷ 10 = 20

14. 3-7 Dividing by Decimals 3 Solve Continued
Course 1
3-7
Dividing by Decimals 3
Solve Continued
Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 2,163 2 .6
Place the decimal point in the quotient. Divide.
-210 63 -0
630
-630
The York family averaged 20.6 miles per gallon.

15. 3-7 Dividing by Decimals Look Back 4
Course 1
3-7
Dividing by Decimals
Look Back 4
The answer is reasonable since 20.6 is close to the estimate of 20.

16. Understand the Problem
Course 1
3-7
Dividing by Decimals
Check It Out: Example 2
After driving 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 miles. They used 10.5 gallons of gas.

17. 3-7 Dividing by Decimals 2 Make a Plan
Course 1
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.
Solve 3
First estimate the answer. You can use compatible numbers.
191.1 ÷ ÷ 10 = 19

18. 3-7 Dividing by Decimals 3 Solve Continued
Course 1
3-7
Dividing by Decimals 3
Solve Continued
Multiply the divisor and dividend by 10. Think: 10.5 x 10 = x 10 = 1,911 1 8 .2
Place the decimal point in the quotient. Divide.
-105
861
-840
210
-210
The Chang family averaged 18.2 miles per gallon.

19. 3-7 Dividing by Decimals Look Back 4
Course 1
3-7
Dividing by Decimals
Look Back 4
The answer is reasonable since 18.2 is close to the estimate of 19.

20. Insert Lesson Title Here
Course 1
3-7
Dividing by Decimals
Insert Lesson Title Here
Lesson Quiz
Find each quotient.
1. 49 ÷ 0.7
÷ 2.1
÷ 6.1
÷ 5.2
5. John spent $13.44 renting 4 videos for the weekend. What was the cost per video? 70
10.3
6.3
3.25
$3.36