1. Dividing by Decimals

2. Dividing by Decimals
Essential Question: How do operations with decimals compare to operations with whole numbers?

3. Sunshine State Standards
MA.6.A.1.3 Solve real-world problems involving…division of…decimals.
Also MA.6.A.1.1, MA.6.A.1.2. MA.6.A.5.3

4. Warm Up
Divide.
÷ 2
÷ 7
÷ 3
÷ 4
2.4
2.3
0.12
6.32

5. Remember!
Quotient
0.15 5
0.75
Divisor
Dividend

6. Terminating vs. Repeating Decimal
What is a terminating decimal?
What is a repeating decimal?

7. Terminating vs. Repeating Decimal
What is a terminating decimal?
What is a repeating decimal?
A terminating decimal is one that terminates or ends.

8. Terminating vs. Repeating Decimal
What is a terminating decimal?
What is a repeating decimal?
A terminating decimal is one that terminates or ends.
A repeating decimal is one that keeps going and repeats a pattern.

9. Terminating vs. Repeating Decimal
What is a terminating decimal?
What is a repeating decimal?
A terminating decimal is one that terminates or ends. 1 ÷ 8 = .125
A repeating decimal is one that keeps going and repeats a pattern.

10. Terminating vs. Repeating Decimal
What is a terminating decimal?
What is a repeating decimal?
A terminating decimal is one that terminates or ends. 1 ÷ 8 = .125
A repeating decimal is one that keeps going and repeats a pattern. _ 1 ÷ 3 = .3

11. Can you list some common repeating decimals and their matching division problem?

12. Let’s try some multiplying and dividing shortcuts:

13. Complete the table below:
Whole Number
Powers of 10
Decimal
10 x 8.3 =
0.1 x 8.3 =
100 x 8.3 =
0.01 x 8.3 =
1,000 x 8.3 =
x 8.3 =
10,000 x 8.3 =
x 8.3 =

14. Complete the table below:
Whole Number
Powers of 10
Decimal
10 x 8.3 =
0.1 x 8.3 =
100 x 8.3 =
0.01 x 8.3 =
1,000 x 8.3 = 8,300
x 8.3 =
10,000 x 8.3 = 83,000
x 8.3 =

15. Complete the table below:
Whole Number
Powers of 10
Decimal
10 x 8.3 =
0.1 x 8.3 =
100 x 8.3 =
0.01 x 8.3 =
1,000 x 8.3 = 8,300
x 8.3 =
10,000 x 8.3 = 83,000
x 8.3 =

16. What do you notice about the decimal point when you multiply by whole number powers of 10? Of decimal powers of 10?

17. Multiplying by Powers of 10
 Multiplying by whole number powers of 10:
Move the decimal point one place to the right for each zero in the whole number power of 10.
x =
Multiplying by decimal powers of 10:
Move the decimal point one place to the left for each decimal place in the decimal power of 10.
399.5 x =

18. What do you think will happen to the decimal point when you divide by whole number powers of 10? Of decimal powers of 10?

19. Dividing by Powers of 10
 Dividing by whole number powers of 10:
Move the decimal point one place to the left for each zero in the whole number power of 10.
35 ÷ 100 =
 Dividing by decimal powers of 10:
Move the decimal one place to the right for each decimal place in the decimal power of 10.
 35 ÷ =

20. Multiplying the divisor and the dividend by the same number does not change the quotient.
42 ÷ 6 = 7
10  10
420 ÷ 60 = 7
  10
4,200 ÷ 600 = 7
Helpful Hint

21. Dividing a Decimal by a Decimal
Find the quotient.
5.2 ÷ 1.3
Multiply the divisor by 101, or 10 to make it a whole number. Multiply the dividend by the same power of 10. 4
Think: 1.3 x 10 = x 10 = 52
13 52
Divide as with whole numbers.
–52
5.2 ÷ 1.3 = 4

22. Check It Out:
51.2 ÷ 0.24
Multiply the divisor by 102, or 100, to make it a whole number. Multiply the dividend by the same power of 10.
Think: 0.24 x 100 = x 100 = 5,120

23. Place the decimal point in the quotient. Divide as with whole numbers.
Check It Out: 2 1 3 .3 3
24 5,120.00
Place the decimal point in the quotient. Divide as with whole numbers.
-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 = 213.3 __

24. Make a Problem Solving Plan:1
Understand the Problem 2
Make a Plan
Solve 3
Look Back 4

25. Understand the Problem
Problem Solving Application
After driving miles, the Yorks 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 gallons of gas.

26. 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

27. 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 as with whole numbers.
-210 63 -0
630
-630
The York family averaged 20.6 miles per gallon.

28. Look Back 4
The answer is reasonable since 20.6 is close to the estimate of 20.

29. John spent $13. 44 renting 4 videos for the weekend
John spent $ renting 4 videos for the weekend. What was the cost per video?

30. John spent $13. 44 renting 4 videos for the weekend
John spent $ renting 4 videos for the weekend. What was the cost per video?
$3.36