1. Multiplication and Division of Decimals Unit
M5N3: Students will further develop their understanding of the meaning of multiplication and division with decimal fractions and use them.

2. Model Multiplication of Decimals
M5N3a: Model multiplication and division of decimal fractions by another decimal fraction.

3. Steps to Using a model to multiply decimals
Count the number of rows across and multiply by 0.10.
3 rows x 0.10 squares in each row
0.30
2) Count the number of rows down and multiply by 0.10.
5 rows x 0.10 squares in each row
0.50
3) Count the number of squares where the colors overlap
15 squares = 0.15
4) Write the multiplication problem:
0.30 x 0.50 = 0.15

4. Guided Practice 5 x .10 = 0.50 5 x .10 = 0.50 25 x .10 = 0.25
How many rows across?
How many rows down?
How many overlap?
Multiplication sentence
5 x .10 = 0.50
5 x .10 = 0.50
25 x .10 = 0.25
0.5 x 0.5 = 0.25

5. Guided Practice 7 x .10 = 0.70 4 x .10 = 0.40 28 x .10 = 0.28
How many rows across?
How many rows down?
How many overlap?
Multiplication sentence
7 x .10 = 0.70
4 x .10 = 0.40
28 x .10 = 0.28
0.7 x 0.4 = 0.28

6. Individual Practice
0.7 x 0.6 = 0.42

7. Individual Practice
0.4 x 0.5 = 0.20

8. Checkpoint Choose the multiplication problem for the following models.
1) What multiplication equation does this model show?
A) 0.6 x 0.6 = 3.6
B) 0.6 x 0.6 = 0.36
C) 0.6 x 0.6 = .036
D) 0.6 x 0.6 = 36

9. 2) What multiplication equation does this model show?
A) 0.5 x 0.4 = 20
B) 0.5 x 0.4 = 0.20
C) 0.5 x 0.4 = 2.0
D) 0.5 x 0.4 = 0.020

10. 3) What multiplication equation does this model show?
A) 0.6 x 0.5 = 0.30
B) 0.6 x 0.5 = 30
C) 0.6 x 0.5 = 3.0
D) 0.6 x 0.5 = 0.030

11. 4) Complete the multiplication sentence for the model.
0. 3 X y = 0.15
A) y = 5.0
B) y = 50
C) y = 0.05
D) y = 0.50

12. 5) Complete the multiplication sentence for the model.
0.5 x y = 0.30
A) y = 60
B) y = 6.0
C) y = 0.06
D) y = 0.6

13. Explain multiplication of decimals
M5N3b: Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimal fractions.

14. Multiplying Decimals
Write the multiplication problem down WITH decimals.
Multiply as you would whole numbers (IGNORE THE DECIMALS).
Count the number of digits to the right of the decimals in the original problem.
Starting at the right (ones place), count out the SAME NUMBER of digits and place your decimal.

15. Example (by one digit) 3.5 x 0.2 Rewrite: 3.5 x 0.2 Multiply 7 0
Count numbers TO THE RIGHT OF the decimal
Starting in the ones place (RIGHT), count the SAME amount and place a decimal (and zero placeholder if necessary).

16. Example (by one digit) 12.3 x 3.5 Rewrite: 12.3 x 3.5 Multiply 615
+ 369
Count numbers TO THE RIGHT OF the decimal
Starting in the ones place (RIGHT), count the SAME amount and place a decimal (and zero placeholder if necessary). 1 1 1 1

17. Practice
4.2 x 1.3
36 x 0.2
5.63 x 5.4
1.07 x 8.1
9.3 x 0.02

18. Model Division of Decimals
M5N3a: Model multiplication and division of decimal fractions by another decimal fraction.

19. Steps to using a model to divide decimals
Create a model to represent the decimal being divided.
Divide the model into groups of the divisor.
Count how many different groups.
2.6 ÷ 1.3
= 2

20. Other models
1.0 ÷ 0.5 = 2
1.0 ÷ 0.2 = 5

21. Guided Practice 2.1 ÷ 0.7 Make a Model (using tenths)
Count out groups of 0.7
3) 2.1 ÷ 0.7 = 3

22. Individual Practice
3.6 ÷ 0.9 = ? Make a model Mark out groups of 0.9 Count how many groups. 4

23. Checkpoint 1) What division problem does this model show? 30 ÷ 10 = 3
3.3 ÷ 1.1 = 3
33 ÷ 11 = 3
1.1 ÷ 3.3 = 3

24. 2) What division problem does this model show?
15 ÷ 3 = 5
0.15 ÷ 3 = 0.05
1.5 ÷ 0.5 = 3
0.15 ÷ 5 = 3

25. 3) What division problem does this model show?
5 ÷ 4 = 20
0.20 ÷ 0.40 = 5
0.50 ÷ 0.40 = 0.20
2.0 ÷ 0.4 = 5

26. 3) Use the model to determine the value of y.

27. 2) Use the model to determine the value of t?
y ÷ 0.3 = 4
y = 12
y = 1.2
y = 0.12
y = 0.012

28. Explain division of decimals
M5N3b: Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimal fractions.

29. Steps to multiplying decimal by whole number
3.6 ÷ 2
Steps to Division
Example 1 8
Step 1: Write the division problem Step 2: Divide, keeping the quotient above the correct place. Step 3: Move the decimal from the dividend straight up into the quotient.
- 2 1 6
- 1 6

30. Steps to multiplying a decimal by a decimal
3.6 ÷ 1.2
Example
Step 1: Write the division problem. Step 2: Move the decimal in the divisor to the right of the last digit (count how many spaces). Step 3: Move the decimal in the dividend the SAME number of spaces to the right. Divide as whole number. 3
- 3 6