1. Model Multiplication of Decimals
5.NBT.7
Deanna Cross
Hutto Middle School

2. Model Multiplication
Decimal x Whole Number

3. 0.7 x 3
Shade in 0.7 in the vertical columns

4. 0.7 x 3
Repeat this model so that you have a total of 3 grids.

5. 0.7 x 3 Count the total number of hundredths shaded
210 hundredths = 2 wholes and 10 hundredths = 2.10 or 2.1

6. 0.05 x 6
Shade in 0.05 in the vertical columns

7. 0.05 x 6
Repeat the 0.05 for a total of 6 times (on the same grid).

8. 0.05 x 6 Count the total number of shaded hundredths.
30 shaded boxes =
30 hundredths = 0.30 or 0.3

9. Model Multiplication
Decimal x Decimal

10. 0.8 x 0.5
Shade in 0.8 in the vertical columns

11. 0.8 x 0.5
Shade in 0.5 in the horizontal rows.

12. 0.8 x 0.5 Overlap the two models Count the overlapping squares.
40 hundredths
Write as decimal
0.40

13. 1.2 x 0.9
Draw a model to represent 1.2 (vertically).

14. 1.2 x 0.9
Draw a model to represent 0.9 (horizontally).

15. 1.2 x 0.9
Overlap 1.2 by 0.9 on both grids.

16. 1.2 x 0.9
Count overlapping squares 108 hundredths or 1 whole and 8 hundredths = 1.08

17. Practice Recognizing Multiplication Models

18. What multiplication equation does this model show?
A) 0.5 x 0.3 = 15 B) 0.5 x 0.3 = 0.15 C) 0.5 x 0.3 = 1.5 D) 0.5 x 0.3 = .015

19. What multiplication equation does this model show?
A) 0.7 x 0.6 = 4.2 B) 0.7 x 0.6 = 0.42 C) 0.7 x 0.6 = D) 0.7 X 0.6 = 42

20. What multiplication equation does this model show?
0.6 x 0.5 = 0.30
0.5 x 0.4 = 0.20
0.6 x 0.4 = 0.24
0.5 x 0.5 = 0.25

21. What multiplication equation does this model show?
--- //
0.5 x 0.5 = 0.25
0.5 x 0.2 = 0.40
0.5 x 0.4 = 0.20
0.2 x 0.4 = 0.5

22. What multiplication equation does this model show?
--- //
0.9 x 0.2 = 18
0.9 x 0.2 = 0.018
0.9 x 0.2 = 0.18
0.9 x 0.2 = 1.8

23. Use the model to determine the missing factor? 0.05 x ___ = 0.25
0.5 5 50

24. Use the model to determine the missing factor? 0.3 x ___ = 0.930 3
0.3
0.03

25. Determining an algorithm

26. Problems from Examples:
Decimals 0.7 x 3 = x 6 = x 0.5 = x 0.9 = 1.08
Without Decimals 7 x 3 = 21 5 x 6 = 30 8 x 5 = x 9 = 108
Do you see a pattern?

27. 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

28. Algorithm When you multiply decimals, follow these steps:
Write the problem down.
Move the decimals in both multiplicands to the right until you have no more decimals in your problem (count how many times you move).
Multiply as you would whole numbers.
Replace the decimal in the answer (starting from the right) the same amount you moved out.

29. 3 1.52 x 0.6 Example #1 Count how many total times you moved
Rewrite the problem.
Remove the decimals (to the right)
1.52 x 0.6 = ? 3 2
1.52
x 0.6 1

30. 3 152 x 06 9 1 2 Example #1 Rewrite the problem as whole numbers
Replace the decimal (from right)
Multiply
Rewrite the problem as whole numbers
1.52 x 0.6 = ? 3 1 3
152
x 06 9 1 2
1.52 x 0.6 = 0.912

31. 1 142 x 0.9 Example #2 Count how many total times you moved
Remove the decimals (to the right)
Count how many total times you moved
Rewrite the problem.
142 x 0.9 = ? 1
142
x 0.9 1

32. 1 142 x 09 12 7 8 Example #2 Rewrite the problem as whole numbers
Replace the decimal (from right)
Multiply
Rewrite the problem as whole numbers
142 x 0.9 = ? 3 1 1
142
x 09 12 7 8
142 x 0.9 = 127.8

33. Guided 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
5.46
7.2
30.402
8.667
0.186