1. Module 2 – Lesson 10
Objective: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

2. Fluency Practice – Multiply then Divide by the Same Number6
3 x 2 =
3 x 2 x 10 / (divide by) 10 =
5 x 0.3 =
5 x 0.3 x 10 / 10 =
3 x 2.5 =
3 x 2.5 x 10 /10 =
2 x 3.4 =
2 x 3.4 x 10 /10 =
Why are the products the same when we multiply by 10 and then divide by 10?
You are undoing what you did when you multiplied by 10. We’re moving over one place to the left on the place value chart and then back to the right again. Because, it’s just like multiplying by 1. 6
1.5
1.5
7.5
7.5
6.8
6.8

3. Fluency Practice – Decompose Decimals
Say 7.463
Seven and four hundred sixty-three thousandths.
Represent this number in a two-part number bond with ones as one part and thousandths as the other part.
7.463
463 thousandths
7 ones

4. Fluency Practice – Decompose Decimals
Represent this number in a two-part number bond with tenths as one part and thousandths as the other part.
Represent this number in a two-part number bond with hundredths as one part and thousandths as the other part.
7.463
63 thousandths
74 tenths
7.463
746 hundredths
3 thousandths

5. Fluency Practice – Decompose Decimals
Represent in a two-part number bond with tenths as one part and thousandths as the other part.
Represent in a two-part number bond with hundredths as one part and thousandths as the other part.
8.972
72 thousandths
89 tenths
8.972
897 hundredths
2 thousandths

6. Fluency Practice – Decompose Decimals
Represent in a two-part number bond with ones as one part and thousandths as the other part.
Represent in a two-part number bond with hundredths as one part and thousandths as the other part.
6.849
849 thousandths
6 ones
6.849
684 hundredths
9 thousandths

7. Application Problem
The fifth-grade craft club is making aprons to sell. Each apron takes 1.25 yards of fabric that costs $3 per yard and 4.5 yards of trim that costs $2 per yard. What does it cost the club to make one apron? If the club wants to make $1.75 profit on each apron, how much should they charge per apron?
One apron costs to make. The club must charge $14.50 for each apron to make $1.75 profit.
apron
1.25
4.5
X $3
X $2
1.25 x 3 = 3.75
4.5 x 2 = 9.00
1.75
= = 14.50

8. Concept Development – Problem 1
43 x 2.4
Round the factors to estimate the product. What are your rounded numbers and the products?
40 x 2 = 80
Predict whether our estimate is greater or less than the actual product. Why?
Less than, because both factors were rounded to the numbers less than the actual factors.
We have 43 units of Rename 2.4 using only tenths. How many tenths are in 2.4?
24 tenths.
Decompose those 24 tenths into expanded form and place along the length of an area model. (Suggestions: write tenths off to the sides, so you don’t forget the units you are working in.)
Decompose 43 into expanded form along the width.

9. Concept Development – Problem 1
43 x 2.4
What partial products do the rows represent?
3 x 24 tenths and 40 x 24 tenths.
Find the partial products and the final product.
What did you find as the final product?
1,032 tenths
What is that in standard form?
103.2 20 + 4
tenths 3 60 12 +
= 1,032 tenths = 103.2 40
800
160

10. Concept Development – Problem 1
43 x 2.4
What was our estimate? 80
Is our answer reasonable compared to the estimate?
Yes
Let’s solve using the standard algorithm. 1 1
24 tenths
X 43
------ 72
+960
1032 tenths = 103.2
24 tenths
X 43
------ 72
Step 1
Step 2

11. Concept Development – Problem 1
43 x 2.4
Another way to look at it is. 1
Count the number of decimal places to the right of the decimal in all numbers. Your answer must have that many places to the right. 1
2.4
X 43
------ 72
+960
103.2 1 +0
----
2.4
X 43
------ 72
Step 1
Step 2

12. Concept Development – Problem 2
3.5 x 42
Round the factors and estimate the product.
4 x 40 = 160
Rename 3.5 to unit form
35 tenths
Draw an area model.
35 tenths X 70
1400
------
1470 tenths = 147 30 +
5 tenths 2 60 10 +
1200
200 40

13. Concept Development – Problem 2
3.5 x 42
Standard Algorithm
3.5
X 42
------ 70
How many decimals places are in each number? 1 -- 1
1400
-----
1470

14. Concept Development – Problem 370 3
15.6 x 73
Estimate the product
Rename 15.6 to tenths
Draw an area model
Standard Algorithm
Estimate = 16 x 70 = 1120
156 tenths 6
420 18 50
3500
150
300
7000
100
tenths 3 4 1 1
156 tenths
X 73
-----
468 =
10920 =
11388 tenths = 1,138.8 1
156
X 73
-----
468
15.6
X 73
468
10920
1138.8

15. Exit Ticket