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

Fluency Practice – Multiply then Divide by the Same Number 6 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

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

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

Fluency Practice – Decompose Decimals Represent 8.972 in a two-part number bond with tenths as one part and thousandths as the other part. Represent 8.972 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

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

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 12.75 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 3.75 + 9.00 = 12.75 + 1.75 = 14.50

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 2.4. 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.

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 + 800 + 160 + 60 + 12 = 1,032 tenths = 103.2 40 800 160

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

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

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 X42 ------ 70 1400 ------ 1470 tenths = 147 30 + 5 tenths 2 60 10 + 1200 200 40

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

Concept Development – Problem 3 70 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 = 18 + 150 + 300 10920 = 420 + 3500 + 7000 ------- 11388 tenths = 1,138.8 1 156 X 73 ----- 468 15.6 X 73 ------- 468 10920 1138.8

Exit Ticket