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**Partial Product (Multiplication Algorithm)**

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**Review of Partial Products**

Set up the problem vertically. Separate all parts. Find the products. Add to find the sum.

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**82 x 3_ (80+2) (3) 240 6 246 = 80 x 3 = 2 x 3 Here’s an example.**

+_____ 246

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**Try this one using your slate**

Try this one using your slate. Use the blank worksheet to help guide you. 42 x 3_ (40+2) (3) 120 6 = 40 x 3 = 2 x 3 +_____ 126

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**Try another one using your slate**

Try another one using your slate. Use the blank worksheet to help guide you. 71 x 4_ (70+1) (4) 280 4 = 70 x 4 = 1 x 4 +_____ 284

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Now, we are going to learn to multiply a 2 digit number by a 2 digit number using the Partial Products Algorithm.

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**We will use the same steps:**

Set up the problem vertically. Separate all parts. Find the products. Add to find the sum.

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**25 x32 (20 + 5) (30 + 2) 800 Here’s an example. +_____ = 20 x 30 600**

You must separate and multiply all parts. Remember this phrase: Down, down, crisscross = 20 x 30 = 5 x 2 = 20 x 2 = 5 x 30 600 10 40 150 Find the products. +_____ 800 Add.

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**Here’s another example.**

54 x23 (50 + 4) (20 + 3) You must multiply all parts. Remember this phrase: Down, down, crisscross = 50 x 20 = 4 x 3 = 50 x 3 = 4 x 20 1000 12 150 80 Find the products. +_____ 1242 Add.

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**Here is another way of looking at the problem.**

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**2 7 X 6 4 1,200 420 80 28 + 1,728 Partial Product (20+7) (60+4)**

When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 6 4 (60+4) 1,200 Multiply 20 X 60 (tens by tens) 420 Multiply 60 X 7 (tens by ones) 80 Multiply 4 X 20 (ones by tens) 28 + Multiply 7 X 4 (ones by ones) Add the results 1,728

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**4 8 X 5 3 2,000 400 120 24 + 2,544 Partial Product (40+8) (50+3)**

When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 5 3 (50+3) 2,000 Multiply 40 X 50 (tens by tens) 400 Multiply 50 X 8 (tens by ones) 120 Multiply 3 X 40 (ones by tens) 24 + Multiply 8 X 3 (ones by ones) Add the results 2,544

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**6 9 X 5 8 3,000 450 480 72 + 4,002 Partial Product (60+9) (50+8)**

When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 5 8 (50+8) 3,000 Multiply 60 X 50 (tens by tens) 450 Multiply 50 X 9 (tens by ones) 480 Multiply 8 X 60 (ones by tens) 72 + Multiply 9 X 8 (ones by ones) Add the results 4,002

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**Now it’s time to try some on your own! Use the blank paper to guide you.**

59 x14 (50 + 9) (10 + 4) Separate the parts. Multiply (down, down, crisscross) Add. 500 36 200 90 = 50 x 10 = 9 x 4 = 50 x 4 = 9 x 10 +_____ 826

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**Another! Use the blank paper to guide you.**

84 x26 (80 + 4) (20 + 6) Separate the parts. Multiply (down, down, crisscross) Add. 1600 24 480 80 = 80 x 20 = 4 x 6 = 80 x 6 = 4 x 20 +_____ 2184

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**Last One! Use the blank paper to guide you.**

75 x48 (70 + 5) (40 + 8) Separate the parts. Multiply (down, down, crisscross) Add. 2800 40 560 200 = 70 x 40 = 5 x 8 = 70 x 8 = 5 x 40 +_____ 3600

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Homework * You will complete a worksheet with 4 multiplication problems which you will use Partial Products to solve.

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