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Partial Product (Multiplication Algorithm)

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Partial Product (Multiplication Algorithm). Review of Partial Products. Set up the problem vertically. Separate all parts. Find the products. Add to find the sum. Here’s an example. ( 80 + 2 ) ( 3 ). 82 x 3_. 240 6. = 80 x 3 = 2 x 3. +_____ 246.

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Partial Product (Multiplication Algorithm)

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  1. Partial Product (Multiplication Algorithm)

  2. Review of Partial Products • Set up the problem vertically. • Separate all parts. • Find the products. • Add to find the sum.

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

  4. 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

  5. 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

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

  7. We will use the same steps: • Set up the problem vertically. • Separate all parts. • Find the products. • Add to find the sum.

  8. Here’s an example. 25 x32 (20 + 5) (30 + 2) 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.

  9. 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.

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

  11. + Partial Product 2 7 (20+7) 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

  12. + Partial Product 4 8 (40+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 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

  13. + Partial Product 6 9 (60+9) 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

  14. 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

  15. 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

  16. 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

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

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