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Partial Product (Multiplication Algorithm)

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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