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Partial Product (Multiplication Algorithm) Review of Partial Products 1. 2. 3. 4. Set up the problem vertically. Write the numbers in expanded form. Find the products. Add to find the sum. Here’s an example. 82 (80+2) (3) x 3_ 240 = 80 x 3 +_____ 6 =2x3 246 Try this one using your slate. Use the blank worksheet to help guide you. 42 (40+2) (3) x 120 = 40 x 3 3_ 6 =2x3 +_____ 126 Try another one using your slate. Use the blank worksheet to help guide you. 71 x 4_ (70+1) (4) 280 = 70 x 4 4 =1x4 +_____ 284 Now, we are going to learn to multiply a 2 digit number by a 2 digit number using the Partial Products Algorithm. We will use the same steps: 1. 2. 3. 4. Set up the problem vertically. Write the numbers in expanded form. Find the products. Add to find the sum. Here’s an example. 25 (20 + 5) x32 (30 + 2) 600 = 20 x 30 Find the products. Add. 10 = 5 x 2 40 = 20 x 2 +_____ 150 = 5 x 30 800 You must separate and multiply all parts. Remember this phrase: Down, down, crisscross Here’s another example. 54 (50 + 4) x23 (20 + 3) 1000 = 50 x 20 Find the products. Add. 12 = 4 x 3 150 = 50 x 3 +_____ 80 = 4 x 20 1242 You must multiply all parts. Remember this phrase: Down, down, crisscross Here is another way of looking at the problem. When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. Multiply 20 X 60 (tens by tens) Multiply 60 X 7 (tens by ones) Multiply 4 X 20 (ones by tens) Multiply 7 X 4 (ones by ones) Add the results 2 7 (20+7) X 6 4 (60+4) 1,200 420 80 + 28 1,728 When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. Multiply 40 X 50 (tens by tens) Multiply 50 X 8 (tens by ones) Multiply 3 X 40 (ones by tens) Multiply 8 X 3 (ones by ones) Add the results 4 8 (40+8) X 5 3 (50+3) 2,000 400 120 + 24 2,544 When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. Multiply 60 X 50 (tens by tens) Multiply 50 X 9 (tens by ones) Multiply 8 X 60 (ones by tens) Multiply 9 X 8 (ones by ones) Add the results 6 9 (60+9) X 5 8 (50+8) 3,000 450 480 + 72 4,002 Now it’s time to try some on your own! Use the blank paper to guide you. Separate the parts. Multiply (down, down, crisscross) Add. 59 (50 + 9) x14 (10 + 4) 500 = 50 x 10 36 = 9 x 4 200 = 50 x 4 90 = 9 x 10 +_____ 826 Another! Use the blank paper to guide you. Separate the parts. Multiply (down, down, crisscross) Add. 84 (80 + 4) x26 (20 + 6) 1600 = 80 x 20 24 = 4 x 6 480 = 80 x 6 80 = 4 x 20 +_____ 2184 Last One! Use the blank paper to guide you. Separate the parts. Multiply (down, down, crisscross) Add. 75 (70 + 5) x48 (40 + 8) 2800 = 70 x 40 40 = 5 x 8 560 = 70 x 8 200 = 5 x 40 +_____ 3600 Homework * You will complete a worksheet with 4 multiplication problems which you will use Partial Products to solve.