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Multiplication

Multiplication. Multiplication. Multiplication is increasing the value of a number by adding in equal sets. 3 x 4 means add 3 together 4 times 3 + 3 + 3 + 3 Multiplying larger numbers is the same 22 x 14 means add 22 together 14 times

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Multiplication

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  1. Multiplication

  2. Multiplication • Multiplication is increasing the value of a number by adding in equal sets. • 3 x 4 means add 3 together 4 times 3 + 3 + 3 + 3 • Multiplying larger numbers is the same • 22 x 14 means add 22 together 14 times • This takes too long, so we have memorized the simple multiplication facts to make this process easier. 3 x 9 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27 3 x 9 = 27

  3. Traditional Multiplication 3 45 X 16 270 450 720

  4. Try It Out • Use traditional multiplication on these problems to solve for m. 2231 * 3 = m 24 * 46 = m 2342 * 14 = m 758 * 13 = m 24 * 12 = m

  5. Try It Out • Use traditional multiplication on these problems to solve for m. 2231 * 3 = m 24 * 46 = m 2342 * 14 = m 758 * 13 = m 24 * 12 = m M=6693 M=1536 M=32788 M=9854 M=288

  6. Partial Products • In the partial-products method, you must keep track of the place value of each digit. It may help to label each place value column. 100s 10s 1s • 3 * 197 = ? Multiply each part of 197 by 3 100 * 3 = 3 0 0 90 * 3 = 2 7 0 7 * 3 = 2 1 5 9 1

  7. Partial Products • 64 * 72 = 100s 10s 1s • 60 + 4 * 70 +2 = 60 * 70 = 42 0 0 60 * 2 = 1 2 0 4 * 70 = 2 8 0 4 * 2 = 8 45 10 8 46 0 8

  8. Try It Out • Use partial products multiplication on these problems to solve for m. 137 * 65 = m 625 * 30 = m 72 * 15 = m 420 * 31 = m 23 * 21 = m

  9. Try It Out • Use partial products multiplication on these problems to solve for m. 137 * 65 = m 625 * 30 = m 72 * 15 = m 420 * 31 = m 23 * 21 = m M = 8905 M =1875 M =1080 M =13020 M =483

  10. Lattice Method

  11. Try It Out • Use lattice method of multiplication on these problems to solve for m. 76 * 49 = m 53 * 83 = m 92 * 56 = m 63 * 15 = m 48 * 27 = m M = 3724 M =4399 M = 5152 M =945 M =1296

  12. Multiplying with Decimals • When you are multiplying a whole number by a decimal, you are going to find the value of that smaller amount of the big piece. • 16 * .25 means what is .25 or 25% of the total of 16 • We know .25 or 25% is 1 of 4 groups of the total. • If we break 16 into 4 equal groups, we get 4 in each group. 16 X .25 8 0 3 2 0 4 .0 0 • We have multiplied, but we have gotten a smaller answer than either one of the factors of the problem because we are looking at the value of that smaller piece in the whole.

  13. Multiplying with Decimals • If you multiply a decimal by a decimal, you are still looking at the problem in the same way. • If the problem is .89 * .16, you are looking at what is .16 of .89. In this case, .89 becomes the whole and .16 is the piece you are trying to find the value of. .89 X .16 5 3 4 8 9 0 .1424

  14. But How Do You Place the Decimal? • First count the numbers that sit in decimal place values. .89 X .16 5 3 4 8 9 0 1 4 2 4 • Next, start at the back of the number (right side) and count toward the front the same number of place value spots. 1 4 2 4 4 . 4 3 2 1

  15. Try It Out • Use lattice or partial-products method of multiplication on these problems to solve for m. Be sure you show the path you followed to place the decimal. 0.3 * 14 = m 6.8 * 4.5 = m 0.12 * 0.9 = m 0.3 * 0.919 = m 2.7 * 5.6 = m M = 4.2 M = 30.60 or 30.6 M = 0.108 M = 0.2754 M = 15.12

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