1. Multiplication

2. 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. . 4 3 2 1 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

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