Multiplying Fractions
Remember the different meanings of multiplication. The first meaning is repeated addition. 7 times 8 means 8 groups of 7.
We could add:
7+7 = 14,
14+7 = 21,
21 + 7 = 28,
28 + 7 = 35
35 + 7 = 42,
42 + 7 = 49 and finally
49 + 7 = 56
The second meaning of multiplication is an array, or area, model. This rectangle has length = 7 and width = 8. How many squares do you count?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 |
| 29 | 30 | 31 | 32 | 33 | 34 | 35 |
| 36 | 37 | 38 | 39 | 40 | 41 | 42 |
| 43 | 44 | 45 | 46 | 47 | 48 | 49 |
| 50 | 51 | 52 | 53 | 54 | 55 | 56 |
The area is 56 squares.
So let's use these same ideas when we think about multiplying fractions.