Sunday, October 3, 2010

A Basic Trick on Multiplying by Nine

As:

x * 9 = [(x-1)*10] + 9 - (x-1)

We can say:

1 * 9 = [(1-1) * 10] + 9 - (1-1) = 9
2 * 9 = [(2-1) * 10] + 9 - (2-1) = 18
3 * 9 = [(3-1) * 10] + 9 - (3-1) = 27

So:

4 * 9 = ?
a = 4 - 1 = 3
b = 9 - a = 9 - 3 = 6
4 * 9 = (3*10) + 6 = 36

8 * 9 = ?
8-1=7
9-7=2
8 * 9 = 72

9 * 9 = ?
9 - 1 = 8
9 - 8 = 1
9 * 9 = 81

10 * 9 = ?
10 - 1 = 9
9 - 9 = 0
10 * 9 = 90

11 * 9 = ?
11 - 1 = 10
9 - 10 = -1
11 * 9 = (10 * 10) - 1 = 99

12 * 9 = ?
12 - 1 = 11
9 - 11= -2
12 * 9 = 110 - 2 = 108

13 * 9 = ?
13 - 1 = 12
9 - 12 = -3
13 * 9 = 120 - 3 = 117

14 * 9 = ?
14 - 1 = 13
9 - 13 = -4
14 * 9 = 126

...

x * 9 = [(x-1) * 10] + 9 - (x-1)