Saturday, June 9, 2012

Multiplying by 9, 99, 999, ...

Multiplying by 9 is as multiplying by 10-1. So, 9 * 8 is as (10 - 1) * 8 that is:

9 * 8 = (10 - 1) * 8 = 80 - 8 = 72

Another example:

26 * 9 = 26 * (10 - 1) = 260 - 26 = 234

To multiply by 99, one must multiply by 100-1:

53 * 99 = 53 * (100 - 1) = 5300 - 53 = 5200 + 100 - 53 = 5200 + 47 = 5247

Similarly, to multiply by 999, one must multiply by 1000-1:

87 * 999 = 87 * (1000 - 1) = 87000 - 87 = 86000 + 1000 - 87 = 86000 + 913 = 86913





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