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Multiplying by 9 is really multiplying by 10-1. So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81. Lets try a harder example: 46x9 = 46x10-46 = 460-46 = 414. One more example: 68x9 = 680-68 = 612. To multiply by 99, you multiply by 100-1. So, 46x99 = 46x(100-1) = 4600-46 = 4554. Multiplying by 999 is similar to multiplying by 9 and by 99. 38x999 = 38x(1000-1) = 38000-38 = 37962.
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