**1. Multiplying by 9, or 99, or 999**

Multiplying by 9 is really multiplying by 10-1.

So, 9×9 is just 9x(10-1) which is 9×10-9 which is 90-9 or 81.

Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414.

One more example: 68×9 = 680-68 = 612.

To multiply by 99, you multiply by 100-1.

So, 46×99 = 46x(100-1) = 4600-46 = 4554.

Multiplying by 999 is similar to multiplying by 9 and by 99.

38×999 = 38x(1000-1) = 38000-38 = 37962.

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