Multiplication by 9, 99, 999, etc.

One way to multiply a number by 9 is to multiply by 10 and then subtract the number from the product. For example,

 23·9 = 230 - 23 = 207.

The rule is based on the distributive law and applies in other similar situations. For example, to multiply by 99, multiply by 100 and then subtract the number:

23·99 = 2300 - 23 = 2277.

To multiply by 999, multiply by 1000 and subtract the number from the product:

23·999 = 23000 - 23 = 22977.


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