MULTIPLICATION BY 9, 99, 999, ETC.

MULTIPLICATION BY 9, 99, 999, ETC.

There is another way to multiply fast by 9 that has an analogue for multiplication by 99, 999 and all such numbers. Let's start with the multiplication by 9.

To multiply a one digit number a by 9, first subtract 1 and form b = a - 1. Next, subtract b from 9: c = 9 - b.Then just write b and c next to each other:

9a = bc.

For example, find 6×9 (so that a = 6.) First subtract: 5 = 6 - 1. Subract the second time: 4 = 9 - 5. Lastly, form the product 6×9 = 54.

Similarly, for a 2-digit a:

bc	= 100b + c
	= 100(a - 1) + (99 - (a - 1))
	= 100a - 100 + 100 - a
	= 99a.

Do try the same derivation for a three digit number. As an example,

543×999	= 1000×542 + (999 - 542)
	= 542457.