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Multiplication Tricks

Multiplication with 11

Let's call the number that will be multiplied by 11 is Multiplier.

If we multiply a n-digit number (Multiplier) by 11,
then the "Multiplication Result" (MR) will have n+1 digit or n+2 digit result.

For example:
If we multiply a one-digit number by 11, the MR will have a two-digit, or a three-digit result.
If we multiply a two-digit number by 11, the MR will have a three-digit, or a four-digit result.

The MR's first digit is equal to the Multiplier's left-most digit.
The MR's last digit is equal to the Multiplier's ones.
In the middle of those two digit, add the Multiplier's digit from right to left, two at a time.

For Example:

				the multiplier's tens	add the tens and the ones ( 2 + 3) = 5	the multiplier's ones

23	x	11	=	2	5	3

				the multiplier's tens	add the tens and the ones ( 5 + 1) = 6	the multiplier's ones

51	x	11	=	5	6	1

If the sum of those addition has 2 digits, carry the tens to the next left digit.
For example:

				the multiplier's tens + carry	add the tens and the ones ( 7 + 9) = 16	the multiplier's ones
				7 + 1 = 8
79	x	11	=	8	6	9

Using the same rules

					( 7 + 2) = 9	( 2 + 3) = 5

723	x	11	=	8	9	5	3

					( 1 + 6) + 1 =8	( 6 + 8) = 14

168	x	11	=	1	8	4	8