Fast multiplication by 11

One of my favourite techniques is that which allows us to fast multiplication by 11. To get your attention I will say that I can multiply in my head the following numbers:

748346274 x 11 = 8231809014

The technique is quite simple:

• the last digit of our product will be the last digit of number which is not 11 (e.g.  748346274) : 4

• the next digit of our product is calculate by adding the n digit to the n-1 digit: 4 + 7 = 11; we write down 1 and save 1 into memory

• the next digit of our product is calculated by adding the n-1 digit to the n-2 digit: 7 + 2 = 9; recall the 1 saved previously so we get 10; the next digit of our product becomes 0 and save 1 into memory

• the next digit of our product is calculated by adding the n-2 digit to the n-3 digit: 2 + 6 = 8; recall the 1 saved previously so we get 9; the next digit of our product becomes 9

• we continue the process until to the first digit (on the left) of our number; that way we obtain the final product as 8231809014

Very simple!