Why the Multiplication by 11 Trick Works
One of the famous tricks that you have probably known is how to multiply numbers by 11. If we multiply a 2-digit number by 11, we copy the ones digit to the ones digit of the product, add the ones and the tens digit and place the sum in the tens digit of the product, and then copy the tens digit to the hundreds digit of the product. For example, if we multiply 34 × 11.
(1) We copy 4 and place it in the ones digit of the product.
(2) Add 3 and 4 = 7 and place it in the tens digit of the product.
(3) Copy 3 and place it in the hundreds digit of the product.
Therefore, 34 × 11 = 374. » Read more