Multiplying by 11

The Trick: When multiplying a figure by 11, follow this pattern: leave the last and first digits alone, then sum each and every pair of digits next to each other (this makes the most sense when seen in example):

Examples: 4,281 x 11 becomes the following digits: (4)(4+2),(2+8)(8+1)(1) or 47,091.

When the sum of a pair is greater than 10, carry that digit to the next left pair (as seen above, where 2+8 was 10).

Let's try something harder. 9,621,576,521 x 11 becomes: (9)(9+6),(6+2)(2+1)(1+5),(5+7)(7+6)(6+5),(5+2)(2+1)(1) or 105,837,341,731.

This is a neat trick of our base 10 place value system. Because 11 = 10 + 1, multiplying a number by 11 is the same as multiplying that number by 10 and then adding it back to itself. Multiplying a number by 10 means we shift all our digits one place over to the left and stick a zero on the end, so when we add this to the original number, we get exactly the paring up of digits that we saw.