How to multiply by 11 in your head
Multiplying a two-digit number by 11 takes one addition. Split the digits apart and put their sum in the middle.
The basic trick
36 × 11: 3 _ 6 → 3 + 6 = 9 → 396 52 × 11: 5 _ 2 → 5 + 2 = 7 → 572 81 × 11: 8 _ 1 → 8 + 1 = 9 → 891It works because 11 × 36 = 10 × 36 + 36 = 360 + 36. The tens digit of 36 and the units digit of 360 line up in the middle and get added.
When the digits add to 10 or more
Put the units digit of the sum in the middle and carry the 1 into the first digit.
78 × 11: 7 + 8 = 15 → 7 _ 8 becomes (7+1) 5 8 → 858 95 × 11: 9 + 5 = 14 → (9+1) 4 5 → 1,045Three-digit numbers
Keep the first and last digits, and fill the middle with the sums of each neighbouring pair, carrying from right to left.
243 × 11: 2 | 2+4 | 4+3 | 3 → 2 6 7 3 → 2,673 576 × 11: 5 | 5+7 | 7+6 | 6 → 5 12 13 6 → carry → 6,336For the second one, work right to left: 6; 13 → write 3, carry 1; 12 + 1 = 13 → write 3, carry 1; 5 + 1 = 6. The answer is 6,336.
Practice
The trick sticks after about fifty reps. R3CK0N's ×11 drill throws random two-digit numbers at you against the clock, and the mental math tricks guide covers ×9, ×5 and ×25 the same way.
Drill the ×11 trick