Multiplying by 11

Multiply any two-digit number by 11 by adding its digits and dropping the sum in the middle.

Multiply any two-digit number by 11 in one step.

The trick

Split the digits apart. Add them. Put the sum in the gap.

When the digits sum to 10 or more, carry the 1 into the first digit.

Why it works

11 is 10 + 1, so multiplying by 11 means adding a number to itself shifted one place left. Written out for a two-digit number ab:

The a stays in the hundreds, the b stays in the units, and a + b occupies the tens — which is exactly “drop the sum in the middle”. The carry is not a special case bolted on: it is what happens when a + b needs two places.

It goes further

The same shift-and-add works for longer numbers: add each adjacent pair of digits, right to left, carrying as you go. 3142 × 11 gives 3, 3+1, 1+4, 4+2, 2 → 34562.