How to Multiply by 11 in Your Head

Level 2 Mental multiplication · Reviewed by The NumThink editorial team · Last reviewed

Short version: For a 2-digit number, split it and put the digit-sum in the middle: 72 × 11 = 7_(7+2)_2 = 792.

The 11 rule is the classic party trick — but it's real mathematics: split the digits and add the neighbours. The only skill you need is handling the carry.

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Why it works

Multiplying by 11 means multiplying by 10 and adding the number once: 72 × 11 = 720 + 72. Written vertically, the digits of 72 appear twice, shifted — which is exactly "split and add the neighbours".

For any length number, the rule is the same: each answer digit is the sum of the two neighbouring digits of the original (with edge digits copied outside), carrying when a sum passes 9.

The steps

  1. Split the number. Write the first digit, a gap, the last digit: 7 _ 2 for 72.
  2. Add the neighbours. The middle digit is 7 + 2 = 9, giving 792.
  3. Carry when needed. 87 × 11: 8 _(8+7)_ 7 → 8, 15, 7. The 15 contributes 5 and carries 1: 957.

Worked examples

easy 43 × 11

Show the thinking

Split: 4 _ 3

Middle: 4 + 3 = 7

43 × 11 = 473.

Answer: 473

medium 87 × 11

Show the thinking

Split: 8 _ 7

Middle: 8 + 7 = 15 — write 5, carry 1

8+1 = 9, so 87 × 11 = 957.

Answer: 957

hard 234 × 11

Show the thinking

Edge digits: 2 ... 4

Inside sums: 2+3 = 5, 3+4 = 7

234 × 11 = 2,574.

Answer: 2,574

When to use it

  • Any ×11 — this is one of the fastest mental-math moves that exists.
  • ×11 extended: ×33, ×22 etc. can reuse the same idea after halving or thirding the other factor.

When not to use it

  • Do not force it on ×12 — that is ×11 plus the number, a different move.
  • With 4+ digit numbers the carry bookkeeping grows; standard ×10-then-add is fine there.

Common mistakes

Forgetting the carry. 87 × 11 answered as 8,15,7 or 8157. Fix: A middle sum above 9 always carries 1 into the digit to its left.
Adding all digits into the middle. For 3-digit numbers, dumping every digit-sum into one place. Fix: Each interior digit of the answer is one adjacent pair only — the pairs overlap.
Check yourself: The alternating digit sum of a multiple of 11 is a multiple of 11: 957 → 9 − 5 + 7 = 11 ✓.