How to Multiply by 11 in Your Head
Level 2 Mental multiplication · Reviewed by The NumThink editorial team · Last reviewed
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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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
- Split the number. Write the first digit, a gap, the last digit: 7 _ 2 for 72.
- Add the neighbours. The middle digit is 7 + 2 = 9, giving 792.
- 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.