Multiply by 11 Trick
💡Multiplying by 11 is the same as multiplying by 10 and adding the number once more. For two-digit numbers you can also spread the digits and add the middle.
Try it — multiply any number by 11
liveMultiply by 10, then add the number once more.
- 1
Multiply by 10
63 × 10 = 630
- 2
Add the number once more
630 + 63 = 693
- 3
Or use the digit trick
6_3 → put 6+3=9 in the middle → 693
⏱️ Practice against the clock
A worked example
11 × 63: think 63 × 10 = 630, plus 63, gives 693. The digit trick: 6 _ 3 with 6+3=9 in the middle also gives 693.
Why splitting the digits works
Here is the trick most people meet first: to do 63 × 11, pull the 6 and the 3 apart, add them to get 9, and drop that in the middle. 693. Feels like a magic trick the first time you see it.
It is not. Write 63 as 10a + b and multiply by 11, and you land on 100a + 10(a+b) + b. So the hundreds digit is a, the ones digit is b, and the middle is just a+b. That is the whole rule, and it holds for any two-digit number you throw at it.
When the middle does not fit
The rule needs one patch. If the two digits add up to more than 9, the middle overflows. Take 76 × 11: the middle wants to be 7 + 6 = 13, which will not fit in one slot. Write the 3, carry the 1 over to the 7, and you land on 836.
If that trips you up halfway through, drop back to the slow-but-safe version: 76 × 10 is 760, add 76, done. Same 836. That fallback never needs a carry rule, so it is a good safety net when the digits run big.
Questions people ask
What happens when the middle digits add to more than 9? ▾
Carry the extra into the next digit. For 11 × 76, the middle is 7 + 6 = 13, so you write 3 and carry 1 into the 7, giving 836.
Does the trick work for three-digit numbers? ▾
Yes, but the ×10-plus-itself method scales better there. Add each digit to its neighbour from right to left and carry as needed.