The multiply by 11 trick, for any number.
To multiply a number by 11, keep its outside digits and write the sum of each pair of neighbouring digits in between. For 43 × 11, keep 4 and 3 and put 4 + 3 = 7 in the middle: 473. Below you will see what to do when a sum reaches 10, how the trick works for 3-digit and longer numbers, and why it always works.
The trick for 2-digit numbers
Split the number apart, add its two digits, and put the sum in the gap. For 72 × 11: 7 + 2 = 9, so the answer is 792.
72 × 11 → 7 _ 2 → 7 (7 + 2) 2 = 792
When the digits add up to 10 or more
This is where most people go wrong. If the middle sum is 10 or more, write only its last digit and carry the 1 to the left. For 58 × 11: 5 + 8 = 13. Write 3, then add the carried 1 to the 5 to get 6. The answer is 638, not 5138.
58 × 11 = 638
Check it the long way: 580 + 58 = 638.
The trick for multiplying 3-digit numbers by 11
With more digits, work from right to left. Write the last digit, then add each pair of neighbours, then write the first digit. For 324 × 11:
Write 4.
Write 6.
Write 5.
Write 3. Reading left to right, the answer is 3,564.
324 × 11 = 3,564
Carries work the same way as before. Our Trachtenberg multiplication guide walks through 497 × 11 = 5,467, where two neighbouring sums need a carry.
A trick to multiply any number by 11
The same steps work for 4, 5 or more digits: last digit, every neighbouring pair, first digit. For 2,531 × 11, write 1, then 3 + 1 = 4, 5 + 3 = 8, 2 + 5 = 7, and finally 2. The answer is 27,841. This is the ×11 rule of the Trachtenberg method, a system of digit-by-digit rules for mental calculation.
Why does the 11 trick work?
Multiplying by 11 is the same as multiplying by 10 and adding the number once more: 43 × 11 = 430 + 43. When you line those two numbers up, each column adds a digit to its neighbour. The trick simply does that column addition in one pass, which is also why carries behave exactly as they do in ordinary addition.
43 × 11 = 430 + 43 = 473
Multiply by 11, in your head.
Try any two-digit number. The answer appears one small step at a time.
Enter a two-digit number to see the rule.
4 + 3 = 7. Put that sum between the two original digits.
Multiply by 11 practice worksheet
Print this page or copy the list. Work each one with the trick, then check a few by the long way. They start easy and add carries and longer numbers as you go.
- 23 × 11
- 45 × 11
- 61 × 11
- 36 × 11
- 67 × 11
- 89 × 11
- 152 × 11
- 408 × 11
- 786 × 11
- 1,234 × 11
Teaching the 11 trick to kids
Start with numbers whose digits add up to less than 10, such as 23, 45 and 61, and have your child say each step aloud: “outside digit, add the neighbours, outside digit.” Introduce carries only once that sequence is automatic. Children enjoy the trick most when they can check it themselves, so let them prove one answer the long way.
For more, see mental math tricks for kids or the Trachtenberg Kids app, where the ×11 lesson is free.