How to Multiply by 11 in Your Head

How do you multiply by 11 in your head?

To multiply a two-digit number by 11, write its two digits with their sum between them. For 43 × 11, the first digit is 4, the middle is 4 + 3 = 7, and the last digit is 3, giving 473.

It works because 11 is 10 + 1, so 43 × 11 = 430 + 43, and adding those two lines puts the 4 in the hundreds, the 3 in the units, and 4 + 3 in the tens.

When the digits add to 10 or more, the sum is too big for one place, so write its units digit in the middle and carry the 1 into the hundreds: 86 × 11 has 8 + 6 = 14, so write 4 and raise the 8 to 9, giving 946. A three-digit number works the same way with two middle sums: 123 × 11 is 1, then 1 + 2 = 3, then 2 + 3 = 5, then 3, so 1353.

What if the digits add to 10 or more?

The sum still goes in the middle, but it has two digits now, so the 1 carries into the hundreds. For 75 × 11, 7 + 5 = 12: write the 2 in the middle and add the 1 to the 7, which gives 825. Check it the long way: 750 + 75 = 825.

How do you multiply a three-digit number by 11?

Keep the first and last digits and put the sum of each neighboring pair between them. For 234 × 11 the first digit is 2, then 2 + 3 = 5, then 3 + 4 = 7, then the last digit 4, so 2574. It is the same addition as before: 2340 + 234 lines each digit up beside its neighbor.

Work from the right so the carries land. For 687 × 11 the last digit 7 stays; 8 + 7 = 15, so write 5 and carry 1; 6 + 8 + 1 = 15, so write 5 and carry 1; and the leading 6 takes that carry to make 7. Read it off: 7557. Check: 6870 + 687 = 7557.