How to multiply by 11
This is the single fastest shortcut in this guide — once it's automatic, ×11 stops being a multiplication and becomes reading the digits off the number itself.
The rule
For any two-digit number, add its two digits together. Put that sum between the original digits. If the sum is 10 or more, carry the 1 into the leading digit.
Why it works
Multiplying by 11 is the same as multiplying by 10 and adding the number once more: n × 11 = n × 10 + n. For a two-digit number "ab" (meaning 10a + b), that sum lines up digit-by-digit so the tens and units overlap exactly in the middle — which is what produces the "insert the sum between the digits" pattern.
Worked examples
23 × 11 — 2 + 3 = 5. Insert between: 253.
41 × 11 — 4 + 1 = 5. Insert between: 451.
47 × 11 — 4 + 7 = 11. That's 10 or more, so carry: write 1, carry 1 into the 4 → 517.
85 × 11 — 8 + 5 = 13. Carry: write 3, carry 1 into the 8 → 935.
The part people get wrong
The carry step is where this trick actually needs attention. If the digit sum is 10 or greater, you can't just write two digits in the middle — write the units digit of the sum, and add 1 to the leading digit. 47 × 11 is not "4(11)7"; it's 5-1-7, because the extra ten from "11" bumps the 4 up to 5.
Beyond two digits
The same idea extends to three-digit numbers — add each adjacent pair of digits moving from right to left, carrying as needed — but it's slower to execute reliably in your head past two digits, so this is where most people stop using it as a mental shortcut and switch back to direct calculation.