How to multiply any 2-digit number by 11 instantly

Multiplying by 11 is one of the fastest wins in mental math — a two-digit number times 11 can be written down almost instantly, once you know the pattern. No long multiplication needed.

The core rule

For a two-digit number with digits A and B (so the number is "AB"), the rule is:

That's it — as long as A + B is a single digit, this gives you the answer directly.

Worked example: 34 × 11

• Digits: A = 3, B = 4
• A + B = 3 + 4 = 7
• Place 7 between 3 and 4

Worked example: 52 × 11

• Digits: A = 5, B = 2
• A + B = 5 + 2 = 7
• Place 7 between 5 and 2

When the middle sum is 10 or more (the carry case)

If A + B is 10 or greater, you can't just drop a two-digit number in the middle — you carry the extra 1 over to the left digit, same as in normal addition.

Worked example: 68 × 11

• Digits: A = 6, B = 8
• A + B = 6 + 8 = 14
• Write down the 4, carry the 1
• Add the carried 1 to A: 6 + 1 = 7

Worked example: 95 × 11

• Digits: A = 9, B = 5
• A + B = 9 + 5 = 14
• Write down the 4, carry the 1
• Add the carried 1 to A: 9 + 1 = 10

Since A itself becomes a two-digit number here, that carries again into the next place to the left.

Why this works

Multiplying by 11 is the same as multiplying by 10 and then adding the original number once more:

Writing N × 10 shifts every digit one place left and puts a 0 at the end. Adding N back in lines up each digit with its neighbor, which is exactly why the middle digit ends up being the sum of the two original digits — the "0 + B" and "A + 0" additions on the ends stay as A and B, while the middle position gets A + B.

Extending to 3-digit numbers

The same shift-and-add idea extends further, though it's less commonly needed for exam-level questions. For a 3-digit number ABC × 11, the digits of the answer (from right to left) are: C, B+C, A+B, A — handling carries the same way as above. It's worth knowing this exists, but the 2-digit version is by far the more useful one to make automatic first.

Where this actually helps

This shortcut shows up constantly in simplification and approximation questions on bank exams, and it's often faster to spot a hidden "× 11" in a calculation than to notice it and still do standard long multiplication. Once it's automatic, you save a full working-out step every time it appears.