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Multiplication Tricks

Multiplying by 11 – Split and Add the Middle

Two-digit numbers times 11 have a lovely shortcut: spread the digits apart and put their sum in the gap.

This page explains the rule, shows why it works, and walks through worked examples. Then you can try it yourself and check your understanding with practice questions. Use the previous and next links at the bottom to move through the tricks in order.

The rule

The Rule: To multiply a two-digit number by 11, add the digits together and place the sum in between them. If the sum is 10 or more, carry the extra 1 into the first digit.

Why it works

Why It Works: Any two-digit number can be thought of as “ten lots of the first digit, plus the second digit.” Multiplying that whole thing by 11 is the same as multiplying by 10 and then adding one more full copy of the original number — and adding that extra copy happens to slot the digit sum neatly into the middle, between the two original digits.

Formal Proof (for advanced learners)

Let the two-digit number be N = 10a + b (digits a and b). Then N×11 = N×10 + N = (100a + 10b) + (10a + b) = 100a + 10(a+b) + b. When a+b < 10, this is literally the three-digit number with digits a, (a+b), b. When a+b ≥ 10, the tens column overflows into the hundreds column — which is exactly the “carry the 1” step.

Examples

  • 23 × 11 → 2 + 3 = 5, placed between: 253.
  • 45 × 11 → 4 + 5 = 9, placed between: 495.
  • 57 × 11 → 5 + 7 = 12, so carry the 1: (5+1) 2 7 = 627.

Step by step

Example A: 36 × 11

  1. Add the digits: 3 + 6 = 9.
  2. Put 9 between 3 and 6: 396.

Example B: 78 × 11

  1. Add the digits: 7 + 8 = 15, which is 10 or more.
  2. Write the ones digit (5) in the middle and carry the 1 into the first digit: (7 + 1) 5 8.
  3. That gives 858.

Try it yourself

Now it is your turn. A new random question appears each time. Type your answer in the box and press Check Answer. If you are right, we show how the trick got you there, step by step. If you are not, you will see the full working two ways, the shortcut and the usual method, so you can spot exactly where your answer differed. Press New Question as often as you like: a few quick rounds is the best way to make the trick feel automatic.

Try It Yourself

Practice questions

Have a go on paper first, then tap Show answer to check your method.

  1. Work out 23 × 11.

    Show answer

    253. Add the digits: 2 + 3 = 5. Put 5 between 2 and 3: 253.

  2. Work out 54 × 11.

    Show answer

    594. Add the digits: 5 + 4 = 9. Put 9 between 5 and 4: 594.

  3. Work out 67 × 11.

    Show answer

    737. Add the digits: 6 + 7 = 13, which is 10 or more. Write the ones digit (3) in the middle and carry the 1 into the first digit: (6 + 1) 3 7. That gives 737.

  4. Work out 89 × 11.

    Show answer

    979. Add the digits: 8 + 9 = 17, which is 10 or more. Write the ones digit (7) in the middle and carry the 1 into the first digit: (8 + 1) 7 9. That gives 979.

  5. A theatre has rows of 11 seats. How many seats are in 42 rows?

    Show answer

    462. Add the digits: 4 + 2 = 6. Put 6 between 4 and 2: 462.

Tips and watch-outs

  • Quick check: the answer should be just over ten times the number. 36 × 11 = 396 is a little above 360.
  • If the middle sum is 10 or more, carry: 78 × 11 has 7 + 8 = 15, so it is (7+1) 5 8 = 858.