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Multiply by 11 board for 72 times 11
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5 Mental Math Tricks for Faster Calculations

Pick one shortcut and run a two-minute drill.

April 10, 2026Math Gym3 min read

Try the shortcut

Multiply by 11 without a column setup

Keep the outside digits, add the middle pair, then carry only if needed.

Multiply by 11 board for 72 times 11
  1. 1Place the first digit, 7.
  2. 2Add the two digits for the middle: 7 + 2 = 9.
  3. 3Place 2, then check against 72 x 10 + 72.
Why it works

Multiplying by 11 is multiplying by 10 and adding the original number once more.

Carry check

Bridge a sticky addition through ten

When the units feel crowded, complete ten first and carry only the leftover part.

Bridge-to-ten board for 7 plus 8
  1. 1Use 3 from 8 to make 10.
  2. 2Keep the leftover 5 visible.
  3. 3Read 10 + 5 = 15.
When to use it

Use complements when a units carry is likely but the next ten is easy to reach.

Fast mental arithmetic is mostly method selection. The aim is not to memorize a trick for every number. It is to notice when one of a small set of structures makes the work shorter, then check the answer with a second view.

1. Multiply a two-digit number by 11

For a two-digit number 10a + b, multiplying by 11 gives 100a + 10(a + b) + b. That is why the outside digits stay in place and their sum fills the middle.

Worked example: For 68 x 11, start with 6 | 14 | 8. The middle is larger than 9, so carry 1 left: 6 | 14 | 8 = 748.

Quick check: 68 x 10 + 68 = 680 + 68 = 748. This method is useful only when the carry is handled explicitly.

2. Round and compensate

Replace an awkward number with a nearby friendly one, calculate, then undo the change.

Worked example: 347 + 198 = 347 + 200 - 2 = 545.

The same idea works for multiplication: 63 x 19 = 63 x 20 - 63 = 1,260 - 63 = 1,197. Before finishing, note that the exact product must be a little below 1,260.

3. Double one factor and halve the other

In a product, doubling one factor and halving the other keeps the result unchanged. Use it when one factor is even and the transformed pair becomes easier.

Worked example: 25 x 48 = 50 x 24 = 100 x 12 = 1,200.

Stop if halving creates an awkward decimal. For 35 x 27, this move does not simplify the pair, so distribution is clearer: 35 x (30 - 3).

4. Split an unfamiliar percentage

Build a percentage from parts you can calculate reliably, such as 10%, 5%, 1%, halves, or quarters.

Worked example: To find 17% of 240, use 10% + 5% + 2%: 24 + 12 + 4.8 = 40.8.

Quick check: 20% of 240 is 48, so 17% must be below 48. Keep the unit attached: a 17% discount on a $240 item is $40.80, while the sale price is $199.20.

5. Use a difference of squares

When two factors are equally far from the same center, use (a + d)(a - d) = a^2 - d^2.

Worked example: 53 x 47 = (50 + 3)(50 - 3) = 50^2 - 3^2 = 2,500 - 9 = 2,491.

This is a poor choice when the factors do not share a convenient midpoint. Do not force 54 x 41 into the pattern; round and compensate or use ordinary multiplication instead.

A five-minute practice ladder

  1. Solve 72 x 11 and 86 x 11.
  2. Solve 489 + 297 and 42 x 99 by compensation.
  3. Solve 16 x 75 by doubling and halving.
  4. Find 18% of 150 by splitting the percentage.
  5. Solve 62 x 58 as a difference of squares.

For every answer, write a one-line estimate. A shortcut earns its place only when it is both shorter and easy to verify.