SIXTYmental math · 60-second sprintAll guides
Techniques

What are the fastest multiplication tricks?

Most multiplication speed comes from a handful of patterns tied to easy numbers: 2, 5, 9, 10, 11, and 25. Once these are reflexes, a lot of products fall out in one step instead of a grind.

Learn each trick on its own, then drill until you stop deciding which to use and just see it. SIXTY pushes harder facts as you get faster and replays the ones you miss, which is exactly how these patterns become automatic.

How do I multiply by 2, 4, and 8 quickly?

Doubling is the easiest operation to do in your head, so handle 4 and 8 as repeated doubling rather than as separate facts. Multiplying by 4 is two doubles; by 8 is three doubles.

For 23 × 8: double 23 to 46, double again to 92, double once more to 184. For 35 × 4: double to 70, double to 140.

  1. Double once for ×2.
  2. Double twice for ×4.
  3. Double three times for ×8.

What is the fast way to multiply by 5?

Multiplying by 5 is the same as multiplying by 10 and halving, since 5 is half of 10. Add a zero, then take half.

For 48 × 5: 48 × 10 = 480, then halve to get 240. If the number is odd, halving leaves a .5, so 27 × 5 is 270 ÷ 2 = 135.

  1. Multiply the number by 10 (append a zero).
  2. Halve the result.

How do I multiply by 9 in my head?

Nine is one less than ten, so multiply by 10 and subtract the original number. This beats reciting the nine times table.

For 9 × 7: 10 × 7 = 70, then subtract 7 to get 63. For 9 × 46: 10 × 46 = 460, subtract 46 to get 414.

  1. Multiply the number by 10.
  2. Subtract the original number from that.

What is the trick for multiplying a two-digit number by 11?

To multiply a two-digit number by 11, add its two digits and drop the sum between them. The outer digits stay the same when there is no carry.

For 11 × 36: 3 and 6 sum to 9, so place 9 between 3 and 6 to get 396. When the digit sum is 10 or more, carry: for 11 × 57, 5 + 7 = 12, write the 2 in the middle and carry the 1 into the 5, giving 627.

  1. Write down the first and last digits with a gap between them.
  2. Add the two digits.
  3. Put that sum in the gap; if it is 10 or more, carry the 1 to the left digit.

How do I multiply by 25 fast?

Twenty-five is 100 ÷ 4, so multiply by 100 and divide by 4 (or divide by 4 first if that is cleaner). This turns big multiplications into a quick quarter.

For 25 × 16: 16 ÷ 4 = 4, then 4 × 100 = 400. For 25 × 36: 3600 ÷ 4 = 900.

  1. Multiply the number by 100 (append two zeros), or divide it by 4 first.
  2. Divide by 4 (or multiply by 100) to finish.

When does doubling and halving help?

If one factor is even, you can halve it and double the other factor without changing the product. Repeat until one factor becomes an easy number like 50 or 100.

For 16 × 25: halve 16 to 8 and double 25 to 50, giving 8 × 50 = 400. For 14 × 50: halve to 7, double to 100, giving 7 × 100 = 700.

  1. Halve the even factor and double the other factor.
  2. Repeat until one factor is easy to multiply.
  3. Multiply the simplified pair.

Reading is review. Recall is what sticks.

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