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7 mental math tricks for multiplication

Multiplication gets fast in your head when you turn hard products into multiplying by 10 or 100, doubling and halving. Each of the 7 tricks below fits in one line and comes with an example you can try right now.

The tricks at a glance

TrickRuleExample
Two-digit × 11Split the digits and put their sum in the middle43 × 11 → 4 (4+3) 3 = 473
× 25Multiply by 100, divide by 436 × 25 = 3600 ÷ 4 = 900
× 5Multiply by 10, then halve48 × 5 = 480 ÷ 2 = 240
× 4Double twice23 × 4 → 46 → 92
× 9Multiply by 10, subtract once34 × 9 = 340 − 34 = 306
Halve and doubleHalve the even number, double the other16 × 35 = 8 × 70 = 560
Squares ending in 5First digit × (first digit + 1), then 2535² → 3 × 4 = 12 → 1225

×11 when the middle sum is 10 or more

If the middle sum is 10 or more, carry the 1 to the left. For 78 × 11: 7, (7 + 8 = 15), 8, so the 7 becomes 8 and the answer is 858.

Why squares ending in 5 work

65² is 6 × 7 = 42 followed by 25, so 4225. It always works because (10a + 5)² = 100·a(a + 1) + 25.

Split bigger products

When no trick fits, split one number into tens and ones. 68 × 12 = 68 × 10 + 68 × 2 = 680 + 136 = 816. 47 × 63 = 47 × 60 + 47 × 3 = 2820 + 141 = 2961.

How to practice them

  • Learn one trick a day
  • Solve 10 examples without a timer
  • Mix them into timed multiplication at medium level (24 × 7)
  • Use splitting for expert level (47 × 63)

Practice with Sumbolt

Sumbolt's Tricks tab has 12 tricks, including make a ten, ×9, ×11, ×25 and squares ending in 5. Each one has three short steps, a one-line reason it works, and 10 practice problems. Then use them against the clock in multiplication & division mode.

FAQ

Which multiplication tricks should I learn first?
Start with ×5, ×9 and ×11. They come up often and take about a day to feel natural.
Does the ×11 trick work for three-digit numbers?
Yes. 243 × 11 is 2, (2+4), (4+3), 3 → 2673. Insert the sum of each neighbouring pair.
How do I multiply two two-digit numbers in my head?
Split one into tens and ones: 47 × 63 = 47 × 60 + 47 × 3 = 2961.
Don't tricks slow you down at first?
For a few days, yes. After about ten problems a trick becomes automatic, and then it's faster.

12 tricks with practice problems in Sumbolt

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