Mental arithmetic tricks worth learning

A handful of shortcuts cover most everyday arithmetic. These are the ones that pay for the effort of learning them.

Speed comes from replacing hard operations with easy ones, not from thinking faster.

Multiplication

Round and correct. 19 × 7 is 20 × 7 minus 7, so 133. Almost any awkward multiplication has a nearby round number.

Halve and double. 14 × 35 becomes 7 × 70, which is 490. Whenever one factor is even and the other is awkward, this helps.

Multiply by 5 by halving and multiplying by 10. 48 × 5 is 240.

Multiply by 11 (two digits) by adding the digits and putting the sum in the middle. 52 × 11: 5, 5+2, 2 → 572. Carry if the middle exceeds 9.

Squares ending in 5. 65² : take 6, multiply by 7 to get 42, append 25 → 4225. Always works.

Percentages

Percentages commute. 8% of 25 equals 25% of 8, which is obviously 2. When one direction looks hard, flip it — this single fact removes most percentage difficulty.

Build from 10%. 10% is a decimal shift; 5% is half of that; 1% is two shifts. Most percentages are a short sum of these.

Tips. 15% is 10% plus half of it. 20% is double 10%.

Division

Divide by 5 by doubling and dividing by 10. Divide by 25 by multiplying by 4 and dividing by 100. Both turn an awkward division into a shift.

Estimate before you calculate

Knowing the answer to 47 × 21 is "about a thousand" catches a slip that produces 98 or 9,870. An estimate first is the cheapest error check available, and it is the habit that most separates people who are quick from people who are merely fast.

Frequently asked questions

Which trick is worth learning first?

That percentages commute — 8% of 25 is the same as 25% of 8. It takes a moment to learn and removes a large share of everyday percentage difficulty.

Does timed practice help or just add pressure?

Both modes exist for that reason. Untimed practice is where you learn a technique; timed practice is where it becomes automatic. Learning under time pressure mostly reinforces whatever you already do.

How do I get faster at multiplication?

Stop computing and start rearranging — round to a nearby number and correct, or halve one factor and double the other. Speed comes from making the problem easier, not from calculating quicker.