Find 10% first. Almost everything else is built from it.
To get 10% of any number, move the decimal point one place left. 10% of 840 is 84. 10% of 62.50 is 6.25. That single move does most of the work.
Building from 10%
Once you have 10%, the common percentages are one step away:
| Want | Do this to 10% |
|---|---|
| 5% | halve it |
| 20% | double it |
| 30% | triple it |
| 15% | add half of it again |
| 1% | move the decimal one more place |
| 2.5% | quarter it |
For 15% of 840: ten per cent is 84, half of that is 42, so 126.
Anything can be assembled this way. 35% is 30% plus 5% — triple it, then add half. 45% is half minus 5%.
The reversal trick
This is the one most people have never seen, and it turns hard problems into obvious ones.
x% of y is always exactly y% of x.
Both are (x × y) ÷ 100, so the order genuinely does not matter.
- 4% of 75 — awkward. But 75% of 4 is three-quarters of 4, which is 3.
- 8% of 50 — flip it. 50% of 8 is 4.
- 16% of 25 — flip it. 25% of 16 is 4.
- 12% of 50 — flip it. 50% of 12 is 6.
Whenever one of the numbers is a friendly fraction — 25, 50, 75, 20 — flip it and the problem usually solves itself.
Fractions beat decimals
Some percentages are just fractions wearing a disguise, and the fraction is nearly always faster:
| Percentage | Fraction | Do this |
|---|---|---|
| 50% | ½ | halve |
| 25% | ¼ | halve twice |
| 75% | ¾ | halve twice, then triple |
| 20% | ⅕ | divide by 5 |
| 33⅓% | ⅓ | divide by 3 |
| 12.5% | ⅛ | halve three times |
75% of 60: halve to 30, halve to 15, triple to 45. No decimals anywhere.
Working backwards
“18 is what percent of 40?” Get to a hundred-ish denominator.
40 goes into 100 two and a half times, so multiply both numbers by 2.5: 18 becomes 45, 40 becomes 100. The answer is 45%.
Or use the halving route: 18 out of 40 is a bit under half, and half would be 20 — so somewhere in the mid-forties. Close enough for most decisions, and it takes a second.
Estimate first, always
Even when reaching for a calculator, guess the rough answer before you type. 20% of 340 should land near 70. If the screen says 6.8 or 680, you mistyped something.
This habit catches decimal-point errors, which are the ones that actually cause damage. Being slightly out rarely matters. Being out by a factor of ten always does.