Percentages Without a Calculator
Percentages are the arithmetic most adults actually need and most adults quietly avoid. Tips, discounts, interest, a pay rise, a statistic in the news — all of it is percentages, and almost all of it can be done in your head in a couple of seconds once you stop treating it as a formula.
Everything starts from ten per cent
Ten per cent is a decimal point moved one place left. That is the whole of it.
10% of 240 is 24. 10% of 85 is 8.5. 10% of 1,340 is 134.
Every other percentage is built from that one by doubling, halving or adding.
| You want | Do this | Example on 240 |
|---|---|---|
| 5% | Half of 10% | 24 → 12 |
| 15% | 10% plus half of it | 24 + 12 = 36 |
| 20% | Double 10% | 24 × 2 = 48 |
| 25% | Quarter — halve twice | 120 → 60 |
| 30% | Triple 10% | 24 × 3 = 72 |
| 1% | Two places instead of one | 2.4 |
The swap that saves the most time
Any percentage of a number equals that number as a percentage of the first. In other words, x% of y is the same as y% of x — and one of the two is usually obvious.
8% of 50looks awkward.50% of 8is 4.4% of 75→75% of 4= 3.18% of 50→50% of 18= 9.
It works because both are the same multiplication with the numbers written in a different order. Whenever one side is 50, 25 or 10, flip it.
Tips and service
For a bill of £62:
- 10% → £6.20
- 20% → double it, £12.40
- 15% → £6.20 + £3.10 = £9.30
- 12.5% → 10% + a quarter of that → £6.20 + £1.55 = £7.75
Discounts, and the trap in them
For a shop taking 30% off, do not work out the discount and subtract it — work out what you are paying directly. 30% off means you pay 70%.
A £45 coat at 30% off: 10% is £4.50, so 70% is £31.50. One step instead of two, and no subtraction to get wrong.
The trap worth knowing: successive percentages do not add. A 20% discount followed by a further 10% off is not 30% off. You pay 80%, then 90% of that — which is 72%, so the true discount is 28%. Shops are not being dishonest when they advertise it that way, but it is never as good as it sounds.
Percentage increases
To add 15%, multiply by 1.15 — or, more easily, work out 15% and add it on.
A £34,000 salary rising 3%: 1% is £340, so 3% is £1,020, giving £35,020.
To reverse one, do not subtract the same percentage. If a price is £120 after a 20% rise, the original was 120 ÷ 1.2 = £100, not £96. This is the single most common percentage mistake there is.
Going the other way: what percentage is this?
Turn it into a fraction and simplify.
- 18 out of 25 → multiply both by 4 → 72 out of 100 → 72%
- 7 out of 20 → multiply both by 5 → 35 out of 100 → 35%
- 13 out of 40 → multiply both by 2.5 → 32.5 out of 100 → 32.5%
Anything with a denominator that divides neatly into 100 — 4, 5, 10, 20, 25, 50 — is a one-step job.
Fractions worth recognising instantly
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/6 | 16.7% |
| 1/3 | 33.3% | 1/8 | 12.5% |
| 1/4 | 25% | 2/3 | 66.7% |
| 1/5 | 20% | 3/4 | 75% |
Spotting that 12.5% is just an eighth turns a calculation into a division you already know.
Practising it
Percentages reward recognition more than calculation — you are pattern-matching to 10%, to a half, to a familiar fraction. Carry the One‘s Oh Wow Expert mode mixes percentage questions in with the rest precisely because they are the ones people hesitate over longest.
More like this: all the mental arithmetic guides.