Three questions, one calculator — and it shows the working so you can do the next one in your head
Most percentage calculators give you a number and nothing else. This one shows the route as well, because the route is the part worth keeping: once you can see that a percentage is just 1% multiplied up, most everyday percentages stop needing a calculator at all.
Almost every percentage problem is one of three. What is 15% of 60 — a percentage of an amount, which is what tips, discounts and VAT are. 9 is what percent of 60 — turning two numbers into a proportion, which is what test scores and market shares are. And 60 to 75 — a percentage change, which is what price rises, growth rates and pay increases are.
They use different arithmetic, and mixing them up is the most common percentage mistake there is. A 20% rise followed by a 20% fall does not bring you back to where you started, because the second 20% is a percentage of a bigger number.
Find 10% first: move the decimal point one place to the left. 10% of 60 is 6. Everything else is built from that — 5% is half of it, 1% is a tenth of it, 30% is three of them.
That makes awkward percentages easy in steps. 35% of 60 is 10% (6) three times, which is 18, plus half of 6, which is 3 — so 21. No calculator, two seconds.
Percentages also commute, which is the trick most people never learn: x% of y is the same as y% of x. 8% of 50 looks awkward, but 50% of 8 is obviously 4.
For a discount, work out what you pay rather than what you save. 30% off is 70% of the price, which is one multiplication instead of a subtraction after a multiplication.
For a tip, 10% then half again gives 15%; 10% doubled gives 20%. Both are a second's work once the 10% is in your head.
For tax added on top, multiply rather than add twice: a 20% tax means multiplying by 1.2, and removing it means dividing by 1.2, not subtracting 20%.
A percentage change is always measured against the starting value. Going from 40 to 50 is a 25% increase, but going back from 50 to 40 is a 20% decrease — the same ten, a different base.
That asymmetry is why a stock that falls 50% needs a 100% rise to recover, and why 'prices rose 10% then fell 10%' leaves you 1% down rather than level.
Multiply the number by the percentage and divide by 100. For 15% of 60: 60 × 15 ÷ 100 = 9. In your head, find 10% (6), halve it for 5% (3), and add them.
Divide the part by the whole and multiply by 100. 9 out of 60 is 9 ÷ 60 = 0.15, which is 15%.
Subtract the old value from the new one, divide by the old value, then multiply by 100. From 40 to 50: 10 ÷ 40 = 0.25, which is a 25% increase.
Because each percentage is taken from a different starting number. 100 rises 20% to 120, then falls 20% of 120 — which is 24 — leaving 96, not 100.
Build them from 10% and 1%. 17% is 10% + 5% + 2%, and each of those is one easy step from the 10% you already found.