"20% off!", "5% APR", "60% chance of rain", "you scored 45 out of 60" — percentages are the language shops, banks and exam boards all speak. Per cent literally means "out of 100", so 25% means 25 out of every 100 — the same as the fraction 25/100 or the decimal 0.25. Putting everything "out of 100" lets us compare amounts on one common scale.
Why this matters: percentages are how the real world talks about change and comparison — sale prices, interest, test scores, tips, tax. Being fluent means you spot a bad deal in your head and never get caught out by "reverse" percentage tricks in shops.
30% = 30 out of 100 — here 3 of the 10 parts are shaded
Switching between %, fractions and decimals
Three costumes for one amount: 50% fills half the bar = 1/2 = 0.5.
A percentage, a fraction and a decimal are three costumes for the same amount. Learning the common ones off by heart makes everything faster.
Percentage
Fraction
Decimal
50%
1/2
0.5
25%
1/4
0.25
10%
1/10
0.1
75%
3/4
0.75
To turn a % into a decimal, divide by 100 (move the point two places left): 30% → 0.30. To turn a decimal into a %, do the reverse: 0.08 → 8%.
Finding a percentage of an amount
Turn the % into a decimal, then multiply. It really is that short.
30% of 80: 30% = 0.3, so 0.3 × 80 = 24. Handy building blocks: 10% is "divide by 10", and 1% is "divide by 100", so you can build trickier percentages from these in your head.
Multipliers — the fast way to increase or decrease
Start from 100% = 1. +15% adds a slice → ×1.15; −15% removes one → ×0.85.
Instead of finding the percentage and then adding or taking it off in two steps, do it in one. Think of the whole thing as 100% = 1, then adjust:
To increase by a %, the multiplier is 1 + (the % as a decimal). To decrease, it's 1 − (the % as a decimal).
Increase by 15% → × 1.15. Decrease by 15% → × 0.85.
Increase £80 by 15%: 80 × 1.15 = £92 — in one step, no need to find the 15% separately. A shop reducing £80 by 30% just does 80 × 0.7 = £56.
Percentage change
Compare the change (8) to the original (50): (8÷50)×100 = 16% down.
To find what % something went up or down by, compare the change to where it started:
% change = (change ÷ original) × 100.
A price falls from £50 to £42: change = 50 − 42 = 8, so % decrease = (8 ÷ 50) × 100 = 16%.
Common mistake: always divide by the original amount, not the new one. A price going from 40 to 55 is a rise of 15 on the original 40, so (15 ÷ 40) × 100 = 37.5% — not 15 ÷ 55.
Memory hook: % means "out of 100". To find a % of something, multiply by its decimal; to increase or decrease, use a multiplier; for % change, always divide the change by the original.
Drag the slider until you've shaded 35% of the circle: