Learn · Numeracy · 4 min

Percentages, from scratch

Per cent means “per hundred.” A percentage is just a count out of 100:

%shorthand for “÷ 100”
5%5 out of every 100
40%40 out of every 100
100%all 100 — the whole thing

See it: a percentage is a count out of 100

5% = 5 out of 100 = 5100 = 0.05

Drag the slider — the shaded squares are the percentage. Fill all 100 and you have 100% — the whole thing.

The same idea, three ways

Because “%” just means “÷ 100”, every percentage is also a fraction and a decimal:
50% = 50100 = ½ = 0.5 (one half)
25% = 25100 = ¼ = 0.25 (one quarter)
10% = 10100 = 110 = 0.1 (one tenth)

Now — a percentage OF something

“5 out of 100” is easy when there are exactly 100 things. But what’s 25% of 80, or 30% of a $50 price? Same idea — just scaled to the whole you actually have. This next part is where most people slip up, so let’s see it.

The one move that matters

The amount you’re taking a percent of is your whole — think of it as 100%. So if it’s 80, then 80 = 100%. Now just take your slice of that 80:

100% of 80= 80(all of it)
50% of 80= 40(half)
25% of 80= 20(a quarter)
10% of 80= 8(a tenth)

Same slice, different whole → different answer. Change the whole below and watch every result move.

Play with it

The whole (= 100%):

25% of 80 = 20

Drag the slider. Then change the whole — the same % gives a different answer.

Tips & tricks

“of” means × (multiply)

30% of 60 = 30100 × 60 = 18

Going the other way → part over whole × 100

Scored 30 out of 40? 3040 × 100 = 75%

The 10% shortcut — do it in your head

10% is just ÷ 10, then build up: 30% = 3 × 10%. So 30% of 80 → 8 × 3 = 24.

Swap them — a% of b = b% of a

Hard: 4% of 50. Flip it: 50% of 4 = 2. Same answer, way easier.

Worth memorising

50% = ½ · 25% = ¼ · 10% = ÷ 10 · 1% = ÷ 100

⚠ The trap most people fall for

“A bigger percentage means a bigger amount.” Not always. The percentage is meaningless until you know the whole. In the explorer above, try it: 20% of 200 = 40, but 50% of 60 = 30. The smaller percentage won — because its whole was bigger.

Now you try — 0/3

1. What is 25% of 80?

2. A test is out of 40 marks. You scored 30. What percentage is that?

3. Which is bigger?

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