Percent
“A percent is 'how many, if the whole were 100'.”
The formula
p = (a ÷ b) × 100How to read it: A percent is the part divided by the whole, times 100 — the size when the whole counts as 100
- a
- — the part — the amount you're counting
- b
- — the whole — the total you compare to
- p
- — the percent (%)
The hook
'50% off', 'battery at 80%' — a percent tells you how many out of 100 the whole would be.
In plain words
A number that says how much the part is when the whole is treated as 100. The sign % means 'out of 100'.
The intuition
If 20 of 50 kids wear glasses, stretch the whole to 100. Since 20/50 = 40/100, that's 40%. Percent lets you compare different-sized wholes on the same '100' scale.
How it's built
First make the fraction (or decimal) part ÷ whole, then multiply by 100. 0.4 → 40%, 1/2 → 50%. Going back, divide the % by 100 to get the decimal.
Example
If 20 of 50 people wear glasses: 20 ÷ 50 = 0.4, then 0.4 × 100 = 40%. So 20 of 50 is 40%.
Common mistake
100% is 'all' and 50% is 'half'. Percent can go past 100% — when something grows beyond the original, like 120%.
Where it's used
Discounts, test scores, battery levels, statistics — used to compare things of different sizes fairly.
Where it came from
'Per cent' means 'per hundred' in Latin; merchants spread it by figuring interest and taxes per hundred.
Prerequisites
Quick check
You got 30 of 60 questions right. What percent is that?
- 30%
- 50%✓
- 60%
- 3%
Practice
10 of 20 items are red. What percent are red?
Answer: 50
- 10 ÷ 20 = 0.5
- 0.5 × 100 = 50
- → 50%
Takeaway: Part ÷ whole × 100 = percent.
You got 3 of 4 right. What percent?
Answer: 75
- 3 ÷ 4 = 0.75
- 0.75 × 100 = 75
- → 75%
Takeaway: Divide first, then multiply by 100.
What is 25% of 80?
Answer: 20
- 25% = 25 ÷ 100 = 0.25
- 0.25 × 80 = 20
Takeaway: Turn the % into a decimal and multiply to get the part.