Percentage of an Amount

Per cent means "out of 100", so the \% sign is shorthand for \div 100. To find p\% of an amount, turn the percentage into that decimal multiplier and multiply:

p\% \text{ of } A = \frac{p}{100} \times A = A \times (p \div 100)

For example, 25\% of 80. Since 25\% = \frac{25}{100} = 0.25:

25\% \text{ of } 80 = 0.25 \times 80 = 20

A few percentages are so handy that you should know them on sight — each is just a quick division you can do in your head:

10% — divide by 10 (A \div 10)
1% — divide by 100 (A \div 100)
50% — halve it (A \div 2)
25% — a quarter (A \div 4)

Now combine these building blocks to reach any percentage. Want 30\%? That is three lots of 10\%. Want 15\%? That is 10\% + 5\%, and 5\% is just half of 10\%.

p\% \text{ of } A = \dfrac{p}{100} \times A — multiply by the decimal.
10\% = A \div 10 and 1\% = A \div 100.
50\% = half of A; 25\% = a quarter of A.
Build any other percentage from these (e.g. 30\% = 3 \times 10\%).

See it on a bar

Picture the amount as a bar that is the whole — 100\%. Shade a quarter of it and you have shaded 25\%: that part is 25\% of 80, which is 20. Step through it.