Percentages Explained Simply

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum — “per hundred”. When we say 25%, we mean 25 out of every 100.

The three core percentage problems

Almost every percentage question falls into one of three types.

1. Finding a percentage of a value

What is 15% of 80?

Convert the percent to a decimal and multiply:

15% = 15 ÷ 100 = 0.15, then 0.15 × 80 = 12

2. Finding what percent one number is of another

12 is what percent of 48?

Divide, then multiply by 100:

12 ÷ 48 = 0.25, then 0.25 × 100 = 25%

3. Finding the whole from a percentage

30 is 20% of what number?

Divide by the decimal form of the percent:

30 ÷ 0.20 = 150

Percentage change

Percentage change measures how much a value has grown or shrunk relative to where it started:

change % = (new − old) ÷ |old| × 100

Example: a price rises from 40 to 50. The change is (50 − 40) ÷ 40 × 100 = 25%. Note that a 25% increase followed by a 25% decrease does not return to the start — 40 → 50 → 37.5 — because the second percentage applies to a different base.

Quick mental math tricks

• 10% of a number: move the decimal point one place left. 10% of 250 is 25.
• 5%: take 10%, then halve it.
• 15%: add the 10% and 5% figures. 15% of 250 = 25 + 12.5 = 37.5.
• 1%: move the decimal point two places left.

Where percentages go wrong

The most common mistake is mixing up the base. If a stock falls 50% and then rises 50%, you end up at 75% of the starting value — not 100%. Always ask: percentage of what?