Percentages Made Simple: Of, Out Of, and Change
Most percentage confusion comes from mixing up three different questions. Once you can tell them apart, the maths is easy.
Percent means 'per hundred'
A percentage is just a fraction of 100. So 25% is 25/100, or the decimal 0.25. Converting a percentage to a decimal — divide by 100 — is the single most useful trick, because then every percentage question becomes a simple multiplication or division.
The three questions
'What is X% of Y?' Multiply: turn X% into a decimal and multiply by Y. 'X is what percent of Y?' Divide X by Y and multiply by 100. 'What is the percentage change from A to B?' Take the difference, divide by the original value A, and multiply by 100.
The classic mistake is calculating change against the new number instead of the original, or confusing a percentage-point change (10% to 15% is five points) with a relative change (a 50% increase).
Discounts don't reverse the way you'd think
A price cut by 20% isn't undone by adding 20%, because the 20% increase is now taken from a smaller number. And stacked discounts of 20% then 10% give 28% off in total, not 30%. When in doubt, work one step at a time.