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The three percentage questions, answered properly

Quick answer: What is X% of Y, X is what percent of Y, and percent change — all three answered instantly with the arithmetic shown, not just the answer.

Every percentage problem is one of three questions: what is X% of Y, X is what percent of Y, or the percent change from X to Y. Pick the question, enter two numbers, and get the answer with the working shown — 15% of 80 is 12, and you can see why. The change mode carries the warning most calculators skip: percentage change is measured from the starting number, which is why a 50% drop needs a 100% rise to break even.

Common questions

How do I calculate a percentage of a number?

Multiply the number by the percentage and divide by 100: 15% of 80 is 80 × 15 ÷ 100 = 12. The same one-liner handles tips, discounts and tax — a 20% discount on $150 is $30 off, because 150 × 20 ÷ 100 = 30.

How do I work out what percent one number is of another?

Divide the part by the whole and multiply by 100: 12 is 15% of 80 because 12 ÷ 80 × 100 = 15. Getting 42 questions right out of 60 is 70% by exactly the same move.

Why don't a 50% loss and a 50% gain cancel out?

Because each change is measured from where you currently stand. Drop $100 by 50% and you're at $50; gaining 50% from $50 only returns $75. Recovering the full $100 needs a 100% gain — the asymmetry behind most investing and pricing mistakes.

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