Percent Power: Reverse Percentages

Percentages in your head, no calculator.

Smart Mathematician Fractions & Percentages Maths Games for Teenagers Maths Games for Adults

Basics Standard Discounts Reverse Percentages

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How Percent Power: Reverse Percentages works

Every round is a percentage you should be able to do mentally by decomposing it. 15% is 10% plus half of 10%. 20% is a fifth. 5% is half of 10%. Once you see percentages as combinations of easy pieces, the calculator becomes optional.

The discount and tip variants apply exactly the same arithmetic to situations where you actually need it, which is the point — a skill you only use in a maths game is not really a skill.

This version: Find the original number. Your best score is saved in this browser, so you can come back and try to beat it. Nothing is uploaded and no sign-up is needed.

Frequently asked questions

What is the single most useful trick here?

Find 10% first, by moving the decimal point one place left. Almost every other percentage is built from that: 5% is half of it, 20% is double, 15% is one and a half times.

Does x% of y really equal y% of x?

Yes, always, and it is the most underused shortcut in mental arithmetic. 4% of 75 looks unpleasant; 75% of 4 is three.

Are the tip percentages realistic?

They use the 10, 15 and 20 percent bands that are common in practice, so the practice transfers directly.

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