Math

Percent Change

Going from 80 to 100 is a 25% rise, but going from 100 back to 80 is a 20% fall — same 20 units, two different percentages. Below: why the base decides everything and how to spot the trap options.

Choose your difficulty

Pick a level to start playing. You can switch at any time.

How to play

Read the before and after values, then tap the percentage change.

Tip: your progress and best score are saved in this browser only.

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What you are actually practicing

A percentage change always has the same shape: it compares the difference to the starting value, never to the ending value. Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is a 20% decrease — the same 20 units, two different percentages, because the base changed.

That single fact is where almost everyone goes wrong, and it is what this game drills.

How the game works

You are shown a before value and an after value, and four percentages. Pick the percentage change. A wrong pick reveals the right one immediately.

Easy uses increases from round starting values. Medium mixes increases and decreases. Hard uses larger changes, up to a doubling.

The relationship worth knowing

Percent change = difference ÷ original × 100. From 80 to 100: the difference is 20, and 20 ÷ 80 = 0.25, so the change is +25%.

The base is always the original. From 100 down to 80: 20 ÷ 100 = 0.20, so -20%.

Strategies that actually raise your score

Divide by the original, not the new value. Under a countdown the tempting move is to divide by whichever number sits on the right. That is exactly the error the wrong options are built from.

Anchor on ten percent. Ten percent of the original is easy to compute; then count how many of those fit into the difference. From 80 to 100 the difference 20 is two-and-a-half tens of 80, so 25%.

Check the direction first. If the second number is larger the answer must be positive; if smaller, negative. Options with the wrong sign are wrong before you divide.

Use doubling and halving as landmarks. Doubling is +100%, a rise by half is +50%, a rise by a quarter is +25%. Recognising the landmark skips the arithmetic entirely.

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