Leo+DadMade for Leo
Solving Problems Involving Percentages
Rung 3 of 4 · The traps

The Traps Everyone Falls Into

Three slips cost more percentage marks than anything else. Once you've seen each one happen, it's hard to fall for it again.


ExploreFlip between the three traps up top. Push the numbers around and watch each one bite.
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Percentages feel friendly until they don't. These three traps look obvious written down, but they catch nearly everyone in the heat of a question — so let's watch each one happen.

Trap 1 — Up Then Down Doesn't Return You Home

Here's the famous one. A $100 jacket goes up 20% to $120. Then it's marked down 20%. Back to $100? Nope — you land on $96. Why? The 20% increase was taken of $100, but the 20% decrease was taken of the bigger $120, so the cut is bigger than the bump. Same percent, different wholes. In the toy, run "up then down" and watch it always finish short of where it started.

Say it plainly: +20% then −20% is not back to the start, because the second percent is taken of a different number. Percentage changes don't simply cancel.

Trap 2 — a Percentage of which Whole?

"10% off" sounds like a fixed amount, but it isn't — it's 10% of some whole, and you have to know which. 10% of 50 = 5, but 10% of 80 = 8. Same percent, totally different dollars. Whenever you see a percentage floating around, your first question should be "percent of what?" The toy puts two wholes side by side so you can see the same 10% give two different sizes.

Trap 3 — Turning % into a Decimal

To use a percent on a calculator you convert it to a decimal, and the classic slip is dividing by 10 instead of 100. Per cent means "out of 100", so you always divide by 100: 35% = 35/100 = 0.35, not 3.5. Slide the decimal point two places left, not one. Going back the other way, multiply by 100. Practise a few in the toy until the two-places move is automatic.

Us, Thinking Out Loud

Why doesn't "+20% then −20%" bring the price back?

Next time we see "% off", what's the first question to ask?