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.
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.