🏷️ Percentages
Percentages in the Wild
The number on a sale sign isn’t how many euro you save, and it’s easy to mix the two up.
A shop window says 25% off.
It’s easy to think that means €25 off.
If you think that, you’ll expect to save far more than you do.
Start here
Meet the €40 hoodie
Sale rails, battery bars and match stats all use the same word: per cent, which means out of every hundred. Lots of people read “25% off” and think “€25 off”, and this hoodie shows why that’s wrong.
Your turn. Drag the bar (or tap the buttons) and watch what a discount does to the price: how much you pay, and how much comes off.
25% off
Every 1% you drag takes another 40 cent off. The per cent tells you what share of the price comes off.
How much comes off a €40 hoodie at 25% off?
Pick a number and stick with it.
The trap
The €25 mistake
A sign says 25% off a €40 hoodie. How much comes off? Pick your answer before you see the working.
Here’s €40 cut into quarters, and 25% is exactly one of them:
The word itself tells you how it works.
Per cent means per hundred.
The why
Per cent means per hundred
If you split the €40 into 100 equal chips, each chip is worth 40 cent, and that’s 1%. Every percentage is a number of these chips. Drag across the grid to pick your own.
25%
25 chips × 40c = €10.00
If you find 1% first, you can make any other percentage by counting up chips. That works for every percentage sum.
Doing the sums
The 10% trick
You don’t need a calculator in a shop. Find 10% first (move the decimal point one place left), then work up or down from there. It works for any price and any per cent, and you’ll see the tempting answer next to the right one.
There’s one more thing that trips people up.
A percentage is always a percentage of something.
The same per cent gives a different amount depending on what it’s a percentage of.
Going down and back up
20% off, then 20% on, doesn’t take you back to the start
A €50 pair of trainers goes into the sale at 20% off. A week later the shop puts the price back up by 20%. It sounds as if the price should end up where it started, so try it and see.
€50.00
Before you press anything, guess: will it end up back at €50?
Your battery at 37%, a test mark of 82% and “up to 70% off” are all percentages.
Each one tells you how many out of a hundred.
To make sense of any of them, ask per cent of what?
One more thing
You’ll see percentages all over the place: your battery at 37%, 82% on a spelling test, “up to 70% off” on a shop window, and the VAT included in every receipt. Each one tells you how much out of every hundred, and the question to ask about any of them is per cent of what?
If someone tells you 25% off €40 saves €25, ask them what the 25 is out of and let them work it out.