Percentages
One percent is one hundredth. With percentages you compare parts of different sizes and work out discounts and price rises.
Why
In one shop you get 15 euros off a 60-euro jacket, in another 20 euros off a 100-euro jacket. Where is the discount biggest?
20 euros is more than 15 euros, but it depends on the price the discount is taken from. Amounts of different sizes are hard to compare just like that.
Percentages solve this: you look at how much you would get per 100 euros. On the first jacket you get 25% off, on the second 20%. So the first discount is the biggest.
See it
Colour boxes in the 10 by 10 grid. Each box is 1%. See which fraction and which decimal belong to your percentage.
Description of the picture
A grid of 100 boxes with 25 of them coloured. Next to it is 25%=
Get it
Percent means per hundred. 35% is 35 out of 100, so 35/100 or 0.35.
To take a percentage of an amount, first find 1%: divide by 100. Then take that as many times as the percentage says. Handy shortcuts: 10% is dividing by 10, 50% is half, 25% is a quarter.
To find what percentage a part is, write it as a fraction of the whole and turn it into hundredths. 12 out of 50 is 12/50=
With a 20% discount you still pay 80%, so times 0.8. With a 5% rise you pay 105%, so times 1.05.
p% of an amount b is p/100×
Worked example
It is the sales. A pair of trainers costing 80 euros gets 30% off. How much do you still pay?
First find 1% of 80 euros.
80:
100= 0.8 The discount is 30 times as much.
30×
0.8= 24 Subtract the discount from the price.
80−
24= 56 Check: you still pay 70%, and 80×
0.7= 56. That works. - Answer
You still pay 56 euros.
Do it
Pick a level. You get a new exercise every time, checked straight away.
Pitfalls
Wrong: After 50% off and then another 50% off, everything is free.
The second discount is taken from the price that was already halved, not from the original price.
Right: 100 euros first becomes 50 euros and then 25 euros. So you still pay 25%.
Wrong: A price goes up by 10% and then down by 10%, so it is back where it was.
The drop is worked out on the higher price, so it is bigger in euros.
Right: 100 euros becomes 110 euros, and then 110×
0.9= 99 euros. Wrong: After 20% off you pay 40 euros, so the old price was 40 euros plus 20% of 40 euros, which makes 48 euros.
The discount was worked out on the old price, not the new one. 40 euros is 80% of the old price.
Right: Old price =
40: 0.8= 50 euros.
In real life
- In the sales a rack of clothes says −30%. You then pay 70% of the price.
- Your phone shows what percentage of your battery is left.
- A food label tells you what percentage of a product is fat or sugar.
- The weather forecast gives the chance of rain as a percentage, for example a 70% chance of showers.
History
The word percent comes from the Italian per cento: per hundred. Italian merchants and bankers were already working out profit and interest per hundred in the late Middle Ages. The sign % grew later out of an abbreviation of cento that writers kept making shorter.
At the table
Find a receipt or a leaflet with discounts together. What percentage off was it, and how many euros did you really save?
A question to talk about together, for parents and children. There is no wrong answer.