# Percentage calculation

For comparing two numbers and calculating discounts or interest you can use the percentage calculation. You can find out exactly what it is and how it works here. Have a look at our video!

• Percentage calculation simply explained
• Calculate basic value
• Calculate percentage
• Calculate percentage
• Percentage calculation triangle

## Percentage calculation simply explained

Imagine you have a bag of 100 potatoes and take out one. Then this potato is 1 of 100. Mathematically you can then say that the share of the single potato in all 100 potatoes is 1 percent (1%). 1 percent (1%) means the same as 1 : 100.

To calculate percentages you only need three quantities:

• The Basic value G is the whole of which you calculate the share. It always equals 100%. In the case of the potato sack, this would be the 100 potatoes.
• In contrast Percentage W a percentage of the basic value. Contrary to what you might expect, it is not written as a percentage. This corresponds to the single potato in the example.
• The Percentage p% tells you how big the percentage value is compared to the basic value. It is written down as a percentage and would be 1% in our example here.

You can also write the percentage p% without the percent sign. But then you call it the Percentage p . =40\,\%" /> so you can also use it as

=40" /> write.

## Calculate the basic value

Imagine you ask yourself how big your class is. You know 5 students correspond to 25% of your class. The answer to this question is the basic value. Here you can calculate the basic value by using the formula:

= \frac \cdot 100>< \textcolor

>\]" />

The 25% is the percentage and you can therefore use 25 for p. Then the 5 students must be the percentage value. Therefore, replace W with 5 and the task is as good as solved.

= \frac \cdot 100>

> = \frac \cdot 100>> \]" />

100 you can easily divide by 25 and get 4. It remains then only 5 times 4 and that is 20. So the basic value you are looking for must be 20.

And you know that your class as a whole consists of 20 students. The basic value is not difficult at all!

Here are a few more examples of how you recognize the basic value formula in questions:

• You buy a reduced trousers for 75€. Because the pants are reduced, you only have to pay 75% of the original price. How much did the pants cost without discount? (" />)
• You sell your bike for 60% of the money you bought it for. Your buyer pays you 90€. At what price did you buy your bicycle at that time? (" />)

## Calculate percentage

You can find the percentage value by asking, for example: How much is 20 percent of 50 euros?? So you are looking for a percentage of a whole. The whole thing is here the 50 euros and your share you can calculate with the following formula:

= \frac

\cdot \textcolor> \]" />

For your 20% use the number 20 in the formula and instead of G use your 50€!

= \frac

\cdot \textcolor>= \frac \cdot \textcolor>> \]" />

Because 50 is half of 100, you can easily divide it up ( = \nicefrac" />). You then only have to divide 20 by 2.

>> = 10\,\euro<>\]" />

The percentage value is equal to 10 Euro. You now know that 20 percent of 50 euros is exactly 10 euros. It was easy, wasn’t it?

So that you recognize the percentage formula in text tasks, here are two more examples:

• You get a 15% discount on a shirt that normally costs 20€. How much money do you save with the discount? (" />)
• Imagine that 20% of your class does not like to play soccer. How many students is that if your class has 25 classmates? ()

## Calculate percentage

If you’re wondering "What percentage is …?", then you are looking for the percentage. The percentage formula shows you how to calculate it by dividing the percentage value by the base value. Let’s look at the percentage calculation with another example: In an egg pack 3 of 10 eggs are missing. How many percent are still there?

= \frac>> \]" />

Calculating the percent is quite easy. You have 7 eggs left – this is your percentage value. In total there were 10 eggs – that’s your base value. Now you just have to put the two numbers into the right percentage formula.

= \frac>> = \frac>> \]" />

But how can you work it out as a percentage? You must extend the fraction so that there is a 100 under the fraction line. In our example . So multiply the 7 above and the 10 below the fraction line by 10 and you get your percentage in percent.

= \frac = 70\,\% \]" />

So there are still 70% of the eggs in the pack.

Here are two more examples of the percentage formula:

• A backpack costs 80€ in the store, but the salesman offers it to you for 60€. What percentage of the actual price you have to pay? (" />)
• Imagine you spent 16€ on a shirt. A friend paid 20€ for the same shirt. What percentage did you pay compared to your friend? (" />)