**Can you explain percentages so simply that everyone understands them?? We try it here. Imagine a student comes to his grandmother after school and tries to explain to her how calculating with percentages works. Do you think a real granny would understand the following explanations?**

**Student**: Tomorrow there will be a 20 percent discount when you go shopping. Do you know what that means?

**Granny**: That it becomes cheaper?

**Student**Yes. We recently learned in school how calculating with percentages works. Do you still know how?

**Grandma**: No. No idea. So roughly I know what should come out, but really I can not calculate it anymore.

**Student**: Let’s start with what a percent is in the first place. A percent is nothing else than 1 divided by 100. One abbreviates thereby percent with %. This also means that 21% is nothing else than 21 : 100.

**Granny**If it says that 50% of the people in a room are men, it means that 50 out of 100 people in the room are male?

**Student**: That would be one way. But it could also be 100 out of 200 people male or 5 out of 10 people. In percentage calculation, you basically give a calculated percentage of 100.

Once you understand this article, ask yourself this question: can you solve percentage calculation problems by yourself? Find out with our questions and exercises on this topic. Continue to the first task Percentage calculation.

**Formula and example percentage**

**Student**Let’s take the discount example again. Let’s say something to eat costs 1.69 euros. From tomorrow there will be a 20 percent discount on it. How much cheaper will it be?

**Grandma**Well that is a few cents less it costs.

**Student**: True. I think we need now once the formula for the percentage calculation. We would like to calculate a share, this is called percentage W. We know how much discount there is, i.e. the percentage it gets cheaper. You abbreviate it with p %. And we know what it originally cost, so the base value G.

**Granny**I still do not quite understand. Do the math.

**Pupil**We take the following formula and insert 20 % – because that’s how big the discount is – and we insert the basic value G with 1,69 Euro. After that we only have to calculate. From the 20 % we make 20 : 100. After that we can – no matter if with or without calculator – simply calculate the discount of 0,34 Euro.

**Granny**: But it does not say discount but W.

**Pupils**The W is the percentage value, that is the share of the whole that we wanted to calculate.

**Granny**: OK. That means we don’t have to pay 1,69 Euro anymore, but we get 0,34 Euro discount on it.

**Student**: That’s it. Instead of 1,69 Euro we only have to pay 1,35 Euro.

**Formula and example percentage**

**Student**Let’s continue with the introduction to the percentage calculation.

**Granny**Please continue with an explanation for the stupid ones.

**Pupil**Suppose we do not know that it has become 20 % cheaper. We would know instead that it has become 0.34 euros cheaper and it cost 1.69 euros before. Do you know now how to get the 20 % discount?

**Grandma**: No idea. There must be a formula for this?

**Pupil**Actually we have to change the formula of the percentage calculation only after the percentage and calculate it. Means we need the formula converted to p %. Here again, the share of the whole is the percentage value W with 0.34 euros and in total we have the basic value G with 1.69 euros. We insert this and calculate.

**Granny**: There is the 20 percent discount again. And if I have the price before and after?

**Pupils**Then we have again the basic value G with 1,69 Euro. The new price after the discount was 1,35 Euro. This is our share of the whole, the percentage W.

**Granny**But now the result is 80 percent?

**Student**: Clear. The price has fallen from 100 percent to 80 percent.

**Formula and example basic value**

**Pupil**We have forgotten a third possibility.

**Granny**: We don’t know what the food cost before the discount.

**Pupils**: Exactly. The reduced price is 1.35 euros and the discount was 20 percent. What did the meal cost originally?

**Granny**Again some formula for the percentage calculation?

**Pupils**Yes, this time converted to G. We set the percentage of the whole with W = 1,35 Euro. This price is 80 percent of the basic value (20 percent discount).

**Grandma**So that I understand correctly: The 1.35 euros are 80 percent of the price. And the 1,69 Euro are 100 percent of the price, so the original price?

**Student**: That’s it.

**Apply percentage calculation**

**Grandma**I think I understood the examples. What else do you need percentages for??

**Pupil**The interest calculation is the most important application of the percentage calculation. This is for example to calculate interest on financial investments. The next application is the rule of three. But to explain this is a separate topic. We will do that another time.

**Grandma**OK. So I remember that you can really use the percentage calculation in real life.

**Pupil**Yes, sometimes you even do something for reality in mathematics lessons.

**Grandma**I suppose such things are also asked in the recruitment test?

**Student**: That’s what the teacher once said. But I still have a little time before I sit there.

**Granny**: What do students do wrong when calculating percentages??

**Pupil**I think many people don’t realize that 1 percent is nothing more than a hundredth of a percent. Or they can not even think roughly without a calculator, what comes out as the result. Sometimes when calculating you get something completely wrong and if you don’t understand the subject and can’t estimate, you don’t even see that the calculator is giving crap.