How to calculate percentages

Percentage calculation formula donkey? What does this have to do with each other??

Donkeys are stubborn creatures. And donkeys need mnemonic devices. Because the animals are extremely afraid of water. They don’t want to go through even the smallest streams and watercourses, even if the water barely reaches their hooves. In order for them to get to the other side of the bank, small bridges and crossings have to be built for these animals. And these bridges for the donkeys are called "mnemonic bridges".

So that’s where the name comes from: mnemonics help you to grasp a difficult and challenging passage. We use the term mostly in the context of a "mnemonic".

And such a mnemonic I explain to you for the percent formulas.

It is a mnemonic that is rarely if ever talked about in mathematics classes. Teachers do not like this kind of mnemonic. It is too simple and too easy to use. And because you don’t have to transform anything and don’t have to memorize any formulas, this mnemonic is probably just not "mathematical" enough.

As a math teacher, however, I give you the following warning: The mnemonic does not help you to understand the percent calculation better. It only helps you to apply the formulas of the percentage calculation. If you want to fundamentally understand the calculation of percentage, percent value and basic value, you really need to read this article: Percentage Calculation – The Basics Explained Simply

The percentage formulas – that’s what it’s all about

Before I explain the mnemonic, I want you to remember the percent formulas. Depending on the textbook and math teacher, these are formulated and presented a little differently.

Please remember the following:

Distinguish the percentage p% well from the percentage p. The percentage p denotes only the numerical value (for 30% this is the number 30). With the percentage p%, the percentage must always be divided by 100 (30% = 0.3). The percentage p% corresponds to a decimal number!

Why is it like this?

The word "percent" translates as per 100. So, for example, if we talk about 30%, the 30% stands for 30 per hundred. But that is the same as 30 hundredths or 30 divided by 100, which is 0.3 results in. An example should clarify this:

The value of your shares has increased by 12% this year.

The percentage p corresponds to the numerical value 12, the percentage 12% corresponds to the decimal number 0.12 (divided by 100). Why is this remark so important in connection with the percentage formulas??

In every percentage formula the number "100" occurs. Multiplying by or dividing by 100 simply converts the percentage into the percentage (and vice versa).

If you write a percentage formula with the percentage p%, the number "100" does not appear in the formula. The percentage already corresponds to the decimal number, i.e. the percentage divided by 100.

Percentage formula (W)

The formula for the percentage value therefore exists in two variants, expressed with the percentage p:

or directly expressed with the percentage p%:

Percentage formula (p%)

You calculate the percentage p as follows:

or directly the percentage p%:

Basic value formula (G)

The formula for the basic value G is written with the percentage p:

And formulate with the percentage p%:

With this, we have everything together to understand the ingenious mnemonic.

Percentage calculation formula: The mnemonic

And this is how the mnemonic works:

Percentage formula

This triangle says W for the Percentage value , p% for the Percentage (attention decimal number) and G for the Basic value . You need to memorize the arrangement of these letters in the triangle: W is in the top, p% is in the bottom left, and G is in the bottom right.

How does this triangle help you now with the formulas in the percentage calculation??

In every percentage problem, we are looking for either the percentage value, the percentage or the basic value.

Cover in the triangle with your finger the size you are looking for. The still visible part of the triangle tells you how to calculate the quantity you are looking for.

For example, if you want to know how the formula for the percentage p% works, just cover the lower left corner with the p%.

Percentage formula

The visible part of the triangle is the percentage W at the top and the base value G at the bottom right. The horizontal bar is to be read as a fraction (i.e. a division).

For the percentage p% you calculate: p% = W/G

You proceed exactly the same way if you want to calculate the basic value G: Cover the letter G with your finger. The triangle now still shows W/p%. So the formula is G=W/p%:

Base value formula

And exactly the same for the percentage W. If you cover W with your finger, the triangle shows the correct calculation: W=p% – G.

Percentage formula

Examples of use

I’ll show you the foolproof application of this triangle with a few examples:

Example 1:
A garment costs 80€ (G) at regular price and is labeled with 15% (p%) discount. How many euros do you save?
Solution : We are looking for the percentage W. In a first step we write the percentage as a decimal number: p% = 0.15 (15 divided by 100). You cover W in the triangle with your finger and read: W = p% ⋅ G = 0.15 ⋅ 80€ = 12€.

Example 2:
40% of the people (p%) in a tour group buy a ticket for the boat trip. 8 tickets (W) are bought. How many people does the travel group consist of?
Solution : We are looking for the basic value G. Again, we write the percentage as a decimal number first: p% = 0.40. Then we cover in the triangle the quantity G we are looking for and read off: G = W/p%. This gives calculated: G = 8/0.4 = 20. The group consists of 20 people.

Example 3:
A plot of land has a size of 800 m 2 (G). 300 m 2 (W) may not be built over. What is the percentage?
Solution : If the basic value and the percentage value are known, the percentage is to be determined. We cover the percentage p% in the triangle and read off: p% = W/G. Calculated this results in: p% = 300/800 = 0.375. We multiply this decimal number by 100 and get the percentage 37.5.

Percentage formula mnemonic

How to continue?

Do you want to download the mnemonic as a copy template (free of charge)? Then get the pdf here:

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