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Percentage(%) can define as the process of expressing a proportion, that is, the ratio between a pair and a whole. We always use the number 100 to establish this proportion. We can, therefore, say that a percentage is perceived as a fraction but with 100 as the common denominator. It is represented by the following symbol %.

The % is used in several situations: an upward or downward trend; the evaluation of a partial or total value (but starting from a partial value and a percentage or %); the calculation of a rate of change or the evaluation of a ratio between two numbers.

Calculating a percentage can be complicated if you don’t have the right method! Our certified teacher offers you a simple, quick, and clear explanation for percentage calculations: increase, decrease, find the percentage of the value, and vice versa. Follow the guide! We have also added examples to help you understand better.

Calculating a percentage reduction is very useful on a daily basis, for example, for calculating a discount during sales.

To calculate a decrease in y %, we use the following formula:

Base sum x (1 – y / 100)

Note: “(1 – y / 100)” is called the Multiplier Coefficient.

Example of discount calculation: During the sales period, a 30% discount is applied to the price of pants. The pants are initially worth 70 euros. How much is the reduction? How much do the pants cost once the discount is applied?

Answer = 70 x (30/100) = 21 euros

The amount of reduction is 21 euros. The value corresponding to the discount % has been calculated here.

Answer = 70 x (1 – 30/100) = 49 euros

After reduction, the price of the pants is 49 euros

Here is how to calculate a percentage(%) change (or “change rate”).

To calculate an increase in y%, we use the following formula:

Base sum x (1 + y / 100)

Note: “(1 + y / 100)” is called the Multiplier Coefficient.

Example of increase calculation: The Dog of War video game costs 35 euros. Its price increases by 12%. How much is the increase? What is the price of the game after increasing the price?

Answer = 35 x (12/100) = 4.20 euros

The amount of increase is € 4.20.

Answer = 35 x (1 + 12/100) = 39.20 euros

The price of the game has increased from € 35 to € 39.20 with the increase.

To calculate the % of a value, we use the following formula:

(100 x partial value) / Total value

If the partial value is greater than the total value, the percentage(%) will be greater than 100%

If the partial value is less than the total value, the percentage will be less than 100%

Example of calculating the percentage of value: in a class of 30 students ( total value ), 12 are girls ( partial value ). What is the percentage of girls in this class?

Answer = (100 x 12) / 30 = 40%

The percentage of girls in this class is 40%.

To calculate the numerical value of a %, we multiply the total value by the percentage or % / 100. In other words:

Total value x (percentage / 100)

Example of calculating the numerical value of a percentage: In a college of 400 students ( total value ), 28% of the students are in the 3rd. How many students from this college are in the 3rd?

Here we must, therefore, find how much is 28% of 400

Response = 400 x (28/100) = 112

There are, therefore, 112 students in the 3rd grade in this college.

Theoretically, when you calculate the percentage of a value, you use a precise formula, which amounts to multiplying the partial value by 100 and dividing the result obtained by the total value.

(100 x partial value) / total value

However, in a few cases, it is possible to perform much simpler operations, which can be done head-on (and therefore without a calculator!). Here are the main methods to know:

- Calculating 50% of the value is equivalent to dividing it by 2.
- To get 25% of a number, just divide it by 4.
- Calculating 20% of the value is equivalent to dividing it by 5.
- 10% of a number is the same as dividing it by 10.
- To find 5%, just divide the value by 20.
- Calculating 1% of a number is like dividing it by 100.

Thanks to these techniques, it is possible to calculate somewhat more complex percentages:

- 4% of value equals 4 x 1% thereof.
- 15% of a value = 10% of that value, plus 5% of the initial value.
- 60% of a value = 50% of that value, plus 10% of the initial cost.
- 60% of a number also amounts to calculating 3 x 20% of it.
- 75% of a value = 50% of that value, plus 25% of the initial value, etc.

With a little practice, you will rapidly be able to do all these calculations faster and faster.

To practice, you can simply take a random number each day and try to calculate several percentage or % values of that number, head.

At first, it will probably be a bit difficult if you are not too trained in mental arithmetic, but you will be surprised at the progress you will make in a short time!

On a daily basis, we frequently have to use percentages. In the field of commerce, it is by this means that professionals apply a discount on the price of a product.

But it also makes it possible to determine a proportion. For example, the number of students who obtained the baccalaureate is generally presented as a percentage (we will then speak of the success rate).

Whether in a private or professional setting, it is therefore very useful on a daily basis to know how to calculate a percentage or %, and it is even more practical (and impressive!) To know how to do it head-on.

In statistics, the population studied is divided into a class of individuals satisfying the same criteria (same number of children, same political preference, same income bracket, etc.). When the size of the population is too large, or when you want to compare two populations, working on class sizes makes interpretation of the results sometimes difficult. Reducing this to a population of 100 is equivalent to presenting the distribution in the form of percentages. We then speak of frequencies.

Percentages(%) are found in opinion polls when the surveyed population is rarely 100 people. They are also found in election results.

In finances, we find the percentages in the VAT calculations: a VAT of 19.6% consists of adding to a price excluding tax (price excluding tax) a tax corresponding to 19.6% of the price excluding tax. We then obtain a price inclusive of all taxes (price including VAT), which corresponds to the price, excluding VAT multiplied by 1.196.

They are also found in interest rates: a sum invested or borrowed for one year at an interest rate of p% was multiplied at the end of the year by {\ displaystyle 1 + {\ dfrac {p} {100}}}1 + {\ dfrac {p} {100}}.

Tax rates that represent a fraction of a household’s income are also expressed as a percentage.

In economics, an index is the value of an economic quantity compared to a reference value. For example, if, in 2004, the average price of apartments per square meter in a city increased by 22% compared to the year 2000, serving as a reference (index 100), we will say that the index of the average price of apartments is 122 in 2004. The index is, therefore, a particular presentation of a percentage.

Road sign indicating a slope of 10% or an angle of 5.71 °

Road signs indicate the slopes of the roads as a percentage. A slope of 10% means that a horizontal displacement of 100 m corresponds to a vertical displacement of 10 m. The slope then corresponds to the tangent of the inclination angle of the road. Therefore, the tangent arc of the percentage gives the degree of inclination of the slope.

In metrology, measurements cannot be known with absolute precision. The error calculations or uncertainty calculations are often presented as a percentage. When we say that the weight of a can is known to the nearest 5%, it means that if the weight of the can is assumed to be 500 grams, there may be an error of 25 grams over or under.

In oenology, the alcoholic strength of an alcoholic drink is the percentage by volume of pure alcohol contained in a drink. Thus, if we take a glass of 100 ml of wine titrated at 12% vol, we absorb 12 ml of pure alcohol, i.e., approximately {\ display style 12 \ times 0.8 = 9.6}12 \ times 0.8 = 9.6 grams of pure alcohol.

The term degree taken instead of percentage comes from the old unit used: the Gay-Lussac degree (GL). A degree GL corresponding to a percentage or % of pure alcohol of 1%.

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