﻿ Percentage — Math18

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# Percentage

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## What is the percentage?

Percentage is a way of representing the parts of an integer, as is the case with decimal numbers and fractions. In some cases it is easier to write the percentage than the fraction. Mentioning "percentage of" or "percent of" actually refers to saying "for every 100".

### Symbology of the percentage

Its symbol is represented by a diagonal and two circles as shown:

%

## How to calculate the percentage?

In order to calculate the percentage first it is important to first master the fractions, since it is a simpler way of representing a mathematical problem or calculation. Once the fractions are mastered, the percentage can be expressed as a fraction, all you have to do is divide the percentage by 100.

If we are told the percentage of a quantity we can represent the solution as a fraction problem.

Examples:

A) The 50% of 20 can be expressed as:
20 x
50
/ 100
= 10

B) The 20% of 10 can be expressed as:
10 x
20
/ 100
= 2

C) The 15% of 200 can be expressed as:
200 x
15
/ 100
= 30

As you can see, it is a very simple operation and can also be applied if the percentage is greater than 100%.

Examples:

A) The 125% of 30 can be expressed as:
30 x
125 / 100
= 37.5

B) The 200% of 20 can be expressed as:
20 x
200 / 100
= 40

C) The 105% of 5000 can be expressed as:
5000 x
105 / 100
= 5250

Note: As you can see, when the% (percentage) to be calculated is less than 100% the result will be less, if it is 100% then the value remains the same and if the% (percentage) to be calculated is greater than 100% the result will be of greater value.

In some problems you can ask to calculate the total amount, having the percentage and its equivalent, in these cases we only make an accommodation of the mathematical equation, therefore, the main unit is multiplying 100 by the percentage value.

Examples:

A) If 5 is 50%, you want to calculate the total amount:
5 x
100 /
50
= 10

B) If 10 is 20%, you want to calculate the total amount:
10 x
100 /
20
= 50

C) If 8 is 10%, you want to calculate the total amount:
8 x
100 /
10
= 80

Another type of problem consists in finding the equivalent percentage of a quantity, for this the unit must be multiplied by 100 by the total quantity, obtaining as a result the percentage.

Examples:

You want to find the percentage that equals the unit with respect to the total amount.
A) Assuming 2 is the unit and 10 is the total amount:
2 x
100 /
10
= 20%

B) Assuming 4 is the unit and 40 is the total amount:
4 x
100 /
40
= 10%

C) Assuming 10 is the unit and 20 is the total amount:
10 x
100 /
20
= 50%

## Trick to calculate the percentage

When considering the different problems that may exist to calculate the percentage it is possible to summarize everything in a formula, considering that the clearance must be done correctly depending on the variable to be calculated.

(Total quantity) x
(Percentage) /
100
= (Given unit)

By placing the data in the previous equation it is possible to obtain the requested value of a problem, this requires a clearing of the variable.

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