We explain what a percentage is, what it’s used for, how to express it, and how to calculate it. We also offer several practical examples. Please read other MTV articles for more information. If you share it, it will be of little help to us.
What is a percentage?
In mathematics and statistics, a percentage is the expression of a given quantity as a fraction of one hundred (100) equal parts. More simply put, a percentage is the proportional relationship between two units or between a unit and a set of units, expressed in terms of x per 100 units, that is, percent (literally: so much per hundred or so per hundred).
Conventionally, percentages are expressed with the % sign accompanying the percentage figure: 25% (a quarter), 50% (half), or 100% (all). Therefore, with these types of mathematical expressions, we can indicate how much one figure represents of another or of the total of a set of elements.
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For example, if we have one hundred apples in a bag, that total represents 100% of the apples (i.e., 100 apples out of every 100); if we give fifty apples to a friend (50 out of every 100 initial apples), we will then keep 50% of what we had, that is, half; and if 25 apples out of that half turn out to be damaged (25 out of every 100 initial apples), we will end up with only 25% of the initial figure, that is, a quarter of the total.
Percentages are extremely useful for expressing proportions and comparing fractions with others. For this reason, they are often used in various disciplines, such as statistics, demography, and ecology, among many others. In fact, their practical origin in the West dates back to the 15th century, as a tool for calculating taxes owed to the crown, as establishing percentages is much simpler and more practical than working with fractional figures.
For example:
- 1/1 equals 100/100, that is, 100% of the total.
- 1/10 equals 10/100, that is, 10% of the total.
- 1/100 equals 0.1/100, that is, 1% of the total.
And by the same logic:
- 1/2 equals 50%.
- 1/4 equals 25%.
- ⅔ equals 66.6%.
However, percentages can be expressed in whole or fractional figures, and arithmetic operations can be performed between them, as long as we keep in mind that a percentage does not express an exact figure, but rather a proportion. Therefore, if the reference point of comparison increases or decreases, the percentage will logically be affected.
For example, returning to the previous case of apples, if out of 100% of the available apples (100 apples in total), someone eats 3 without us realizing it, the 100% will go from 100 apples to 97. Therefore, when we give 50 to a friend, we are no longer giving them 50% of the apples, but 48.5%.
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How to calculate a percentage?
To calculate the percentage of a number, we must multiply the number by the desired percentage and divide the total by 100. For example, if we want to know what 30% of 450 is, we simply multiply 30 x 450 and divide the result by 100, which means that 30% of 450 is 135.
Another way to approach this calculation is to establish a rule of 3, as follows:
Since 100% is 450,
then 30% is x.
To solve for the unknown (x), we must multiply diagonally (30 x 450) and divide horizontally (by 100). This means that x = (30 x 450) / 100, or x = 135.
Practical Examples of Percentages
The following are some practical examples of how percentage calculations are applied:
- A worker wants to know how much tax is deducted from his salary. The company informs him that approximately 15% of his monthly salary is withheld. Given that his salary is 1,500.00 pesos, how much tax is deducted monthly? What is the actual amount he receives?
Answer: If his total monthly salary (i.e., 100%) is 1,500 and they deduct 15%, we must multiply 15 x 1,500 and then divide by 100. This equals 225.00 pesos after taxes. This means that instead of receiving 1,500 pesos each month, the employee actually receives 1,275 pesos.
- Another employee from the same company listens to his colleague in the previous example and wants to find out how much is being deducted in taxes. Since he has much more seniority at the company, his salary is higher (2,200.00 pesos), but he only receives 1,870.00 pesos monthly. How much is being deducted in taxes? What percentage of his salary is withheld?
Answer: If the employee’s total salary (100%) is 2,200.00 pesos, but he only receives 1,870.00 pesos, this means that 330 pesos are being deducted in taxes every month. Knowing that 100% of the salary is 2,200.00 pesos, we can calculate the percentage of the withheld 330.00 pesos by multiplying 330 x 100 and dividing by 2,200. This means that the worker is withheld the same 15% in taxes as his colleague.
- The following month, at the same company, managers announce a 7% general salary increase to address inflation. The same two workers then want to calculate how much this increase will represent for each of them, how much their new salary will be, and how much they will pay in taxes going forward.
Answer: Since the increase will be a percentage (7%), the exact figure will vary depending on each worker’s salary.
Let’s start with the employee earning 2,200.00 pesos (100%), who will receive a raise of (7 x 2,200) / 100 pesos, or an additional 154.00 pesos. Their new salary will be 2,200 + 154 pesos, or 2,354 pesos. Since we already know that the monthly tax represents 15% of the salary, we can recalculate how much tax will be withheld from them going forward: if 2,345 pesos is the new 100%, the 15% tax will then be equivalent to (15 x 2,345) / 100 pesos withheld, or 351.75 pesos in taxes.
This means that after the raise, they will actually receive 2,345 – 351.75 pesos, equivalent to 1,993.25 pesos after the withholdings.
On the other hand, his colleague, who earns 1,500 pesos (100%), will receive a raise of (7 x 1,500) / 100 pesos, or only 105 pesos more. His new salary will be 1,500 + 105 pesos, or 1,605 pesos, and the 15% tax on his new salary will then be (15 x 1,605) / 100 pesos withheld, or 240.75 pesos in taxes.
Similarly, after the raise, he will receive 1,605 – 240.75 pesos monthly, equivalent to 1,364.25 pesos after deductions.
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References
All the information we provide is supported by authoritative and up-to-date bibliographic sources, ensuring reliable content in line with our editorial principles.
- Percentage on Wikipedia.
- How to Find the Percentage of a Number in the newspaper Clarín (Argentina).
- Finding a Percent (video) on Khan Academy.
- Percents (%) on Math is Fun.
- Percentage definition, Concept, function, expression, calculation, and examples – concepto.de
