We explain what a percentage is, what it is for, how it is expressed and how it is calculated. In addition, we offer you various practical examples.
What is a percentage?
In math Y statistics, the expression of a given quantity as a fraction of one hundred equal parts is called a percentage. Said more easily, the percentage is the proportionality relationship between two units or between a unit and a set of them, expressed in terms of x for every 100 units, that is, of so much percent (literally: so much For each hundred or every hundred).
Conventionally, the percentage is expressed with the sign %, accompanying the percentage figure: 25% (a quarter), 50% (a half) or 100% (all). Therefore, with this type of mathematical expressions it is possible to indicate how much one figure represents of another or of the total of a set of elements.
For example, if we have a hundred apples in a bag, that total number represents 100% of the apples (that is, 100 apples out of 100); if we give fifty apples to a friend (50 out of every 100 initial apples) then we will 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 compare some fractions with others. For that reason they are often used in different disciplines, such as statistics, demography and the ecology, among many others.In fact, its practical origin in the West dates back to the 15th century, as a tool for calculating taxes that corresponded to the crown, since it is much simpler and more practical to establish percentages than to operate 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:
- ½ equals 50%.
- ¼ equals 25%.
- ⅔ equals 66.6%.
However, percentages can be expressed as whole or fractional figures, and arithmetic operations can be performed between them, as long as it is taken into account that a percentage does not express an exact figure, but rather a proportion. So if the comparison benchmark increases or decreases, the percentage will logically be affected.
For example, going back to the previous case of apples, if out of 100% of the available apples (100 apples in total) someone eats 3 without us noticing, 100% will go from 100 apples to 97. Then, when we give 50 to a friend, we are no longer giving him 50% of the apples, but 48.5%.
How to calculate a percentage?
To calculate the percentage of a number we must multiply the number by the desired percentage and divide it all by 100. For example, if we want to know how much 30% of 450 is, we just multiply 30 x 450 and divide the result by 100, which which returns that 30% of 450 is 135.
Another way to approach this operation is to establish a rule of 3, as follows:
since 100% is 450
so 30% is X
To clear 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 applying the calculation of percentages:
- A worker wants to know how much he is deducted from taxes when he collects his salary. In the company they inform him that approximately 15% of his monthly salary is withheld. Given that said salary is 1,500.00 pesos, how much do they take out of tax monthly? How much is the figure that he actually charges?
Answer: If your total monthly salary (that is, 100%) is 1,500 and 15% is taken away, we must multiply 15 x 1,500 and then divide by 100. That is equivalent to 225.00 pesos deducted from taxes. Which means that the worker, instead of receiving 1,500 each month, actually receives 1,275.
- Another worker, from the same company, listens to his colleague in the previous example and wants to find out how much he is deducted for taxes. Since he has much more seniority in the company, his salary is higher (2,200.00 pesos), but he only receives 1,870.00 a month. How much do they take out of taxes? What percentage of his salary does the withholding represent?
Answer: If the employee's total salary (100%) is 2,200.00 pesos, but he receives only 1,870.00, it means that 330 pesos of taxes are deducted every month. Knowing that 100% of the salary is 2,200.00 pesos, we can calculate what percentage the 330.00 pesos withheld represent by multiplying 330 x 100 and dividing it by 2,200. This means that the worker is withheld for taxes the same 15% as his or her co-worker.
- The following month, at the same company, the managers announce a general salary increase of 7% to deal with inflation. The same two workers want, then, to calculate how much this increase will represent for each one, how much their new salary will be and how much they will pay in taxes from now on.
Answer: Since the increase will be a percentage (7%), the exact figure will vary depending on the salary of each worker.
Let's start with the employee who earns $2,200.00 (100%), who will receive a raise of (7 x $2,200) / $100, or an additional $154.00. His new salary will be 2,200 + 154 pesos, that is, 2,354 pesos. Since we already know that the monthly tax represents 15% of salary, we can calculate again how much will be withheld for taxes going forward: if 2,345 pesos is the new 100%, then 15% taxes will be equal to (15 x 2,345) / 100 pesos withheld, that is, at 351.75 pesos of taxes.
This means that after the increase he will actually receive 2,345 – 351.75 pesos, equivalent to 1,993.25 pesos once the withholdings have been made.
Instead, your partner who earns 1,500 pesos (100%) will receive a raise of (7 x 1,500) / 100 pesos, that is, only an additional 105 pesos. His new salary will be 1,500 + 105 pesos, that is, 1,605 pesos, and the 15% tax on his new salary will then be (15 x 1,605) / 100 pesos withheld, that is, 240.75 tax weights.
Similarly, after the increase, he will receive monthly 1,605 – 240.75 pesos, equivalent to 1,364.25 pesos once the withholdings have been made.