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 mathematics and statistics, a percentage is called the expression of a given quantity as a fraction of one hundred (100) equal parts. More simply put, 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, so much percent (literally: so much for each hundred or each hundred).
Conventionally, the percentage is expressed with the sign %accompanying the percentage figure: 25% (a quarter), 50% (half) or 100% (all). Therefore, with this type of mathematical expressions you can indicate how much one figure represents of another or of the total of a set of elements.
For example, if we have one 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) we will then keep 50% of what we had, that is, half; and if 25 apples of that half turn out to be damaged (25 out of every 100 initial apples), we will only end up with 25% of the initial figure, that is, a quarter of the total.
The percentages are extremely useful for expressing proportions and comparing some fractions with others. For this reason they are often used in different disciplines, such as statistics, demography and ecology, among many others. In fact, its practical origin in the West dates back to the 15th century, as a tool to calculate taxes that corresponded to the crown, since it is much simpler and more practical to establish percentages than to operate with fractional figures.
So, for example:
- 1/1 is equivalent to 100/100, that is, 100% of the total.
- 1/10 is equivalent to 10/100, that is, 10% of the total.
- 1/100 is equivalent to 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 in 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 number, but rather a proportion. So if the comparison reference increases or decreases, the percentage will logically be affected.
For example, and returning to the previous case of apples, if of 100% of the available apples (100 apples in total) someone eats 3 without us realizing it, 100% will go from being 100 apples to being 97. So, When we give 50 to a friend, we will no longer be 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 figure by the desired percentage and divide everything by 100. For example, if we want to know how much 30% of 450 is, we simply multiply 30 x 450 and divide the result by 100, which shows that 30% of 450 is 135.
Another way to approach this operation is set a rule of 3 as follows:
since 100% is 450
so 30% is X
To solve the unknown (x), we must multiply diagonally (30 x 450) and divide horizontally (by 100). This means that x = (30 x 450) / 100, that is, x = 135.
Practical examples of percentages
The following are some practical examples of applying percentage calculations:
- A worker wants to know how much taxes are taken from him when he receives his salary. The company informs him that approximately 15% of his monthly salary is withheld. Given that said salary is 1,500.00 pesos, how much tax is taken out monthly? How much is the amount you actually charge?
Answer: If the total of your monthly salary (that is, 100%) is 1500 and they take away 15%, we must multiply 15 x 1500 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 they take away in 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 monthly. How much do they take out of taxes? What percentage of your 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 taken away 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 buddy.
- The following month, in the same company, managers announce a general salary increase of 7% to address inflation. The same two workers then want 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 pesos (100%), who will receive an increase of (7 x 2,200) / 100 pesos, that is, an additional 154.00 pesos. Your new salary will be 2200 + 154 pesos, that is, 2354 pesos. Since we already know that the monthly tax represents 15% of the salary, we can calculate again how much they will withhold taxes from now on: if 2,345 pesos is the new 100%, the 15% tax will then be equivalent to (15 x 2,345) / 100 pesos withheld, that is, at 351.75 pesos of taxes.
This means that after the increase you will actually receive 2,345 – 351.75 pesos, equivalent to 1,993.25 pesos once the withholdings have been made.
On the other hand, your partner who earns 1,500 pesos (100%) will receive an increase of (7 x 1,500) / 100 pesos, that is, only 105 additional pesos. Your new salary will be 1500 + 105 pesos, that is, 1605 pesos, and the 15% tax on your new salary will then be (15 x 1605) / 100 pesos withheld, that is, 240.75 pesos in taxes.
Similarly, after the increase you will receive 1605 – 240.75 pesos monthly, equivalent to 1364.25 pesos once the withholdings have been made.
Continue with: Probability
References
- “Percentage” in Wikipedia.
- “How to get the percentage of a number” in the Clarín newspaper (Argentina).
- “Finding a percent” (video) on Khan Academy.
- “Percents (%)” in Math is Fun.
