The word percentage has its origin in the English "percentage", a term used to write numbers under the guise of a fraction of one hundred. The symbol of this concept is %, which is called “percent” and translates as “out of every hundred”. For example: Ten percent is a percentage that is written as 10% and is understood as ten out of every hundred. If it is said that 10% of a group of thirty people have red hair, the sentence assumes that three of those people are redheads.
In mathematics, a proportional portion of the number 100 is called a percentage, or percentage, therefore it can be expressed as a fraction. If we say 50% (this is the symbol that represents the percentage) it means half of a hundred; 100% is the total. If we say that 15% of the city works informally, there are 15 out of every 100 who do so, while 85%, by exclusion, would have access to the formal market, provided that it has been taken for the study, exclusively, the entire economically active population.
Percentage is a mathematical symbol, which represents a quantity given as a fraction into 100 equal parts. It is also commonly called a percent where percent means "out of every hundred units." It is used to define relationships between two quantities, so that the percentage of a quantity, where the percentage is a number, refers to the part proportional to that number of units of every hundred of that quantity.
The percentage is denoted using the symbol "%", which is mathematically equivalent to the factor 0.01 and must be written after the number to which it refers, leaving a separating space. For example, "thirty-two percent" is represented by 32% and means 'thirty-two out of every hundred'.
To calculate the percentage of a number we must take that figure and multiply it by the respective percentage and divide it by 100.
Example: if we have 130 students in an educational entity and we want to calculate 12% of that group, we must multiply 130*12/100=15.6.
On the other hand, if we seek to calculate the percentage between two figures, we must divide the smaller by the larger and multiply by one hundred.
Example: if we have 200 people and we want to know what percentage a sample of 30 people from said group is equivalent to, we must proceed as follows: 30/200*100=15%. Thus, we conclude that the sample is 15% of the 200 people.
When we want to calculate a certain percentage of a number, we multiply the percentage we need by the number, and then divide it by one hundred.
Example: 25% of 70 would be 70 x 25=1,750, and we divide that result by 100, which gives us: 17.50. On the calculator we would put 70 x 25%.
If you want to convert fractions to percentages, which makes it easier to understand the number in everyday life, we must first divide the numerator by the denominator, and then multiply that result by 100.
If you want to convert a percentage into a fraction, place the percentage number as the numerator and the number 100 as the denominator. As we see, any fraction or decimal number can be expressed in percentages, and vice versa.
Percentages were used, as early as the Roman Empire, to calculate taxes, and later it was extended to grant commissions to employees on their sales, to recharge accounts with compensatory or punitive interest, to determine how much they have risen or prices have been lowered, to know if profits have increased, to make sales, to make statistics, etc. Of course, when we make a discount, we will deduct the percentage from the total, and when we give a prize or incentive, or a surcharge, we will add it. So if an item costs $1,000, and we offer a 15% discount, we will sell it for $850, but if an employee earns $1,000 in salary and we increase them 15% for their good work performance, they will earn $1,150.
Converting percentages to decimal figures is simple if you keep in mind that 100% is represented as the number 1.
Therefore, 50% corresponds to the number 0.5. 16% corresponds to 0.16, and so on.
We can use the following formula: decimal figure = percentage/100.
Stating percentages as fractions follows the same formula or method.
For example, 35% corresponds to the fraction 35/100.
We can then simplify the fraction by dividing the numerator and denominator by the same number. If we divide the numerator and denominator of 35/100 by 5, we get: 7/20. This is the simplest representation of this fraction since we cannot further divide the numerator and denominator by the same number.
To clearly list the above we have created a useful table:
| Percentage | Decimal | Fraction |
|---|---|---|
| 100% | 1 | 1 |
| 90% | 0.9 | 9/10 |
| 80% | 0.8 | 4/5 |
| 75% | 0.75 | 3/4 |
| 66% | 0.66 | 2/3 |
| 60% | 0.6 | 3/5 |
| 50% | 0.5 | 1/2 |
| 40% | 0.4 | 2/5 |
| 33% | 0.33 | 1/3 |
| 30% | 0.3 | 3/10 |
| 25% | 0.25 | 1/4 |
| 20% | 0.2 | 1/5 |
| 10% | 0.1 | 1/10 |
To calculate what amount corresponds to a certain percentage discount, you must carry out a normal percentage calculation.
The formula for that is: discount = (P/100)*V
Where P is the discount percentage and V is the price.
For example: If you get a 13% discount on a price of $65, what is the amount of this discount? Discount = (13/100)*65 = $8.45. The final price will then be: $59.51.
However, if you receive a discount of a certain amount on a total price, what percentage discount is applied?
You can use this formula P = (100/V2)*V1
For example: you get a discount of $12 on a total price of $88. The discount percentage is then equal to (100/88)*12 = 13.64%