There are different ways to name or write the same value: fractions, percentages and decimals. For example, if we talk about a half, we can write:
- As a fraction: 1/2
- As a percentage: 50 %
- As a decimal: 0.5
It is possible to convert one of these forms to another, that is, convert fractions to percentages or vice versa, among others.
Fractions to percentages
If we want to convert a fraction to a percentage, we must follow the following steps:
- We convert the fraction to a decimal. This is accomplished by dividing the numerator by the denominator.
- We multiply the value by 100.
- We end our value with the % symbol.
Example: Convert the fraction 2/5 to a percentage.
By dividing the numerator by the denominator we obtain:
2/5 = 0,4
We multiply this value by 100 and add the percentage sign to it:
0.4 × 100 = 40 %
There is another method that we can use:
- Determine a number that, when multiplied by the denominator, results in 100.
- We multiply the numerator and denominator by that number.
- We write the number that results in the numerator followed by the symbol %.
Let's use the fraction of the previous one as an example: 2/5.
A number A that when multiplied by 5 results in 100, is 20.
A × 5 = 100
A = 100/5 = 20
We multiply the numerator and denominator by 20:
(2 × 20) / (5 × 20) = 40/100
The result is 40 %.
Percentages to fractions
If we want to convert a percentage to a fraction, we must follow the following steps:
- We divide the percentage by 100. If this is not an integer, instead of doing the above, we multiply up and down by 10 once for each number in the decimal point.
- We simplify the fraction, if necessary.
Example 1: express 42.5 % as a fraction:
Let's see that the percentage is not an integer, therefore, we multiply up and down once by 10 (because there is only one decimal number):
(42.5 × 10) / (100 × 10) = 425/1000
We simplify the previous fraction:
425 / 1000 = 17 / 40
Example 2: express 72% as a fraction:
Let's see that the percentage is an integer, therefore, we divide it by 100 and then simplify:
72/100 = 18/25