Question

How does a percent relate to a proportion

Answer 1

Percent means per hundred, which means, when you are using a percent, you are actually using a ratio to compare the number of your percent to one hundred.
For example, suppose we have 5%. The percent symbol (%) indicates that we are using a ratio to compare 5 to 100, and remember that we use fractions to express ratios, so we can express 5% as the ratio
`(5)/(100)`. Notice that we can simplify our ratio, both numerator and denominator are divisible by 5, so lets simplify it:
`(5)/(100) = (1)/(20)`. We can conclude that we can express 5% as the ratio
`(1)/(20)`.

Now that we know we can express a percent as ratio, lets show how the percent is related to a proportion:
Suppose that in a class of 30 students are 12 girls, and you want to find how many percent of girls are in your class using a proportion:
Let
`x`% be the percent girls. Since we know that percents can be expressed as ratios,
`x`%=
`(x)/(100)`: Now we can use the fact that the students are in a ratio 12 to 30 to establish our proportion:

`(12)/(30) = (x)/(100)`

`x= ((12)(100))/(30)`

`x=40`
We just prove that 40% of the students are girls.

The proportion that we used in this problem is called a percent proportion, and its formula:
`(a)/(b) = (x)/(100)` can be use to relate a percent with a proportion.