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 $\frac{5}{100}$. Notice that we can simplify our ratio, both numerator and denominator are divisible by 5, so lets simplify it: $\frac{5}{100} = \frac{1}{20}$. We can conclude that we can express 5% as the ratio $\frac{1}{20}$.

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, $x$%=$\frac{x}{100}$: Now we can use the fact that the students are in a ratio 12 to 30 to establish our proportion:
$\frac{12}{30} = \frac{x}{100}$
$x= \frac{(12)(100)}{30}$
$x=40$
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: $\frac{a}{b} = \frac{x}{100}$ can be use to relate a percent with a proportion.