# Calculating with percents

As we discussed in pre-algebra, percent is a ratio that compares a number to 100. Percent means per hundred. Percent is usually expressed with the percent symbol %.

Percent problems are usually solved by using proportions.

Example

In a classroom 14 of the 21 students are female. How many percent does that correspond to?

We know that the ratio of girls to all students is

$\frac{14}{21}$

And we know that this ratio is a proportion to a ratio with the denominator 100.

$\frac{14}{21}=\frac{x}{100}$

As we saw in the last section from here we can calculate x

$x=100\cdot \frac{14}{21}$

$x=\frac{1400}{21}$

$x\approx 67$

i.e. 67% of the students in the class are female.

One of the ratios in these proportions is always a comparison of two numbers (above 14/21). This numbers are called the percentage (14) and the base (21). The other ratio is called the rate and always has the denominator 100.

$\frac{percentage}{base}=rate$

Another way of saying this is that

$percent=\frac{part}{whole}$

Percent of change, or p%, indicates how much a quantity has increased or decreased in comparison with the original amount. It's calculated as:

$percent\: of\: change=\frac{amount\: of\: increase\: or\: decrease}{old\: amount}$

Example

Johnny is at the store where there is a big sign telling him that there is a $4.99 discount on a shirt that originally costs$39.99. But how big is the discount in percent?

$\frac{\ 4.99}{\ 39.99}\approx 0.12$

$0.12=12\%$

The prize of the shirt has decreased by 12%.

## Video lesson

A prize increases from $500 to$585. How big is the increase in percent?