Calculating with percentages

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.


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


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


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

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


$$x\approx 67$$

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.


Another way of saying this is that


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

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


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?

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


The price of the shirt has decreased by 12%.

Video lesson

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