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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.


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

1421

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

1421=x100

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

x=1001421

x=140021

x67

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.

percentagebase=rate

Another way of saying this is that

percent=partwhole

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

percentofchange=amountofincreaseordecreaseoldamount


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?

$4.99$39.990.12

0.12=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?