Calculating with Percentages

You don’t always start with a whole pizza or a whole hundred dollar bill. You must also be able to find $30$ % of $$250$, or $25$ % of 700 grams of sugar, as but two examples.

You have already seen that calculating with percentages is the same as using fractions. A fraction is a part of a whole. This whole could be 700 grams of sugar, for example, and we want to know how much $25$ % $\left(\frac{25}{100}\right)$ of that is.

This is the most important rule about percentages. The rule tells you that you can swap the percent sign (%) for the fraction $\frac{1}{100}$.

When you calculate with percentages, it’s often concerning money. For that reason, here’s an example with money:

Percentages are also used to study the ratio between a part and a whole. The fraction $\frac{3}{4}$ can be the ratio between three croissants and a whole pack of four croissants. Here, you need to remember that

$$\frac{1}{4}=0.25=25\text{\%}$$

This means that one croissant is $25$ %, and three croissants are

$$3\times 25\text{\%}=75\text{\%}$$

of all the croissants in the bag.

Remember that all fractions express a ratio.