How Do You Figure Out Ratios?

Since a ratio is just a comparison between two quantities, figure out ratios by dividing the initial quantity by the quantity that follows. For example, if there are 12 males in a classroom and 15 females, the ratio of males to females is obtained by dividing 12 by 15.

The order is extremely important, as explained by What comes first in the ratio is always divided by what comes second. It is never the other way around.

Ratios can be written using three different types of notation. The ratio in the above example is written 12 to 15 when expressed in words. However, ratios can also be written in the form of odds or expressed as fractions.

When ratios are written using odds notation, the two quantities being compared are separated by a semicolon. This means the ratio of males to females from the above example can be written 12 : 15. Expressed as a fraction, the same ratio is 12/15.

Keep in mind however that ratios do not necessarily give the absolute amounts for what is there, but may merely represent how many units of one group are present for every so many units of another.

For instance, given the class described above, the ratio of males to females can also be expressed as 4 to 5 since there are 4 males for every 5 females. Whether 4 is divided by 5 or 12 is divided by 15, their relative quotients both reveal there are 0.8 males for every female.