Math CentralQuandaries & Queries


Question from Alissa, a student:

What is the formula for writing the ratio of two numbers as a fraction?

Hi Alissa,

A ratio is a comparison of two numbers and we are most familiar with ratios when they are written using a colon (:) to separate the terms.

Ratios can also be written in the form of a fraction as well. To convert a ratio with a colon to a ratio as a fraction, simply have the first term of the ratio (the one on the left) become the numerator of the fraction and the other term of the ratio (the one on the right) become the denominator.

For example, the ratio 3:8 would be 3/8 as a ratio in "fraction form".

Now, if you wanted to know how to form fractions to represent parts of group with a given ratio, we take a slightly different approach.

For example, if a group of people were in a ratio of 3:8 women to men, what fraction of the group is women and what fraction of the group is men? For this type of question, the fractions become 3/11 of the group are women and 8/11 of the group are men. The numerators of the fractions come from the terms of the given ratio, and the denominator is the sum of both terms.

Hope this helps,

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS