A ratio is a comparison of two things.  In math, we compare two numbers by division.  For example, if we have 14 girls and 12 boys in a classroom, then we can have a ratio of boys to girls (12 to 14) or girls to the entire class (14 to 25).

We can write ratios in several ways:

• 12 to 14
• 12:14
• 12/14

No matter how we write the ratios, we would say "12 to 14."

We usually express ratios in simplest form.  Therefore we would write the ratio 12/14 as 6/7. 

If we have a ratio of 14/12, we would reduce it to 7/6, but we would not write it as a mixed number; we would keep the fraction in its improper form, as that gives a better representation of the two numbers we are comparing.  For the same reason, we do not normally write ratio as decimals, but keep them in fraction form.

Ratios are used in many applications, including unit rates, scale drawings, percents, probability, odds, and slope.

These class notes provide further explanation and examples.