Ratios and Proportions

 

A ratio is a comparison of two numbers by division. The ratio of a to b can be expressed as:

 

 a to b; a:b; a/b

 

Example: the ratio of boys to girls in your class is 12 to 14, or 12:14, or 12/14

If you have three classes with the same ratio of boys to girls, the total number of boys in the three classes would be 36, and the total number of girls would be 42, the ratio would be 36:42, which is the same as 12:14.

 

When two ratios are equal, they form a proportion. In the example above, the proportion is:

 

12/14 = 36/42

 

A way to determine if ratios are equal is to find their cross products. In the example, the cross products are:

 

12 x 42  and 14 x 36

 

12 x 42 = 504

14 x 36 = 504

 

Since the cross products are equal, the ratios 12/14 and 36/42 form a proportion.

 

A special ratio useful when working with maps is called a scale. A scale is the ratio of a measurement on the map to the actual distance on the globe. For example if a map has a scale of 1:100, this means that a distance of one inch on the map represents a distance of 100 miles.