If there are seven boys and twelve girls in a class, then the ratio of boys to girls can be expressed as 7 to 12, , or 7:12. A ratio compares the size, or magnitude, of two numbers. Two other related concepts, rate and proportion, together with ratio, are used for solving many real-world problems that involve comparing different quantities.

Calculating Ratios

Suppose a parking garage contains six blue cars and two green cars. The ratio of blue cars to green cars can be expressed as a fraction . If the two green cars leave the garage, then there are zero green cars and the ratio becomes . Division by zero, however, is not defined, so this form of the ratio is meaningless. Expressing a ratio as a fraction, , is valid as long as b is not equal to zero. However, the ratio of blue to green cars...