# Ratio

A ratio is simply a fraction. The following notations all express the ratio of*x*to

*y*:

*x*:

*y*,

*x*Ã·

*y*, or

*x*/

*y*. Writing two numbers as a ratio provides a convenient way to compare their sizes.

Just as you cannot compare apples and oranges, so to must the numbers you are comparing have the same units.

Before you form any ratio, make sure the two numbers are expressed in the same units.

Example-1

Column A | Column B |

The ratio of 2 miles to 4 miles | The ratio of 2 feet to 4 yards |

Forming the ratio in Column A yields

The ratio in Column B cannot be formed until the numbers are expressed in the same units. Letâ€™s turn the yards into feet. Since there are 3 feet in a yard, 4 yards = 4 Ã— 3 feet = 12 feet. Forming the ratio yields

Hence, Column A is larger.

**Note: **Taking the reciprocal of a fraction usually changes its size. For example, . So order is important in a ratio: 3 : 4 â‰ 4 : 3.