# Ratio

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

*y*:

*x*:

*y*,

*x*Â¸

*y*, or

*x*/

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

For example, since , we know that 3 is less than Ï€. A ratio compares two numbers. Just as you cannot compare apples and oranges, so to must the numbers you are comparing have the same units.

Example

*What is the ratio of 2 feet to 4 yards?*

*1:9**1:8**1:7**1:6**1:5*

Solution

The ratio 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 x 3 feet = 12 feet.

Forming the ratio yields

The answer is (D).

**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.