Ratio, << RAY shee oh or RAY shoh, >> is an ordered pair or set that represents a relationship between numbers or quantities. The numbers in a ratio are called the terms of the ratio.
The ratio of two numbers or quantities represented by the letters a and b may be written as a:b, (a,b), or a/b. All fractions and percentages are ratios. The expression “40 per cent” may be restated as 40/100 or 40:100. Two ratios are equal when each term of one ratio can be multiplied by a certain number to produce the terms of the other ratio. The expressions 2:3, 4:6, and 6:9 represent equal ratios. Two equal ratios make up a proportion (see Proportion ).
Ratios may be used to describe a variety of relationships. For example, a ratio may express the relationship between the amounts of two ingredients in a liquid mixture. If a mixture contains 5 gallons of syrup and 15 gallons of water, the relationship, or ratio, of syrup to water is 5:15 or 1:3. A ratio may also indicate the rate at which something occurs, such as the use of gasoline by an automobile. The rate of gasoline-use for an automobile that travels 30 miles on a gallon of gas is expressed by the ratio 30:1. Such a ratio may also be stated as “30 miles per gallon.” A ratio may also describe the probability of the occurrence of an event. For example, the probability of drawing an ace from a well-shuffled deck of cards is described by the ratio 4:52 or 1:13. The terms of this ratio are derived from the number of aces (4) and the total number of cards (52) in the deck.
Ratio ranks as one of the most widely used mathematical concepts. It plays an important role in the physical sciences, the social sciences, and the arts. In physics, for example, ratio provides a basis for the concepts of speed and acceleration.
