Proportion:

A proportion is a statement of equality among two ratios.  For example, if a car travels 40 miles in 1 hour and 80 miles within 2 hours, the ratio of the distance traveled is 40 miles: 80 miles, or 40 miles/80 miles, and the ratio of time is 1 hour:2 hours, or 1 hour/2 hours.  The proportion associating these two ratios is:

40 miles:80 miles = 1 hour:2 hours

40  miles/80 miles                                1 hour/2 hours

A proportion consists of four words.  The first and fourth terms are known as the extremes of the proportion; the second and third terms are known as the means.  If the letters a, b, c and d are used to represent the terms in a proportion, that can be written in general form.

a/b =c/d

Multiplication of both sides of this equation through bd results in the following.

(bd) a/b = c/d (bd)

ad = cb

Therefore, the product of the extremes of a proportion (ad) equals the product of the means (bc).  For instance, in the proportion 40 miles:80 miles = 1 hour:2 hours, the product of the extremes is (40 miles)(2 hours) that equals 80 miles-hours, and the product of the means is (80 miles)(1 hour), that also equals 80 miles-hours.

Ratio & proportion are familiar ideas.  Several people use them without realizing it.  While a recipe calls for 1½ cups of flour to make a serving for 6 people, and the cook needs to determine how several cups of flour to use to make a serving for 8 people, she uses the concepts of ratios & proportions.  When the price of onions is 2 pounds for 49 cents and the cost of 3½ pounds is computed, ratio and proportion are used.  Many people know how to solve ratio and proportion problems such as these without knowing the exact steps used.

Ratio and proportion problems are solved through using an unknown such as x for the missing word. The output proportion is solved for the value of x through setting the product of the extremes equivalent to the product of the means.