Proportion is a relationship of equivalence between two ratios. For example, the equation a/b = c/d is a proportion. The equation states that a is related to b in the same way that c is related to d. It can also be written as a:b = c:d. Equivalent ratios are said to be in proportion.
In the proportion a/b = c/d, a is called the first term; b, the second term; c, the third term; and d, the fourth term. The first and fourth terms are called the extremes of the proportion, and the second and third terms, the means. For all proportions, the product of the means equals the product of the extremes. For the proportion a/b = c/d it is therefore true that a X d = b X c. This property of proportions provides a formal way of finding an unknown term of a proportion when the three remaining terms are known. For example, the unknown term n in the proportion 9/3 = 15/n can be determined by solving the equation 9 X n = 3 X 15:
9n = 3 X 15
9n = 45
n = 5
When two ratios are in proportion, the terms of one ratio can be multiplied by a certain number to produce the terms of the other ratio. In the proportion 2/4 = 4/8, for example, both terms of the ratio 2/4 can be multiplied by 2 to produce 4/8.
All ratios considered as numbers that are in proportion to one another equal the same number. This number is called a constant of proportionality. For example, the ratio of the circumference (c) to the diameter (d) of any circle is in proportion to the same ratio for any other circle. All such ratios (c/d ) are equal to 3.14159. This constant of proportionality is known as pi.
The idea of proportion is the basis for many laws of astronomy, biology, chemistry, and physics. Many of these laws contain famous constants of proportionality. The idea of proportion is also used in the social sciences and the arts. Architects use it in designing scale models and drawing building plans.
