What is a proportion
A proportion is an equality between two ratios, written as A:B = C:D. It states that the relationship between A and B is the same relationship between C and D, even if the numbers involved are different. For example, 2:3 and 10:15 represent the same proportion, since 10 is 2 multiplied by 5, and 15 is 3 multiplied by 5.
How to check whether two ratios form a proportion
The most direct way to check a proportion is cross-multiplication: in A:B = C:D, A and D are called the extremes, and B and C are the means. The equality is only a true proportion when the product of the extremes equals the product of the means, that is, A × D = B × C.
How to find the missing term
Knowing three of the four terms of a proportion, the fourth can be found by isolating it in the same cross-multiplication equality. If the unknown term is D, the formula becomes D = (B × C) / A. This is the mathematical basis behind the rule of three.
Practical example
A map uses a 1:50,000 scale, meaning 1 cm on the map represents 50,000 cm (500 meters) in reality. If a distance on the map measures 3.4 cm, the missing term in the proportion 1:50,000 = 3.4:D gives the real distance: 170,000 cm, or 1.7 km.