Applied Mathematics

Probability Theory

What are ratios and proportions?

A ratio is the comparison of two numbers; it is most often written as a fraction or with a “:”, as in 3/4 or 3:4 to separate the two numbers. For example, if we want to know the ratio of dogs in a shelter that houses 24 animals to the total count, we first determine the number of dogs (say, 10); then the ratio of dogs to animals in the shelter becomes 10/24, or 10:24, which is also said as “10 to 24.” But there are rules to ratios. For example, order matters when talking about ratios; therefore, the ratio 7:1 is not the same as 1:7.

A proportion is an equation with a ratio on each side, and is a statement that two ratios are equal. For example, ½ = 4/8, or ½ is proportional to 4/8. In order to “solve the proportion”—or when one of the four numbers in a proportion is unknown—we need to use cross products to find the unknown number. For example, to solve for x in the following: 1/4 = x/8; using cross product, 4x = 1 × 8; thus, x = 2.


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