Concept

Proportion

A proportion is an equation showing the equivalence of two ratios, or fractions, with different numerators and denominators.

\frac{a}{b} = \frac{c}{d} or a : b = c : d

The first and last numbers in the proportion are called the extremes, while the other two numbers are called the means.

a d ↓ means : ↑ b = ↑ c : e x t r e m e s d ↓

In a proportion, by the Cross Products Property, the product of the $extremes$ is equal to the product of the $means .$

If $\frac{a}{b} = \frac{c}{d},$ then $a d = b c .$

As an example of proportionality, consider slices of pizza. Depending on the number of times it has been sliced, the same amount of pizza could be cut into $1,$ $2,$ or $4$ pieces.

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In this case, one-third of a pizza is the same amount of pizza as two-sixths or four-twelfths. If the simplified forms of two fractions are equal, then they are said to be proportional. For example, one-third is proportional to two-sixths and four-twelfths.

Note that proportions are often used in geometric concepts such as the Triangle Proportionality Theorem or when determining if two figures are similar.

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