PROPORTION

In mathematics, two quantities are proportional if they vary in such a way that one of them is a constant multiple of the other.

The mathematical symbol '∝' is used to indicate that two values are proportional. For example, A ∝ B.

If the two or more ratio quantities encompass all of the quantities in a particular situation, for example two apples and three oranges in a fruit basket containing no other types of fruit, it could be said that "the whole" contains five parts, made up of two parts apples and three parts oranges. In this case, 2/5 , or 40% of the whole are apples and 3/5, or 60% of the whole are oranges. This comparison of a specific quantity to "the whole" is sometimes called a proportion. Proportions are sometimes expressed as percentages as demonstrated above.

Direct proportionality

Given two variables x and y, y is (directly) proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that

y = kx

The relation is often denoted

y ∝ x

and the constant ratio

k = y/x

is called the proportionality constant or constant of proportionality.

Inverse proportionality

As noted in the definition above, two proportional variables are sometimes said to be directly proportional. This is done so as to contrast direct proportionality with inverse proportionality.

Two variables are inversely proportional (or varying inversely, or in inverse variation, or in inverse proportion or reciprocal proportion) if one of the variables is directly proportional with the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. It follows that the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that

y = k/x