Equality of two ratios.


  • A proportion written as \(\dfrac {a} {b} =\dfrac {c} {d}\), where a : b :: c : d is read as “a is to b as c is to d” and is written : ad = bc.
  • The elements a and d are called extremes (or extreme terms) and the elements b and c are called the means (or mean terms).
  • In a proportion with three terms \(\dfrac {a}{b} =\dfrac {b} {c}\) , the second term b is called a mean proportional.

The following operations can be carried out based on the proportion \(\dfrac {a} {b} =\dfrac {c} {d}\) :

\(\dfrac{a + b}{b}\) = \(\dfrac{c + d}{d}\) and \(\dfrac{a\space –\space b}{b}\) = \(\dfrac{c\space –\space d}{d}\)

\(\dfrac{a}{a + b}\) = \(\dfrac{c}{c + d}\) and \(\dfrac{a}{a\space –\space b}\) = \(\dfrac{c}{c\space –\space d}\)

\(\dfrac{a}{b}\) = \(\dfrac{c}{d}\) = \(\dfrac{a + c}{b + d}\) = \(\dfrac{a\space –\space c}{b\space –\space d}\)


To calculate 15% of 200, we start by writing the following proportion : \(\dfrac{15}{100}\) = \(\dfrac{x}{200}\).

The rules to solve a first-degree equation in one unknown are then applied, and we obtain :
x = 30.

Educational note

In the case of a proportion with three terms, the mean proportional (second term) is the geometric mean of the first and third terms.

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