Proportion
Equality of two ratios.
Terminology
- A proportion written as [latex]\dfrac {a} {b} =\dfrac {c} {d}[/latex], 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 [latex]\dfrac {a}{b} =\dfrac {b} {c}[/latex] , the second term b is called a mean proportional.
The following operations can be carried out based on the proportion [latex]\dfrac {a} {b} =\dfrac {c} {d}[/latex] :
[latex]\dfrac{a + b}{b}[/latex] = [latex]\dfrac{c + d}{d}[/latex] and [latex]\dfrac{a\space –\space b}{b}[/latex] = [latex]\dfrac{c\space –\space d}{d}[/latex]
[latex]\dfrac{a}{a + b}[/latex] = [latex]\dfrac{c}{c + d}[/latex] and [latex]\dfrac{a}{a\space –\space b}[/latex] = [latex]\dfrac{c}{c\space –\space d}[/latex]
[latex]\dfrac{a}{b}[/latex] = [latex]\dfrac{c}{d}[/latex] = [latex]\dfrac{a + c}{b + d}[/latex] = [latex]\dfrac{a\space –\space c}{b\space –\space d}[/latex]