# Definition:Rational Number/Fraction/Vulgar

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## Definition

A vulgar fraction is a rational number whose absolute value is less than $1$, expressed in the form $r = \dfrac p q$, where $p$ and $q$ are integers.

## Examples

$\dfrac 1 2$ is a vulgar fraction.
$\dfrac {-3} 4$ is a vulgar fraction.
$\dfrac 6 {10}$ is a vulgar fraction, although not in canonical form.

$\dfrac 3 2$ is not a vulgar fraction, as its absolute value is greater than $1$: it is in fact an improper fraction.

## Also known as

A vulgar fraction is also known as a proper fraction.

## Linguistic Note

The original everyday meaning of the word vulgar was at one point common, in the sense usual or everyday.

It derives from the Latin vulgus, meaning the common people in the sense of the public.

Through the process of the euphemism treadmill, the word in natural language has since gained the meaning rude or impolite.

Incidentally, it is also worth noting that the word common has gone the same way.