# 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**.

## Also see

## 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.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**vulgar fraction** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**vulgar fraction** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**vulgar fraction** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**vulgar fraction** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**fraction**