# Definition:Rational Number/Fraction/Improper

< Definition:Rational Number | Fraction(Redirected from Definition:Improper Fraction)

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## Definition

An **improper fraction** is a rational number whose absolute value is greater than $1$, specifically when expressed in the form $r = \dfrac p q$ where $p$ and $q$ are integers such that $p > q$.

## Examples

- $\dfrac 3 2$ is an
**improper fraction**.

- $\dfrac {-5} 4$ is an
**improper fraction**.

- $\dfrac {16} {10}$ is an
**improper fraction**, although not in canonical form.

- $1 \frac 1 2$ is
*not*an**improper fraction**: it is in fact a mixed number.

## Also known as

An **improper fraction** is also known informally as a **top-heavy fraction**.

## Also see

## Linguistic Note

The word **improper** has evolved to mean **rude** or **offensive**, or even **invasive** (of privacy, personal space or sexual integrity).

Stand-up comedians may wish to take the opportunity to riff on why language hates **fractions** so much, that they are either **improper** or merely **vulgar**.

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**fraction**