# Definition:Rational Number/Fraction/Improper

## 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 fraction.

## Also known as

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