Definition:Rational Number/Fraction/Improper

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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 fraction.


Also known as

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