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 number.

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

Also see

 * Definition:Vulgar Fraction


 * Definition:Proper Fraction
 * Definition:Mixed Number