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:Mixed Number

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