Definition:Rational Number/Fraction/Proper

Definition
A proper fraction is a rational number whose absolute value is less than $1$, expressed in the form $r = \dfrac p q$, where $p$ and $q$ are integers.

Examples

 * $\dfrac 1 2$ is a proper fraction.


 * $\dfrac {-3} 4$ is a proper fraction.


 * $\dfrac 6 {10}$ is a proper fraction, although not in canonical form.


 * $\dfrac 3 2$ is not a proper fraction, as its absolute value is greater than $1$: it is in fact an improper fraction.

Also known as
A proper fraction is often also known as a vulgar fraction, but this is usually reserved for the general rational number expressed as one integer over another.

Also see

 * Definition:Vulgar Fraction


 * Definition:Improper Fraction
 * Definition:Mixed Number