Definition:Fraction/Proper

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Definition

A proper fraction is a fraction representing 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

Example: $\frac 3 4$

$\dfrac 3 4$ is a proper fraction.


Example: $\frac 7 8$

$\dfrac 7 8$ is a proper fraction.


Example: $\frac {-3} 4$

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


Example: $\frac 6 {10}$

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


Example: $\frac 3 2$

$\dfrac 3 2$ 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 fraction representing a rational number expressed as one integer over another.

Some sources use the term common fraction or simple fraction, but those are also used as other terms for a vulgar fraction.


Also see

  • Results about proper fractions can be found here.


Sources

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