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
- Definition:Vulgar Fraction
- Definition:Improper Fraction
- Definition:Mixed Fraction
- Definition:Complex Fraction
- Results about proper fractions can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): proper fraction
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): simple fraction, common fraction or proper fraction
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): fraction
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): improper fraction
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): proper fraction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fraction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): improper fraction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): proper fraction
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): fraction
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): proper fraction
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): proper fraction