A fraction is a rational number expressed in the form nd or n/d, where n is designated the numerator and d the denominator. The slash between them is known as a solidus when the fraction is expressed as n/d.

The fraction n/d has value n÷d. For instance, 3/2=3÷2=1.5.

If n and d are positive, and n/d<1, then n/d is known as a proper fraction. Otherwise, it is an improper fraction. If n and d are relatively prime, then n/d is said to be in lowest terms. Each rational number can be expressed uniquely as a fraction in lowest terms. To get a fraction in lowest terms, simply divide the numerator and the denominator by their greatest common divisorMathworldPlanetmathPlanetmath:


The rules for manipulating fractions are

ab   = kakb
ab+cd   = ad+bcbd
ab-cd   = ad-bcbd
ab×cd   = acbd
ab÷cd   = adbc.
Title fraction
Canonical name Fraction
Date of creation 2013-03-22 12:34:11
Last modified on 2013-03-22 12:34:11
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 11
Author bwebste (988)
Entry type Definition
Classification msc 11-01
Related topic RationalNumber
Related topic Number
Related topic CategoryOfAdditiveFractions
Defines solidus
Defines proper fraction
Defines numerator
Defines denominator
Defines improper fraction
Defines lowest terms