fraction

A fraction is a rational number expressed in the form $\\frac{n}{d}$ 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 $n\\div d$ . For instance, $3/2=3\\div 2=1.5$ .

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 divisor:

\\frac{60}{84}=\\frac{60\\div 12}{84\\div 12}=\\frac{5}{7}.

The rules for manipulating fractions are

$\\displaystyle\\frac{a}{b}$	$\\displaystyle\\qquad=$	$\\displaystyle\\frac{ka}{kb}$
$\\displaystyle\\frac{a}{b}+\\frac{c}{d}$	$\\displaystyle\\qquad=$	$\\displaystyle\\frac{ad+bc}{bd}$
$\\displaystyle\\frac{a}{b}-\\frac{c}{d}$	$\\displaystyle\\qquad=$	$\\displaystyle\\frac{ad-bc}{bd}$
$\\displaystyle\\frac{a}{b}\\times\\frac{c}{d}$	$\\displaystyle\\qquad=$	$\\displaystyle\\frac{ac}{bd}$
$\\displaystyle\\frac{a}{b}\\div\\frac{c}{d}$	$\\displaystyle\\qquad=$	$\\displaystyle\\frac{ad}{bc}.$

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