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 $n÷d$. For instance, $3/2=3÷2=1.5$.

If $n$ and $d$ are positive, and , 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:

$$\frac{60}{84}=\frac{60÷12}{84÷12}=\frac{5}{7}.$$

The rules for manipulating fractions are

${\displaystyle \frac{a}{b}}$ $\mathrm{\hspace{1em}\hspace{1em}}=$ ${\displaystyle \frac{ka}{kb}}$

${\displaystyle \frac{a}{b}}+{\displaystyle \frac{c}{d}}$ $\mathrm{\hspace{1em}\hspace{1em}}=$ ${\displaystyle \frac{ad+bc}{bd}}$

${\displaystyle \frac{a}{b}}-{\displaystyle \frac{c}{d}}$ $\mathrm{\hspace{1em}\hspace{1em}}=$ ${\displaystyle \frac{ad-bc}{bd}}$

${\displaystyle \frac{a}{b}}\times {\displaystyle \frac{c}{d}}$ $\mathrm{\hspace{1em}\hspace{1em}}=$ ${\displaystyle \frac{ac}{bd}}$

${\displaystyle \frac{a}{b}}÷{\displaystyle \frac{c}{d}}$ $\mathrm{\hspace{1em}\hspace{1em}}=$ ${\displaystyle \frac{ad}{bc}}.$

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