# 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