PlanetMath: fraction

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fraction

(Definition)

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

The fraction has value $n \div d$ . For instance, $3/2 = 3 \div 2 = 1.5$ .

If and are positive, and , then is known as a proper fraction. Otherwise, it is an improper fraction. If and are relatively prime, then 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:

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

The rules for manipulating fractions are

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

"fraction" is owned by bwebste. [ full author list (2) ]

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