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# 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

$\displaystyle\frac{a}{b}$ | $\displaystyle\qquad=$ | $\displaystyle\frac{ka}{kb}$ | ||

$\displaystyle\frac{a}{b}+\frac{c}{d}$ | $\displaystyle\qquad=$ | $\displaystyle\frac{ad+bc}{bd}$ | ||

$\displaystyle\frac{a}{b}-\frac{c}{d}$ | $\displaystyle\qquad=$ | $\displaystyle\frac{ad-bc}{bd}$ | ||

$\displaystyle\frac{a}{b}\times\frac{c}{d}$ | $\displaystyle\qquad=$ | $\displaystyle\frac{ac}{bd}$ | ||

$\displaystyle\frac{a}{b}\div\frac{c}{d}$ | $\displaystyle\qquad=$ | $\displaystyle\frac{ad}{bc}.$ |

Defines:

solidus, proper fraction, numerator, denominator, improper fraction, lowest terms

Related:

RationalNumber, Number, CategoryOfAdditiveFractions

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11-01*no label found*

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An addition by mathcam ✓

Classification? by mathcam ✓

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What are proper fractions? by pahio ✓

Classification? by mathcam ✓

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classification by rspuzio ✓

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