# 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 $n\xf7d$. For instance, $3/2=3\xf72=1.5$.

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^{}:

$$\frac{60}{84}=\frac{60\xf712}{84\xf712}=\frac{5}{7}.$$ |

The rules for manipulating fractions are

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

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

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

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

$\frac{a}{b}}\xf7{\displaystyle \frac{c}{d}$ | $\mathrm{\hspace{1em}\hspace{1em}}=$ | $\frac{ad}{bc}}.$ |

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 |