# unit fraction

An unit fraction^{} $\frac{n}{d}$ is a fraction whose numerator $n=1$.
If its integer denominator $d>1$, then a fraction is also a proper fraction. So there is only one unit fraction which is improper, namely 1.

Such fractions are known from Egyptian mathematics where we can find a lot of special representations of the numbers as a sum of an unit fractions, which are now called Egyptian fractions^{}. From the Rhind papyrus as an example:

$$\frac{2}{71}=\frac{1}{40}+\frac{1}{568}+\frac{1}{710}.$$ |

Many unit fractions are in the pairs of the adjacent fractions. An unit fractions are some successive or non-successive terms of any Farey sequence ${F}_{n}$ of a degree $n$. For example the fractions $\frac{1}{2}$ and $\frac{1}{4}$ are adjacent, but they are not the successive terms in the Farey sequence ${F}_{5}$. The fractions $\frac{1}{3}$ and $\frac{1}{4}$ are also adjacent and they are successive terms in the ${F}_{5}$.

Title | unit fraction |

Canonical name | UnitFraction |

Date of creation | 2013-03-22 12:48:25 |

Last modified on | 2013-03-22 12:48:25 |

Owner | XJamRastafire (349) |

Last modified by | XJamRastafire (349) |

Numerical id | 10 |

Author | XJamRastafire (349) |

Entry type | Definition |

Classification | msc 11A67 |

Related topic | AdjacentFraction |

Related topic | AnyRationalNumberIsASumOfUnitFractions |

Related topic | AnyRationalNumberWithOddDenominatorIsASumOfUnitFractionsWithOddDenominators |

Related topic | UnitFraction |

Related topic | SierpinskiErdosEgyptianFractionConjecture |

Defines | Egyptian fraction |