unit fraction

An $\frac{n}{d}$ 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.

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

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