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 $F_{5}$