## Task 4 - 060734

The number $\frac{16}{15}$ is to be represented in the form $\frac{16}{15}=\frac{a}{m}+\frac{b}{n}$. Here, $a, b, m, n$ should be natural numbers such that the fractions $\frac{a}{m}$ and $\frac{b}{n}$ are not reducible and are not whole numbers.

Give three examples of such a representation, where

in the first example $m=n$ and $a \neq b$ holds, in the second example $a=b$ and $m \neq n$ holds, in the third example $a=b$ and $m=n$ holds!
I. $\frac{16}{15}=\frac{a}{m}+\frac{b}{m}$ can, for example, be achieved with $m=15, a=2, b=14$, where all other conditions of the problem are also met: $\frac{16}{15}=\frac{2}{15}+\frac{14}{15}$.

II. $\frac{16}{15}=\frac{a}{m}+\frac{a}{n}$ can, for example, be achieved with $m=3, n=5, a=2$, where all other conditions of the problem are also met: $\frac{16}{15}=\frac{2}{3}+\frac{2}{5}$.

III. $\frac{16}{15}=\frac{a}{m}+\frac{a}{m}$ can (simultaneously with the conditions of the problem) only be achieved through $m=15, a=8$: $\frac{16}{15}=\frac{8}{15}+\frac{8}{15}$.