1. For the fraction $\frac{m}{n}$, where $m$ and $n$ are natural numbers, it holds that $\frac{1}{3}<\frac{m}{n}<1$. If a natural number is added to the numerator and the denominator is multiplied by this number, the value of the fraction does not change. Find all such fractions $\frac{m}{n}$.
II/1. From $\frac{m}{n}=\frac{m+k}{n \cdot k}$, express $m=\frac{k}{k-1}$. Since $m$ is a natural number, $k$ must be $2$, so $m=2$. Given $\frac{1}{3}<\frac{2}{n}<1$, $2<n<6$. All possible solutions are $\frac{2}{3}, \frac{2}{4}$, and $\frac{2}{5}$.