[tex]\displaystyle\bf\\\frac{m}{n} :\frac{n}{k} \cdot\frac{n}{m}=\frac{m}{n} \cdot\frac{k}{n}\cdot\frac{n}{m} =\underbrace{\Big(\frac{m}{n} \cdot\frac{n}{m} \Big) }_{1}\cdot\frac{k}{n} =1\cdot\frac{k}{n} =\frac{k}{n}[/tex]