Let:
[tex]\begin{gathered} k=constant_{\text{ }}of_{\text{ }}proportionality \\ k\in\N \end{gathered}[/tex][tex]\begin{gathered} 6\colon7=\frac{6}{7} \\ let \\ k=2 \\ \frac{6}{7}\equiv\frac{k}{k}\times\frac{6}{7}=\frac{2}{2}\times\frac{6}{7}=\frac{12}{14} \\ so\colon \\ \frac{6}{7}\equiv\frac{12}{14} \end{gathered}[/tex][tex]\begin{gathered} 9\colon5=\frac{9}{5} \\ let \\ k=3 \\ \frac{9}{5}\equiv\frac{k}{k}\times\frac{9}{5}=\frac{3}{3}\times\frac{9}{5}=\frac{27}{15} \\ so\colon \\ \frac{9}{5}\equiv\frac{27}{15} \end{gathered}[/tex]