[tex]\bf 6\frac{1}{2}:15\frac{1}{6}\qquad
\begin{cases}
6\frac{1}{2}\implies \cfrac{6\cdot 2+1}{2}\\\\
15\frac{1}{6}\implies \cfrac{15\cdot 6+1}{6}
\end{cases}\implies \cfrac{ \frac{6\cdot 2+1}{2}}{\frac{15\cdot 6+1}{6}}\\\\
-----------------------------\\\\
\cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus
\\\\\\
\cfrac{6\cdot 2+1}{2}\cdot \cfrac{6}{15\cdot 6+1}[/tex]
simplify away
