Question

Write the ratio as a ratio of a whole numbers using fractional notation 6 1/2 to 15 1/6

Answer 1

$\bf 6\frac{1}{2}:15\frac{1}{6}\qquad \begin{cases} 6\frac{1}{2}\implies \cfrac{6\cdot 2+1}{2}\\\\ 15\frac{1}{6}\implies \cfrac{15\cdot 6+1}{6} \end{cases}\implies \cfrac{ \frac{6\cdot 2+1}{2}}{\frac{15\cdot 6+1}{6}}\\\\ -----------------------------\\\\ \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus \\\\\\ \cfrac{6\cdot 2+1}{2}\cdot \cfrac{6}{15\cdot 6+1}$

simplify away