Fractions

Well

$$\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{5}}}}\right){\mathtt{\,\times\,}}\left({\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{6}}}}\right) = {\frac{{\mathtt{376}}}{{\mathtt{15}}}} = {\mathtt{25.066\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

$$\frac{37625}{15} = 25\frac{1}{25}$$

so   the quotient of          $$25\frac{1}{15}\quad and \quad 7\frac{5}{6}\quad is \quad 3\frac{1}{5}$$

check:

$${\frac{\left({\mathtt{25}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{15}}}}\right)}{\left({\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{6}}}}\right)}} = {\frac{{\mathtt{16}}}{{\mathtt{5}}}} = {\mathtt{3.2}}$$