If $$M = \frac{3}{7} \div \frac{6}{5} \times \frac{2}{3} + \frac{1}{5} \times \frac{3}{2}$$      and $$N = \frac{2}{5} \times \frac{5}{6} \div \frac{1}{3} + \frac{3}{5} \times \frac{2}{3} \div \frac{3}{5},$$      then what is the value of $$\frac{M}{N}$$?

Solution (By Examveda Team)

$$\eqalign{ & M = \frac{3}{7} \div \frac{6}{5} \times \frac{2}{3} + \frac{1}{5} \times \frac{3}{2} \cr & = \frac{3}{7} \times \frac{5}{6} \times \frac{2}{3} + \frac{3}{{10}} \cr & = \frac{5}{{21}} + \frac{3}{{10}} \cr & = \frac{{50 + 63}}{{210}} \cr & = \frac{{113}}{{210}} \cr & N = \frac{2}{5} \times \frac{5}{6} \div \frac{1}{3} + \frac{3}{5} \times \frac{2}{3} \div \frac{3}{5} \cr & = \frac{2}{5} \times \frac{5}{6} \times \frac{3}{1} + \frac{3}{5} \times \frac{2}{3} \times \frac{5}{3} \cr & = 1 + \frac{2}{3} \cr & = \frac{5}{3} \cr & \frac{M}{N} = \frac{{113}}{{210}} \div \frac{5}{3} \cr & = \frac{{113}}{{210}} \times \frac{3}{5} \cr & = \frac{{113}}{{350}} \cr} $$