$$\eqalign{ & {\text{Simplify if,}} \cr & {\text{I = }}\frac{3}{5} \div \frac{5}{6}{\text{,}} \cr & {\text{II = 3}} \div \left[ {\left( {4 \div 5} \right) \div 6} \right]{\text{,}} \cr & {\text{III = }}\left[ {3 \div \left( {4 \div 5} \right)} \right] \div 6\,, \cr & {\text{IV = 3}} \div {\text{4}}\left( {5 \div 6} \right) \cr & {\text{then }} \cr} $$

Solution(By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & {\text{I = }}\frac{3}{5} \div \frac{5}{6} \cr & {\text{I = }}\frac{3}{5} \times \frac{6}{5} = \frac{18}{{25}} \cr & \cr & {\text{II = 3}} \div \left[ {\frac{4}{5} \times \frac{1}{6}} \right] \cr & {\text{II = 3}} \times \frac{{30}}{4} \cr & {\text{II = }}\frac{{45}}{2} \cr & \cr & {\text{III = }}\left[ {3 \div \left( {4 \div 5} \right)} \right] \div 6\, \cr & {\text{III = }}\left[ {3 \times \frac{5}{4}} \right] \times \frac{1}{6}\, \cr & {\text{III = }}\frac{5}{8} \cr & \cr & {\text{IV = 3}} \div {\text{4}}\left( {5 \div 6} \right) \cr & {\text{IV = 3}} \div {\text{4}} \times \frac{5}{6} \cr & {\text{IV = 3}} \times \frac{6}{{20}} \cr & {\text{IV = }}\frac{9}{{10}} \cr } $$