The value of $${\text{3}}\frac{1}{2} - $$ $$\left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$       = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & {\text{3}}\frac{1}{2} - \left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{3}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2} \times 1} \right\}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \div \frac{3}{4}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \times \frac{4}{3}} \right] \cr & = \frac{7}{2} - 3 \cr & = \frac{{7 - 6}}{2} \cr & = \frac{1}{2} \cr} $$