Solve : $$7\frac{1}{2} - $$  $$\left[ {2\frac{1}{4} ÷ \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$       = ?

Solution(By Examveda Team)

$$ = 7\frac{1}{2} - $$  $$\left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$
$$ = \frac{{15}}{2} - $$   $$\left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{3}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$
$$ = \frac{{15}}{2} - $$   $$\left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{{9 - 2 - 1}}{6}} \right)} \right\}} \right]$$
$$\eqalign{ & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}} \right\}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{{5 - 2}}{4}} \right\}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \frac{3}{4}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \times \frac{4}{3}} \right] \cr & = \frac{{15}}{2} - 3 \cr & = \frac{{15 - 6}}{2} \cr & = \frac{9}{2} \cr & = 4\frac{1}{2} \cr} $$