The value of 31/2 - [ 21/4 ÷ \ 11/4 - 1/2 ( 11/2 - 1/3 - 1/6 ) \ ] = ?

Answer: Option A

$$\begin{array}{rl}& \text{According to question,}\\ & \text{3}\frac{1}{2}-\left[2\frac{1}{4}÷\left\{1\frac{1}{4}-\frac{1}{2}\left(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]\\ & =\frac{7}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]\\ & =\frac{7}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\times 1\right\}\right]\\ & =\frac{7}{2}-\left[\frac{9}{4}÷\frac{3}{4}\right]\\ & =\frac{7}{2}-\left[\frac{9}{4}\times \frac{4}{3}\right]\\ & =\frac{7}{2}-3\\ & =\frac{7-6}{2}\\ & =\frac{1}{2}\end{array}$$