Question : The value of $3\frac{1}{2} - [2\frac{1}{4}+ 1\frac{1}{4} - \frac{1}{2}(1\frac{1}{2}-\frac{1}{3} -\frac{1}{6})]$ is:
Option 1: $\frac{1}{2}$
Option 2: $2\frac{1}{2}$
Option 3: $3\frac{1}{2}$
Option 4: $9\frac{1}{2}$
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Correct Answer: $\frac{1}{2}$
Solution :
$3\frac{1}{2} - [2\frac{1}{4}+ 1\frac{1}{4} -\frac{1}{2}(1\frac{1}{2}-\frac{1}{3} -\frac{1}{6})]$
$=3\frac{1}{2} -[2\frac{1}{4}+ 1\frac{1}{4} - \frac{1}{2}(\frac{3}{2}-\frac{1}{2})]$
$=3\frac{1}{2} -[2\frac{1}{4}+ 1\frac{1}{4} - \frac{1}{2}\times 1]$
$=3\frac{1}{2} -[\frac{9}{4}+\frac{5}{4} - \frac{1}{2}]$
$=3\frac{1}{2} -[\frac{14}{4} - \frac{1}{2}]$
$=3\frac{1}{2} -[\frac{12}{4}]$
$=\frac{7}{2} -3$
$=\frac{1}{2}$
Hence, the correct answer is $\frac{1}{2}$.
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