Question : What is the value of $\frac{3}{2} \div \frac{1}{7} \times[(\frac{1}{2} - \frac{1}{3}) \div \frac{1}{42}]?$
Option 1: $72 \frac{1}{3}$
Option 2: $73 \frac{1}{2}$
Option 3: $72 \frac{1}{2}$
Option 4: $71 \frac{2}{3}$
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Correct Answer: $73 \frac{1}{2}$
Solution :
Given: $\frac{3}{2} \div \frac{1}{7} \times[(\frac{1}{2} - \frac{1}{3}) \div \frac{1}{42}]$
Applying the BODMAS rule,
$=\frac{3}{2} \div \frac{1}{7} \times[(\frac{3-2}{6}) \div \frac{1}{42}]$
$=\frac{3}{2} \div \frac{1}{7} \times[\frac{1}{6} \div \frac{1}{42}]$
$=\frac{3}{2} \div \frac{1}{7} \times[\frac{1}{6} \times{42}]$
$=\frac{3}{2} \div \frac{1}{7} \times7$
$=\frac{21}{2}\times 7$
$=\frac{147}{2}$
$=73\frac{1}{2}$
Hence, the correct answer is $73\frac{1}{2}$.
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