Question : The value of $9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{3}{4}-\frac{1}{3}\right)\right.$ of $\left.\frac{2}{9}\right\}$ is:
Option 1: $\frac{540}{173}$
Option 2: $\frac{340}{173}$
Option 3: $\frac{480}{173}$
Option 4: $\frac{2540}{173}$
Correct Answer: $\frac{540}{173}$
Solution :
$9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{3}{4}-\frac{1}{3}\right)\right.$ of $\left.\frac{2}{9}\right\}$
$=9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{5}{12}\right)\right. \text{of}\left.\frac{2}{9}\right\}$
$=9 \div({\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\frac{5}{54}})$
$=9 \div({\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \times\frac{54}{5}})$
$=9 \div({\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{9}{5} })$
$=9 \div({\frac{30+20+15+108}{60}})$
$=9 \div({\frac{173}{60}})$
$=9 \times({\frac{60}{173}})$
$={\frac{540}{173}}$
Hence, the correct answer is ${\frac{540}{173}}$.
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