Question : What is the value of $\frac{1}{7} \times \frac{1}{8} \div \frac{1}{4}+\frac{1}{3} \times \frac{1}{9}+\frac{1}{6} \div \frac{1}{12}$ of $\frac{3}{7}?$
Option 1: $\frac{1908}{378}$
Option 2: $\frac{1802}{405}$
Option 3: $\frac{1805}{378}$
Option 4: $\frac{1855}{378}$
Correct Answer: $\frac{1805}{378}$
Solution :
Given: $\frac{1}{7} \times \frac{1}{8} \div \frac{1}{4}+\frac{1}{3} \times \frac{1}{9}+\frac{1}{6} \div \frac{1}{12}$ of $\frac{3}{7}$
= $\frac{1}{7} \times \frac{1}{8} \div \frac{1}{4}+\frac{1}{3} \times \frac{1}{9}+\frac{1}{6} \div \frac{1}{28}$
= $\frac{1}{7} \times \frac{1}{2} +\frac{1}{3} \times \frac{1}{9}+\frac{14}{3}$
= $\frac{1}{14} +\frac{1}{27} +\frac{14}{3}$
= $\frac{27+14+1764}{14×27}$
= $\frac{1805}{378}$
Hence, the correct answer is $\frac{1805}{378}$.
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