Question : Simplify: $\frac{1-\frac{3}{7} \div \frac{9}{49} \times \frac{3}{14}}{1+\frac{3}{5} \div \frac{1}{25} \times \frac{1}{30}}$
Option 1: $\frac{1}{7}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{1}{5}$
Correct Answer: $\frac{1}{3}$
Solution : $\frac{1-\frac{3}{7} \div \frac{9}{49} \times \frac{3}{14}}{1+\frac{3}{5} \div \frac{1}{25} \times \frac{1}{30}}$ $=\frac{1-\frac{3}{7} \times \frac{49}{9} \times \frac{3}{14}}{1+\frac{3}{5} \times 25 \times \frac{1}{30}}$ $=\frac{1-\frac{7} {3} \times \frac{3}{14}}{1+5 \times \frac{1}{10}}$ $=\frac{1-\frac{1} {2}}{1+ \frac{1}{2}}$ $=\frac{1}{3}$ Hence, the correct answer is $\frac{1}{3}$.
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