Question : The value of $\left(\frac{2+7 \times 7 \div 9 \text { of } 9+6 \div 6 \times 2}{4 \div 4 \text { of } 5+7 \times 7 \div 7-6+4}\right)$ is:
Option 1: $\frac{1734}{2407}$
Option 2: $\frac{1865}{2106}$
Option 3: $\frac{1857}{2507}$
Option 4: $\frac{1664}{2305}$
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Correct Answer: $\frac{1865}{2106}$
Solution :
Given: $\left(\frac{2+7 \times 7 \div 9 \text { of } 9+6 \div 6 \times 2}{4 \div 4 \text { of } 5+7 \times 7 \div 7-6+4}\right)$
$=\left(\frac{2+7 \times 7 \div (9×9)+6 \div 6 \times 2}{4 \div (4 × 5)+7 \times 7 \div 7-6+4}\right)$
$=\left(\frac{2+\frac{49}{81}+2}{\frac{4}{20}+7-6+4}\right)$
$=\left(\frac{2+\frac{49}{81}+2}{\frac{4}{20}+5}\right)$
$=\left(\frac{\frac{162+49+162}{81}}{\frac{1}{5}+5}\right)$
$=\left(\frac{\frac{373}{81}}{\frac{26}{5}}\right)$
$=\frac{1865}{2106}$
Hence, the correct answer is $\frac{1865}{2106}$.
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