Question : The value of $\frac{1 \frac{1}{2} \div 3 \frac{1}{4}+\frac{1}{2} \div \frac{13}{14}+\frac{1}{5}}{\frac{1}{5} \times 3 \frac{1}{2}-\frac{1}{3} \div 1 \frac{3}{4} \times 3 \frac{1}{2}}$ is:
Option 1: 33
Option 2: 36
Option 3: 38
Option 4: 40
Correct Answer: 36
Solution :
$\frac{1 \frac{1}{2} \div 3 \frac{1}{4}+\frac{1}{2} \div \frac{13}{14}+\frac{1}{5}}{\frac{1}{5} \times 3 \frac{1}{2}-\frac{1}{3} \div 1 \frac{3}{4} \times 3 \frac{1}{2}}$
= $\frac{\frac{1 \frac{1}{2}}{3 \frac{1}{4}} + \frac{\frac{1}{2}}{\frac{13}{14}}+\frac{1}{5}}{\frac{1}{5} ×\ 3 \frac{1}{2} - \frac{\frac{1}{3}} {1\frac{3}{4}} \times 3 \frac{1}{2}}$
= $\frac{\frac{\frac{3}{2}}{\frac{13}{4}} +\frac{7}{13} + \frac{1}{5}}{\frac{1}{5} \times \frac{7}{2} - \frac{\frac{1}{3}} {\frac{7}{4}} \times \frac{7}{2}}$
= $\frac{\frac{6}{13} +\frac{7}{13} + \frac{1}{5}}{\frac{1}{5} \times \frac{7}{2} - \frac{4}{21} \times \frac{7}{2}}$
= $\frac{\frac{13}{13} + \frac{1}{5}}{ \frac{7}{10} - \frac{2}{3} }$
= $\frac{\frac{6}{5}}{ \frac{1}{30}}$
= $\frac{{6}×{30}}{{1}×{5}}$
= 36
Hence, the correct answer is 36
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