Question : The value of $\frac{\frac{5}{2}-\frac{3}{7} \times 1 \frac{4}{5} \div 3 \frac{6}{7}}{\frac{3}{2}+1 \frac{2}{5} \div 3 \frac{1}{2} \times 1 \frac{1}{4}}$ is:
Option 1: $2 \frac{3}{20}$
Option 2: $1\frac{2}{20}$
Option 3: $1 \frac{3}{20}$
Option 4: $1 \frac{7}{20}$
Correct Answer: $1 \frac{3}{20}$
Solution :
$\frac{\frac{5}{2}-\frac{3}{7} \times 1 \frac{4}{5} \div 3 \frac{6}{7}}{\frac{3}{2}+1 \frac{2}{5} \div 3 \frac{1}{2} \times 1 \frac{1}{4}}$
$=\frac{\frac{5}{2}-\frac{3}{7} \times \frac{9}{5} \div \frac{27}{7}}{\frac{3}{2}+ \frac{7}{5} \div \frac{7}{2} \times \frac{5}{4}}$
$=\frac{\frac{5}{2}-\frac{3}{7} \times \frac{9}{5} \times \frac{7}{27}}{\frac{3}{2}+ \frac{7}{5} \times \frac{2}{7} \times \frac{5}{4}}$
$=\frac{\frac{5}{2}-\frac{9}{5} \times \frac{1}{9}}{\frac{3}{2}+ \frac{1}{2}}$
$=\frac{\frac{5}{2}-\frac{1}{5} }{2}$
$=\frac{\frac{23}{10} }{2}$
$=\frac{23}{20} $
$=1\frac{3}{20} $
Hence, the correct answer is $1\frac{3}{20}$.
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