Question : Find the value of the following expression.
$\frac{\left[\frac{5}{8}-\left\{\frac{3}{8}-\left(\frac{5}{8}-\frac{3}{8}\right)\right\}\right] \text { of } 8.8-1.2}{4 \frac{1}{6} \div 2.5 \times 2 \div \frac{1}{6} \text { of } 60+\left(\frac{3}{4}-\frac{3}{8}\right)}$
Option 1: $5 \frac{22}{43}$
Option 2: $3 \frac{23}{67}$
Option 3: $4 \frac{44}{85}$
Option 4: $4 \frac{4}{5}$
Correct Answer: $4 \frac{44}{85}$
Solution :
Given: $\frac{\left[\frac{5}{8}-\left\{\frac{3}{8}-\left(\frac{5}{8}-\frac{3}{8}\right)\right\}\right] \text { of } 8.8-1.2}{4 \frac{1}{6} \div 2.5 \times 2 \div \frac{1}{6} \text { of } 60+\left(\frac{3}{4}-\frac{3}{8}\right)}$
= $\frac{\left[\frac{5}{8}-\left\{\frac{3}{8}-\left(\frac{2}{8}\right)\right\}\right] \text { of } 8.8-1.2}{ \frac{25}{6} \div 2.5 \times 2 \div 10+\left(\frac{3}{8}\right)}$
= $\frac{\left[\frac{5}{8}-{\frac{1}{8}}\right] \text { of } 8.8-1.2}{ \frac{25}{6\times 2.5} \times \frac{2}{10}+\frac{3}{8}}$
= $\frac{\frac{4}{8}-\times 8.8-1.2}{\frac{2}{6}+\frac{3}{8}}$
= $\frac{4.4-1.2}{\frac{2}{6}+\frac{3}{8}}$
= $\frac{3.2}{\frac{2}{6}+\frac{3}{8}}$
= $\frac{\frac{32}{10}}{\frac{8+9}{24}}$
= $\frac{32}{10}×\frac{24}{17}$
= $\frac{384}{85}$
= $4\frac{44}{85}$
Hence, the correct answer is $4\frac{44}{85}$.
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