Question : The value of $\frac{5-2 \div 4 \times[5-(3-4)]+5 \times 4 \div 2 \text { of } 4}{4+4 \div 8 \text { of } 2 \times(8-5) \times 2 \div 3-8 \div 2 \text { of } 8}$ is:
Option 1: $\frac{9}{8}$
Option 2: $\frac{9}{4}$
Option 3: $\frac{15}{32}$
Option 4: $\frac{89}{4}$
Correct Answer: $\frac{9}{8}$
Solution :
Given: $\frac{5-2 \div 4 \times[5-(3-4)]+5 \times 4 \div 2 \text { of } 4}{4+4 \div 8 \text { of } 2 \times(8-5) \times 2 \div 3-8 \div 2 \text { of } 8}$
= $\frac{5-\frac{2}{4} \times6+5 \times 4 \div 8}{4+4 \div 16 \times3 \times 2 \div 3-8 \div 16}$
= $\frac{5-\frac{2}{4} \times6+5 \times \frac{4}{8}}{4+\frac{4}{16} \times3 \times \frac{2}{3}-\frac{8}{16}}$
= $\frac{5-3+5 \times \frac{1}{2}}{4+\frac{1}{2}-\frac{1}{2}}$
= $\frac{2+\frac{5}{2}}{4}$
= $\frac{9}{8}$
Hence, the correct answer is $\frac{9}{8}$.
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