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The value of $$3\frac{1}{5} \div 4\frac{1}{2} \text{of} 5\frac{1}{3} - \frac{1}{8} \div \frac{1}{2} \text{of} \frac{1}{4} + \frac{1}{4}\left(\frac{1}{2} \div \frac{1}{8} \times \frac{1}{4}\right)$$ is:
$$3\frac{1}{5} \div 4\frac{1}{2} \text{of} 5\frac{1}{3} - \frac{1}{8} \div \frac{1}{2} \text{of} \frac{1}{4} + \frac{1}{4}\left(\frac{1}{2} \div \frac{1}{8} \times \frac{1}{4}\right)$$
= $$\frac{16}{5} \div \frac{9}{2} \text{of} \frac{16}{3} - \frac{1}{8} \div \frac{1}{2} \text{of} \frac{1}{4} + \frac{1}{4}\left(\frac{1}{2} \times \frac{8}{1} \times \frac{1}{4}\right)$$
= $$\frac{16}{5}\div24-\frac{1}{8}\div\frac{1}{8}+\frac{1}{4}\left(1\right)$$
= $$\frac{16}{5\times24}-1+\frac{1}{4}$$
= $$\frac{2}{15}-1+\frac{1}{4}$$
= $$\frac{8-60+15}{60}$$
= $$-\frac{37}{60}$$
Hence, the correct answer is Option A
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