The value of $$\frac{3}{5} \times 1 \frac{7}{8} \div 1\frac{1}{3}  of  \frac{3}{16} - \left(3 \frac{1}{5} \div 4 \frac{1}{2}  of  5 \frac{1}{3}\right) \times 2\frac{1}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}$$ is:

$$\frac{3}{5} \times 1 \frac{7}{8} \div 1\frac{1}{3} of \frac{3}{16} - \left(3 \frac{1}{5} \div 4 \frac{1}{2} of 5 \frac{1}{3}\right) \times 2\frac{1}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}$$

By BODMAS rule,

$$\frac{3}{5} \times  \frac{15}{8} \div \frac{4}{3} of \frac{3}{16} - \left( \frac{16}{5} \div  \frac{9}{2} of  \frac{16}{3}\right) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}$$

$$\frac{3}{5} \times \frac{15}{8} \div \frac{1}{4} - ( \frac{16}{5}\div 24) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{8} \times \frac{4}{1}$$

$$\frac{3}{5} \times \frac{15}{8} \times 4 - ( \frac{16}{5} \times \frac{1}{24}) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{2}$$

$$\frac{3}{5} \times \frac{15}{2}  - \frac{2}{15}  \times \frac{5}{2}  + \frac{1}{2} + \frac{1}{2}$$

$$\frac{9}{2}  - \frac{1}{3} +  \frac{1}{4} =  \frac{53}{12}$$ = 4\frac{5}{12}