Evaluate \(\frac{1}{2}+\frac{3}{4}of\frac{2}{5}\div 1\frac{3}{5}\)

A.

\(\frac{15}{16}\)

B.

\(\frac{11}{16}\)

C.

\(\frac{49}{50}\)

D.

\(3\frac{1}{5}\)

Correct answer is B

\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)

= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\)

= \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\)

= \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\)

= \(\frac{1}{2} + \frac{3}{16}\)

= \(\frac{11}{16}\)