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

Answer Details

To evaluate the given expression, we follow the order of operations or BODMAS (Brackets, Order, Division, Multiplication, Addition, and Subtraction) and simplify the expression step by step. First, we simplify the fraction in the middle of the expression, \(\frac{3}{4}of\frac{2}{5} = \frac{3}{4} \times \frac{2}{5} = \frac{3\times 2}{4\times 5} = \frac{3}{10}\) Now, we can rewrite the expression as \(\frac{1}{2}+\frac{3}{10}\div 1\frac{3}{5}\) Next, we simplify the mixed number in the denominator by converting it to an improper fraction, \(1\frac{3}{5} = \frac{8}{5}\) Now, we can rewrite the expression as \(\frac{1}{2}+\frac{3}{10}\div \frac{8}{5}\) To divide by a fraction, we multiply by its reciprocal, \(\frac{1}{2}+\frac{3}{10}\times \frac{5}{8} = \frac{1}{2}+\frac{3\times 5}{10\times 8} = \frac{1}{2}+\frac{3}{16} = \frac{8}{16}+\frac{3}{16} = \frac{11}{16}\) Therefore, the value of the given expression is \(\frac{11}{16}\). Thus, option (B) is the correct answer.