Simplify \(\frac{(\frac{2}{3} - \frac{1}{5}) - \frac{1}{3} \text{of} \frac{2}{5}}{3 - \frac{1}{1 \frac{1}{2}}}\)

A.

\(\frac{1}{7}\)

B.

7

C.

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

D.

3

Correct answer is A

\(\frac{2}{3} - \frac{1}{5}\) = \(\frac{10 - 3}{15}\)

= \(\frac{7}{15}\)

\(\frac{1}{3}\) Of \(\frac{2}{5}\) = \(\frac{1}{3}\) x \(\frac{2}{5}\)

= \(\frac{2}{15}\)

(\(\frac{2}{3} - \frac{1}{5}\)) - \(\frac{1}{3}\) of \(\frac{2}{5}\)

= \(\frac{7}{15} - \frac{2}{15}\) = \(\frac{1}{3}\)

3 - \(\frac{1}{1 \frac{1}{2}}\) = 3 - \(\frac{2}{3}\)

= \(\frac{7}{3}\)

\(\frac{\frac{2}{3} - \frac{1}{5} \text{of} \frac{2}{15}}{3 - \frac{1}{1 \frac{1}{2}}}\)

= \(\frac{\frac{1}{3}}{\frac{7}{3}}\)

= \(\frac{1}{3}\) x \(\frac{3}{7}\)

= \(\frac{1}{7}\)