Solve (\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)

A.

\(\frac{10}{9}\)

B.

\(\frac{9}{10}\)

C.

\(\frac{2}{5}\)

D.

\(\frac{12}{125}\)

Correct answer is A

(\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)

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

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

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

\(\frac{1}{3} \times \frac{5}{1} \times {2}{3} = \frac{10}{9}\)