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
\(\frac{12}{125}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
(\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)
= (\(\frac{3^3}{5^3}\))-\(\frac{1}{3}\)-\(\frac{1}{3}\) x (\(\frac{3^2}{3^2}\))\(\frac{1}{2}\) -\(\frac{1}{2}\)
= \(\frac{3^{-1}}{3^{-1}} \times \frac{2}{3}\)
= \(\frac{\frac{1}{3}}{\frac{1}{5}} \times \frac{2}{3}\)
\(\frac{1}{3} \times \frac{5}{1} \times {2}{3} = \frac{10}{9}\)
Source: Myschool Past Questions Archive (Record #36793)