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: A
Explanation
\(\frac{2}{3} - \frac{1}{5}\) = \(\frac{10 - 3}{15}\)
= \(\frac{7}{15}\)
\(\frac{1}{3}\) 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 \(\frac{3}{7}\)
= \(\frac{1}{7}\)