Evaluate \(\frac{\frac{1}{10}\times\frac{2}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{3}{5}}-\frac{1}{4}}\)

Explanation

\(\frac{\frac{1}{10}\times\frac{2}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{3}{5}}-\frac{1}{4}}\\Numerator \hspace{1mm}\frac{1}{10}\times\frac{2}{3}+\frac{1}{4} = \frac{1}{5}+\frac{1}{4}\\=\frac{4+15}{60}=\frac{19}{60}\\denominator\hspace{1mm}= \frac{\frac{1}{2}}{\frac{3}{5}}-\frac{1}{4}=\frac{1}{2}\times\frac{5}{3}-\frac{1}{4}\\=\frac{5}{6}-\frac{1}{4}\\=\frac{10-3}{12}\\=\frac{7}{12}\\\frac{Numerator}{denominator}=\frac{\frac{19}{60}}{\frac{7}{12}}\\=\frac{19}{60}\times\frac{12}{7}=\frac{19}{35}\)