Mathematics

simplify (frac{frac{7}{9}-frac{2}{3}}{frac{1}{3}+frac{frac{2}{5}}{frac{4}{5}}})

simplify (frac{frac{7}{9}-frac{2}{3}}{frac{1}{3}+frac{frac{2}{5}}{frac{4}{5}}})
  • A.
    (frac{11}{12})
  • B.
    (frac{5}{6})
  • C.
    (frac{1}{5})
  • D.
    (frac{2}{15})
Correct Answer: Option D
Explanation

(frac{frac{7}{9}-frac{2}{3}}{frac{1}{3}+frac{frac{2}{5}}{frac{4}{5}}}\
=frac{frac{7-6}{9}}{frac{1}{3}+frac{frac{2}{5}}{frac{4}{5}}}\
=frac{frac{1}{9}}{frac{1}{3}+left(frac{2}{5}times frac{5}{4}right)}\
=frac{frac{1}{9}}{frac{1}{3}+frac{1}{2}}
=frac{frac{1}{9}}{frac{2+3}{6}}\
=frac{frac{1}{9}}{frac{5}{6}}\
=frac{1}{9}timesfrac{6}{5}\
=frac{2}{15})