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})