Question

\(\dfrac{2}{3}-\dfrac{1}{3}\left(\dfrac{4}{9}-\dfrac{5}{6}\right):\dfrac{7}{12}\)

Answer 1

`2/3 - 1/3. ( 4/9 - 5/6) : 7/12`

` = 2/3 - 1/3 .( 24/56 - 45/54) : 7/12`

` = 2/3 - 1/3 . ( -21/54) : 7/12`

`=2/3 - 1/3 . (-7/18) : 7/12`

` = 2/3 - 1/3 . (7/18) xx 12/7`

`=2/3 - (-7)/54 xx 12/7`

`=2/3 - (-2)/9`

`=2/3 + 2/9`

` = 6/9 + 2/9`

` = 8/9`

Answer 2

\(\dfrac{2}{3}-\dfrac{1}{3}\left(\dfrac{4}{9}-\dfrac{5}{6}\right):\dfrac{7}{12}\\ =\dfrac{2}{3}-\dfrac{1}{3}.\left(-\dfrac{7}{18}\right):\dfrac{7}{12}\\ =\dfrac{2}{3}+\dfrac{7}{54}.\dfrac{12}{7}\\ =\dfrac{2}{3}+\dfrac{2}{9}\\ =\dfrac{6}{9}+\dfrac{2}{9}\\ =\dfrac{8}{9}\)

Answer 3

Answer 4

\(\dfrac{2}{3}-\dfrac{1}{3}\left(\dfrac{4}{9}-\dfrac{5}{6}\right):\dfrac{7}{12}\\ =\dfrac{2-1}{3}\left(\dfrac{4}{9}-\dfrac{5}{6}\right):\dfrac{7}{12}\\ =\dfrac{1}{3}\left(\dfrac{4\times6}{9\times6}-\dfrac{5\times9}{6\times9}\right):\dfrac{7}{12}\\ =\dfrac{1}{3}\left(\dfrac{24}{54}-\dfrac{45}{54}\right):\dfrac{7}{12}\\ =\dfrac{1}{3}\left(\dfrac{24-45}{54}\right):\dfrac{7}{12}\\ =\dfrac{1}{3}.\dfrac{-21}{54}:\dfrac{7}{12}\\ =\dfrac{1}{3}.\dfrac{-7}{18}:\dfrac{7}{12}\\ =\dfrac{1}{3}.\dfrac{-7}{18}.\dfrac{12}{7}\\ =\dfrac{1.\left(-7\right).12}{3.18.7}\\ =\dfrac{-84}{378}\\ =\dfrac{-2}{9}.\)