1.006. Вычислить: \(\dfrac{(13,75+9\dfrac16)\cdot1,2}{(10,3-8\dfrac12)\cdot\frac59}+\dfrac{(6,8-3\dfrac35)\cdot5\dfrac56}{(3\dfrac23-3\dfrac16)\cdot56}-27\dfrac16\).

Question

Вопрос:

1.006. Вычислить: \(\dfrac{(13,75+9\dfrac16)\cdot1,2}{(10,3-8\dfrac12)\cdot\frac59}+\dfrac{(6,8-3\dfrac35)\cdot5\dfrac56}{(3\dfrac23-3\dfrac16)\cdot56}-27\dfrac16\).

Accepted Answer

Первая дробь: \(\dfrac{(13.75+\frac{55}{6})\cdot\frac65}{(10.3-\frac{17}{2})\cdot\frac59}=\dfrac{\frac{275}{12}\cdot\frac65}{\frac95\cdot\frac59}=\dfrac{275}{9}\).

Вторая дробь: \(\dfrac{(6.8-\frac{18}{5})\cdot\frac{35}{6}}{(\frac{11}{3}-\frac{19}{6})\cdot56}=\dfrac{\frac{17}{5}\cdot\frac{35}{6}}{\frac12\cdot56}=\dfrac{17}{24}\).

\(\dfrac{275}{9}+\dfrac{17}{24}-\dfrac{163}{6}=\dfrac{19}{72}\).

Ответ: \(\dfrac{19}{72}\).