10) \(\left(46\dfrac{2}{25}:12+41\dfrac{23}{35}:260\dfrac{5}{14}+800:12\dfrac{28}{31}\right)\times\dfrac{0,8\cdot7,2\cdot4,5\cdot1,3}{6,5\cdot2,7\cdot1,92}\);

Question

Вопрос:

10) \(\left(46\dfrac{2}{25}:12+41\dfrac{23}{35}:260\dfrac{5}{14}+800:12\dfrac{28}{31}\right)\times\dfrac{0,8\cdot7,2\cdot4,5\cdot1,3}{6,5\cdot2,7\cdot1,92}\);

Accepted Answer

Преобразуем смешанные числа:

\(46\dfrac{2}{25}=\dfrac{1152}{25},\quad 41\dfrac{23}{35}=\dfrac{1458}{35},\quad 260\dfrac{5}{14}=\dfrac{3645}{14},\quad 12\dfrac{28}{31}=\dfrac{400}{31}\).

Первая скобка:

\(\dfrac{1152}{25}:12=\dfrac{96}{25}\).

\(\dfrac{1458}{35}:\dfrac{3645}{14}=\dfrac{1458}{35}\cdot\dfrac{14}{3645}=\dfrac{4}{25}\).

\(800:\dfrac{400}{31}=62\).

Значит, \(\dfrac{96}{25}+\dfrac{4}{25}+62=4+62=66\).

Вторая дробь:

\(\dfrac{0.8\cdot7.2\cdot4.5\cdot1.3}{6.5\cdot2.7\cdot1.92}=\dfrac{\frac45\cdot\frac{36}{5}\cdot\frac92\cdot\frac{13}{10}}{\frac{13}{2}\cdot\frac{27}{10}\cdot\frac{48}{25}}=\dfrac{5}{2}\).

Искомое значение: \(66\cdot\dfrac{5}{2}=165\).

Ответ: \(165\).