4. \(\left(\frac{2,5+3\frac{1}{3}}{2,5-1\frac{1}{3}}:\frac{4,6-2\frac{1}{3}}{-4\frac{7}{15}-2\frac{1}{3}}\right)\cdot\left(\frac{0,05}{\frac{1}{7}-0,125}-0,2\right)\)

Question

4. \(\left(\frac{2,5+3\frac{1}{3}}{2,5-1\frac{1}{3}}:\frac{4,6-2\frac{1}{3}}{-4\frac{7}{15}-2\frac{1}{3}}\right)\cdot\left(\frac{0,05}{\frac{1}{7}-0,125}-0,2\right)\)

Accepted Answer

Преобразуем десятичные дроби и смешанные числа:

\(2,5=\frac52\), \(4,6=\frac{23}{5}\), \(0,05=\frac1{20}\), \(0,125=\frac18\), \(0,2=\frac15\).

\(\frac{2,5+3\frac13}{2,5-1\frac13}=\frac{\frac52+\frac{10}{3}}{\frac52-\frac43}=\frac{\frac{35}{6}}{\frac76}=5\).

\(\frac{4,6-2\frac13}{-4\frac7{15}-2\frac13}=\frac{\frac{23}{5}-\frac73}{-\frac{67}{15}-\frac73}=\frac{\frac{34}{15}}{-\frac{34}{5}}=-\frac13\).

Первая скобка: \(5:\left(-\frac13\right)=-15\).

Вторая скобка: \(\frac{0,05}{\frac17-0,125}-0,2=\frac{\frac1{20}}{\frac17-\frac18}-\frac15=\frac{\frac1{20}}{\frac1{56}}-\frac15=\frac{14}{5}-\frac15=\frac{13}{5}\).

\(-15\cdot\frac{13}{5}=-39\).

Ответ: \(-39\).