Вычислите \(\frac{2\frac{2}{7}\cdot2{,}4\cdot1\frac{5}{9}\cdot1\frac{9}{16}}{3\frac{1}{3}\cdot1{,}125\cdot1\frac{5}{7}\cdot1\frac{7}{9}}\).

Question

Вопрос:

Вычислите \(\frac{2\frac{2}{7}\cdot2{,}4\cdot1\frac{5}{9}\cdot1\frac{9}{16}}{3\frac{1}{3}\cdot1{,}125\cdot1\frac{5}{7}\cdot1\frac{7}{9}}\).

Accepted Answer

Преобразуем числа в дроби: \(2\frac27=\frac{16}{7}\), \(2{,}4=\frac{12}{5}\), \(1\frac59=\frac{14}{9}\), \(1\frac9{16}=\frac{25}{16}\); \(3\frac13=\frac{10}{3}\), \(1{,}125=\frac98\), \(1\frac57=\frac{12}{7}\), \(1\frac79=\frac{16}{9}\).

\[\frac{\frac{16}{7}\cdot\frac{12}{5}\cdot\frac{14}{9}\cdot\frac{25}{16}}{\frac{10}{3}\cdot\frac98\cdot\frac{12}{7}\cdot\frac{16}{9}}=\frac{7}{8}.\]

Ответ: \(\frac78\).