Вычислите \(2\frac{2}{7}\times2,4\times1\frac{5}{9}\times1\frac{9}{16}\div\left(3\frac{1}{3}\times1,125\times1\frac{5}{7}\times1\frac{7}{9}\right)\).

Преобразуем числа в неправильные дроби: \(2\frac{2}{7}=\frac{16}{7}\), \(1\frac{5}{9}=\frac{14}{9}\), \(1\frac{9}{16}=\frac{25}{16}\), \(3\frac{1}{3}=\frac{10}{3}\), \(1,125=\frac{9}{8}\), \(1\frac{5}{7}=\frac{12}{7}\), \(1\frac{7}{9}=\frac{16}{9}\), \(2,4=\frac{12}{5}\).

Тогда выражение равно:

\[\frac{16}{7}\cdot\frac{12}{5}\cdot\frac{14}{9}\cdot\frac{25}{16}\div\left(\frac{10}{3}\cdot\frac{9}{8}\cdot\frac{12}{7}\cdot\frac{16}{9}\right)=\frac{7}{4}.\]

Ответ: \(\frac{7}{4}\).