4. Выполните действия: \(\left(8-2\frac{11}{12}\right) \cdot \frac{7}{16}:2\frac{2}{27}.\)

Выполним действия:

1) \(8 - 2\frac{11}{12} = \frac{8 \cdot 12}{12} - \frac{2 \cdot 12 + 11}{12} = \frac{96}{12} - \frac{35}{12} = \frac{96-35}{12} = \frac{61}{12}\)

2) \(\frac{61}{12} \cdot \frac{7}{16} = \frac{61 \cdot 7}{12 \cdot 16} = \frac{427}{192}\)

3) \(2\frac{2}{27} = \frac{2 \cdot 27 + 2}{27} = \frac{54+2}{27} = \frac{56}{27}\)

4) \(\frac{427}{192} : \frac{56}{27} = \frac{427}{192} \cdot \frac{27}{56} = \frac{427 \cdot 27}{192 \cdot 56} = \frac{427 \cdot 27}{192 \cdot 56} = \frac{427 \cdot 9}{64 \cdot 56} = \frac{3843}{3584}\)

Выделим целую часть:

\(\frac{3843}{3584} = 1\frac{259}{3584}\)

Ответ: \(1\frac{259}{3584}\)