3) \(\frac{(6\frac{1}{8}\cdot1\frac{2}{7}-2\frac{11}{14}\cdot1\frac{8}{13})\cdot1\frac{3}{5}}{1\frac{1}{7}\cdot(\frac{9}{16}+4\frac{2}{3}\cdot\frac{9}{56})}\)

Question

Вопрос:

Accepted Answer

Числитель: \(6\frac{1}{8}=\frac{49}{8}\), \(1\frac{2}{7}=\frac{9}{7}\), поэтому \(\frac{49}{8}\cdot\frac{9}{7}=\frac{63}{8}\).

\(2\frac{11}{14}=\frac{39}{14}\), \(1\frac{8}{13}=\frac{21}{13}\), поэтому \(\frac{39}{14}\cdot\frac{21}{13}=\frac{63}{14}=\frac{9}{2}\).

\(\frac{63}{8}-\frac{9}{2}=\frac{27}{8}\), а \(1\frac{3}{5}=\frac{8}{5}\), значит числитель равен \(\frac{27}{5}\).

Знаменатель: \(1\frac{1}{7}=\frac{8}{7}\), \(4\frac{2}{3}=\frac{14}{3}\).

\(\frac{9}{16}+\frac{14}{3}\cdot\frac{9}{56}=\frac{9}{16}+\frac{3}{4}=\frac{21}{16}\).

Знаменатель: \(\frac{8}{7}\cdot\frac{21}{16}=\frac{3}{2}\).

\(\frac{27}{5}:\frac{3}{2}=\frac{18}{5}=3\frac{3}{5}\).

Ответ: \(3\frac{3}{5}\).