1. Найдите значение выражения: а) \(\frac{5}{8}\cdot2\frac{3}{15}\cdot64\); б) \(\left(\frac{2}{9}+1\frac{2}{3}\right)\cdot3\); в) \(\frac{5}{12}\cdot2\frac{3}{7}+\frac{5}{12}\cdot3\frac{4}{7}\); г) \(\left(\frac{9}{16}+4\frac{2}{3}\cdot\frac{9}{56}\right):1\frac{5}{7}\); д) \(\left(11\frac{5}{11}-8\frac{21}{22}\right):1\frac{2}{3}\).

а) \(2\frac{3}{15}=2\frac{1}{5}=\frac{11}{5}\).

\(\frac{5}{8}\cdot\frac{11}{5}\cdot64=11\cdot8=88\).

б) \(1\frac{2}{3}=\frac{5}{3}\).

\(\left(\frac{2}{9}+\frac{5}{3}\right)\cdot3=\left(\frac{2}{9}+\frac{15}{9}\right)\cdot3=\frac{17}{9}\cdot3=\frac{17}{3}=5\frac{2}{3}\).

в) Вынесем общий множитель \(\frac{5}{12}\):

\(\frac{5}{12}\left(2\frac{3}{7}+3\frac{4}{7}\right)=\frac{5}{12}\left(\frac{17}{7}+\frac{25}{7}\right)=\frac{5}{12}\cdot6=\frac{5}{2}=2\frac{1}{2}\).

г) \(4\frac{2}{3}=\frac{14}{3}\), поэтому

\(\left(\frac{9}{16}+\frac{14}{3}\cdot\frac{9}{56}\right):\frac{12}{7}=\left(\frac{9}{16}+\frac{3}{4}\right)\cdot\frac{7}{12}=\frac{21}{16}\cdot\frac{7}{12}=\frac{49}{64}\).

д) \(11\frac{5}{11}=\frac{252}{22}\), \(8\frac{21}{22}=\frac{197}{22}\).

\(\left(\frac{252}{22}-\frac{197}{22}\right):\frac{5}{3}=\frac{55}{22}\cdot\frac{3}{5}=\frac{5}{2}\cdot\frac{3}{5}=\frac{3}{2}=1\frac{1}{2}\).

Ответ: а) 88; б) \(5\frac{2}{3}\); в) \(2\frac{1}{2}\); г) \(\frac{49}{64}\); д) \(1\frac{1}{2}\).