65. Найдите значение выражения: 1) 5 1/3 · 9 − 2 3/4 · 5 1/3 − 7 1/2 · 1 5/9; 2) 2 1/4 · 2 2/27 + (3 1/6 + 4 5/6 · 11/29) · 1 1/15.

1) Вынесем общий множитель \(5\frac{1}{3}\):

\(5\frac{1}{3}\cdot9-2\frac{3}{4}\cdot5\frac{1}{3}-7\frac{1}{2}\cdot1\frac{5}{9}\)

\(=\frac{16}{3}\cdot9-\frac{11}{4}\cdot\frac{16}{3}-\frac{15}{2}\cdot\frac{14}{9}\)

\(=48-\frac{44}{3}-\frac{35}{3}=48-\frac{79}{3}=\frac{65}{3}=21\frac{2}{3}\).

2) \(2\frac{1}{4}\cdot2\frac{2}{27}+\left(3\frac{1}{6}+4\frac{5}{6}\cdot\frac{11}{29}\right)\cdot1\frac{1}{15}\)

\(=\frac{9}{4}\cdot\frac{56}{27}+\left(\frac{19}{6}+\frac{29}{6}\cdot\frac{11}{29}\right)\cdot\frac{16}{15}\)

\(=\frac{14}{3}+\left(\frac{19}{6}+\frac{11}{6}\right)\cdot\frac{16}{15}\)

\(=\frac{14}{3}+5\cdot\frac{16}{15}=\frac{14}{3}+\frac{16}{3}=10\).

Ответ: 1) \(21\frac{2}{3}\); 2) \(10\).