3. Найдите значение выражения: 1) 2 1/4 : 3/8 : 1/2; 2) 2 1/4 : (3/8 : 1/2); 3) (6 3/4 - 5 1/8 : 1 9/32) : 2 1/5; 4) (3 1/4 + 2 1/6) : 2 3/5 - 2/3 * 4/9.

Решение:

1. \(2\frac{1}{4} : \frac{3}{8} : \frac{1}{2}\) = \(\frac{9}{4} : \frac{3}{8} : \frac{1}{2}\) = \(\frac{9}{4} \cdot \frac{8}{3} \cdot \frac{2}{1}\) = \(\frac{9 \cdot 8 \cdot 2}{4 \cdot 3 \cdot 1}\) = \(\frac{3 \cdot 2 \cdot 2}{1 \cdot 1 \cdot 1}\) = 12
2. \(2\frac{1}{4} : (\frac{3}{8} : \frac{1}{2})\) = \(\frac{9}{4} : (\frac{3}{8} \cdot \frac{2}{1})\) = \(\frac{9}{4} : \frac{6}{8}\) = \(\frac{9}{4} : \frac{3}{4}\) = \(\frac{9}{4} \cdot \frac{4}{3}\) = \(\frac{9 \cdot 4}{4 \cdot 3}\) = 3
3. \((6\frac{3}{4} - 5\frac{1}{8} : 1\frac{9}{32}) : 2\frac{1}{5}\) = \((\frac{27}{4} - \frac{41}{8} : \frac{41}{32}) : \frac{11}{5}\) = \((\frac{27}{4} - \frac{41}{8} \cdot \frac{32}{41}) : \frac{11}{5}\) = \((\frac{27}{4} - \frac{32}{8}) : \frac{11}{5}\) = \((\frac{27}{4} - 4) : \frac{11}{5}\) = \((\frac{27}{4} - \frac{16}{4}) : \frac{11}{5}\) = \(\frac{11}{4} : \frac{11}{5}\) = \(\frac{11}{4} \cdot \frac{5}{11}\) = \(\frac{5}{4}\) = \(1\frac{1}{4}\)
4. \((3\frac{1}{4} + 2\frac{1}{6}) : 2\frac{3}{5} - \frac{2}{3} \cdot \frac{4}{9}\) = \((\frac{13}{4} + \frac{13}{6}) : \frac{13}{5} - \frac{8}{27}\) = \((\frac{39}{12} + \frac{26}{12}) : \frac{13}{5} - \frac{8}{27}\) = \((\frac{65}{12}) : \frac{13}{5} - \frac{8}{27}\) = \(\frac{65}{12} \cdot \frac{5}{13} - \frac{8}{27}\) = \(\frac{5 \cdot 5}{12} - \frac{8}{27}\) = \(\frac{25}{12} - \frac{8}{27}\) = \(\frac{25 \cdot 9}{108} - \frac{8 \cdot 4}{108}\) = \(\frac{225 - 32}{108}\) = \(\frac{193}{108}\) = \(1\frac{85}{108}\)

Ответ: 1) 12; 2) 3; 3) \(1\frac{1}{4}\); 4) \(1\frac{85}{108}\).