3. Найдите значение выражения: 1) $$2\frac{1}{4}:\frac{3}{8} \cdot \frac{1}{2}$$; 2) $$2\frac{1}{4}:(\frac{3}{8}:\frac{1}{2})$$; 3) $$(6\frac{3}{4}-5\frac{1}{8}:1\frac{9}{32}):2\frac{1}{5}$$; 4) $$(3\frac{1}{4}+2\frac{1}{6}):2\frac{2}{3}-\frac{2}{3}:\frac{4}{9}$$.

Решение:

1. $$2\frac{1}{4}:\frac{3}{8} \cdot \frac{1}{2} = \frac{9}{4} : \frac{3}{8} \cdot \frac{1}{2} = \frac{9}{4} \cdot \frac{8}{3} \cdot \frac{1}{2} = \frac{9 \cdot 8 \cdot 1}{4 \cdot 3 \cdot 2} = \frac{3 \cdot 3 \cdot 4 \cdot 2}{4 \cdot 3 \cdot 2} = 3$$

   Ответ: 3

2. $$2\frac{1}{4}:(\frac{3}{8}:\frac{1}{2}) = \frac{9}{4} : (\frac{3}{8} \cdot \frac{2}{1}) = \frac{9}{4} : \frac{6}{8} = \frac{9}{4} \cdot \frac{8}{6} = \frac{9 \cdot 8}{4 \cdot 6} = \frac{3 \cdot 3 \cdot 4 \cdot 2}{4 \cdot 2 \cdot 3} = 3$$

   Ответ: 3

3. $$(6\frac{3}{4}-5\frac{1}{8}:1\frac{9}{32}):2\frac{1}{5} = (\frac{27}{4} - \frac{41}{8} : \frac{41}{32}) : \frac{11}{5} = (\frac{27}{4} - \frac{41}{8} \cdot \frac{32}{41}) : \frac{11}{5} = (\frac{27}{4} - \frac{41 \cdot 32}{8 \cdot 41}) : \frac{11}{5} = (\frac{27}{4} - \frac{32}{8}) : \frac{11}{5} = (\frac{27}{4} - 4) : \frac{11}{5} = (\frac{27}{4} - \frac{16}{4}) : \frac{11}{5} = \frac{11}{4} : \frac{11}{5} = \frac{11}{4} \cdot \frac{5}{11} = \frac{11 \cdot 5}{4 \cdot 11} = \frac{5}{4} = 1\frac{1}{4}$$

   Ответ: $$1\frac{1}{4}$$

4. $$(3\frac{1}{4}+2\frac{1}{6}):2\frac{2}{3}-\frac{2}{3}:\frac{4}{9} = (\frac{13}{4} + \frac{13}{6}) : \frac{8}{3} - \frac{2}{3} : \frac{4}{9} = (\frac{39}{12} + \frac{26}{12}) : \frac{8}{3} - \frac{2}{3} \cdot \frac{9}{4} = \frac{65}{12} : \frac{8}{3} - \frac{2 \cdot 9}{3 \cdot 4} = \frac{65}{12} \cdot \frac{3}{8} - \frac{18}{12} = \frac{65 \cdot 3}{12 \cdot 8} - \frac{18}{12} = \frac{65 \cdot 3}{4 \cdot 3 \cdot 8} - \frac{18}{12} = \frac{65}{32} - \frac{18}{12} = \frac{65}{32} - \frac{6}{4} = \frac{65}{32} - \frac{48}{32} = \frac{17}{32}$$

   Ответ: $$\frac{17}{32}$$