Найдите значение выражения: 1) 2¼ : 3⅛ : 1½; 2) 2¼ : (3/8 : 1/2); 3) (6¾ - 5⅛) : 1⅟₅; 4) (3¼ + 2⅙) : (2⅗ - ⅔ ⋅ 4/9).

Решение:

1. \( 2\frac{1}{4} : 3\frac{1}{8} : 1\frac{1}{2} = \frac{9}{4} : \frac{25}{8} : \frac{3}{2} = \frac{9}{4} \cdot \frac{8}{25} \cdot \frac{2}{3} = \frac{9 \cdot 8 \cdot 2}{4 \cdot 25 \cdot 3} = \frac{3 \cdot 3 \cdot 2 \cdot 4 \cdot 2}{4 \cdot 5 \cdot 5 \cdot 3} = \frac{12}{25} \)
2. \( 2\frac{1}{4} : (\frac{3}{8} : \frac{1}{2}) = \frac{9}{4} : (\frac{3}{8} \cdot \frac{2}{1}) = \frac{9}{4} : \frac{6}{8} = \frac{9}{4} : \frac{3}{4} = \frac{9}{4} \cdot \frac{4}{3} = 3 \)
3. \( (6\frac{3}{4} - 5\frac{1}{8}) : 1\frac{2}{5} = (\frac{27}{4} - \frac{41}{8}) : \frac{7}{5} = (\frac{54}{8} - \frac{41}{8}) : \frac{7}{5} = \frac{13}{8} : \frac{7}{5} = \frac{13}{8} \cdot \frac{5}{7} = \frac{65}{56} = 1\frac{9}{56} \)
4. \( (3\frac{1}{4} + 2\frac{1}{6}) : (2\frac{3}{5} - \frac{2}{3} \cdot \frac{4}{9}) = (\frac{13}{4} + \frac{13}{6}) : (\frac{13}{5} - \frac{8}{27}) = (\frac{39}{12} + \frac{26}{12}) : (\frac{13 \cdot 27}{5 \cdot 27} - \frac{8 \cdot 5}{27 \cdot 5}) = \frac{65}{12} : (\frac{351 - 40}{135}) = \frac{65}{12} : \frac{311}{135} = \frac{65}{12} \cdot \frac{135}{311} = \frac{65 \cdot 135}{12 \cdot 311} = \frac{65 \cdot 45 \cdot 3}{4 \cdot 3 \cdot 311} = \frac{2925}{1244} \)

Ответ: 1) 12/25; 2) 3; 3) 1 9/56; 4) 2925/1244.