80. 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 \cdot 4/9.

Ответ: 1) 3; 2) 3/2; 3) 3/2; 4) 173/90

1. 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) \(2 \frac{1}{4} : (\frac{3}{8} : \frac{1}{2}) = \frac{9}{4} : (\frac{3}{8} \cdot \frac{2}{1}) = \frac{9}{4} : \frac{6}{8} = \frac{9}{4} \cdot \frac{8}{6} = \frac{9 \cdot 8}{4 \cdot 6} = \frac{3 \cdot 2}{1 \cdot 2} = 3\)
3. 3) \((6 \frac{3}{4} – 5 \frac{1}{8} : 1 \frac{9}{32}) : 2 \frac{1}{5} = (\frac{27}{4} – \frac{41}{8} : \frac{41}{32}) : \frac{11}{5} = (\frac{27}{4} – \frac{41}{8} \cdot \frac{32}{41}) : \frac{11}{5} = (\frac{27}{4} – \frac{41 \cdot 32}{8 \cdot 41}) : \frac{11}{5} = (\frac{27}{4} – \frac{1 \cdot 4}{1 \cdot 1}) : \frac{11}{5} = (\frac{27}{4} – 4) : \frac{11}{5} = (\frac{27}{4} – \frac{16}{4}) : \frac{11}{5} = \frac{11}{4} : \frac{11}{5} = \frac{11}{4} \cdot \frac{5}{11} = \frac{11 \cdot 5}{4 \cdot 11} = \frac{1 \cdot 5}{4 \cdot 1} = \frac{5}{4} = 1 \frac{1}{4}\)
4. 4) \((3 \frac{1}{4} + 2 \frac{1}{6}) : 2 \frac{3}{5} – \frac{2}{3} \cdot \frac{4}{9} = (\frac{13}{4} + \frac{13}{6}) : \frac{13}{5} – \frac{8}{27} = (\frac{39}{12} + \frac{26}{12}) : \frac{13}{5} – \frac{8}{27} = \frac{65}{12} : \frac{13}{5} – \frac{8}{27} = \frac{65}{12} \cdot \frac{5}{13} – \frac{8}{27} = \frac{65 \cdot 5}{12 \cdot 13} – \frac{8}{27} = \frac{5 \cdot 5}{12 \cdot 1} – \frac{8}{27} = \frac{25}{12} – \frac{8}{27} = \frac{675}{324} – \frac{96}{324} = \frac{579}{324} = \frac{193}{108} = 1 \frac{85}{108}\)

Ответ: 1) 3; 2) 3/2; 3) 3/2; 4) 173/90