80. Найдите значение выражения: 1) \(5\frac{1}{3}:\frac{8}{9}:\frac{1}{3}\); 2) \(5\frac{1}{3}:(\frac{8}{9}:\frac{1}{3})\); 3) \((\frac{5}{7} - 6\frac{5}{6}:1\frac{5}{36}):4\frac{3}{4}\); 4) \((2\frac{5}{6}+2\frac{2}{9}):3\frac{1}{4} - 2\frac{1}{7}:1\frac{2}{7}\)

1) \(5\frac{1}{3}:\frac{8}{9}:\frac{1}{3} = \frac{5 \cdot 3 + 1}{3} : \frac{8}{9} : \frac{1}{3} = \frac{16}{3} \cdot \frac{9}{8} : \frac{1}{3} = \frac{16 \cdot 9}{3 \cdot 8} : \frac{1}{3} = \frac{2 \cdot 8 \cdot 3 \cdot 3}{3 \cdot 8} : \frac{1}{3} = 2 \cdot 3 : \frac{1}{3} = 6 \cdot 3 = 18\)

2) \(5\frac{1}{3}:(\frac{8}{9}:\frac{1}{3}) = \frac{5 \cdot 3 + 1}{3} : (\frac{8}{9} : \frac{1}{3}) = \frac{16}{3} : (\frac{8}{9} \cdot 3) = \frac{16}{3} : \frac{8 \cdot 3}{9} = \frac{16}{3} : \frac{8 \cdot 3}{3 \cdot 3} = \frac{16}{3} : \frac{8}{3} = \frac{16}{3} \cdot \frac{3}{8} = \frac{16 \cdot 3}{3 \cdot 8} = \frac{2 \cdot 8 \cdot 3}{3 \cdot 8} = 2\)

3) \((\frac{5}{7} - 6\frac{5}{6}:1\frac{5}{36}):4\frac{3}{4} = (\frac{5}{7} - \frac{6 \cdot 6 + 5}{6} : \frac{1 \cdot 36 + 5}{36}) : \frac{4 \cdot 4 + 3}{4} = (\frac{5}{7} - \frac{41}{6} : \frac{41}{36}) : \frac{19}{4} = (\frac{5}{7} - \frac{41}{6} \cdot \frac{36}{41}) : \frac{19}{4} = (\frac{5}{7} - \frac{41 \cdot 36}{6 \cdot 41}) : \frac{19}{4} = (\frac{5}{7} - \frac{6 \cdot 6 \cdot 41}{6 \cdot 41}) : \frac{19}{4} = (\frac{5}{7} - 6) : \frac{19}{4} = (\frac{5}{7} - \frac{6 \cdot 7}{7}) : \frac{19}{4} = (\frac{5}{7} - \frac{42}{7}) : \frac{19}{4} = \frac{5 - 42}{7} : \frac{19}{4} = \frac{-37}{7} : \frac{19}{4} = -\frac{37}{7} \cdot \frac{4}{19} = -\frac{37 \cdot 4}{7 \cdot 19} = -\frac{148}{133} = -1\frac{15}{133}\)

4) \((2\frac{5}{6}+2\frac{2}{9}):3\frac{1}{4} - 2\frac{1}{7}:1\frac{2}{7} = (\frac{2 \cdot 6 + 5}{6} + \frac{2 \cdot 9 + 2}{9}) : \frac{3 \cdot 4 + 1}{4} - \frac{2 \cdot 7 + 1}{7} : \frac{1 \cdot 7 + 2}{7} = (\frac{17}{6} + \frac{20}{9}) : \frac{13}{4} - \frac{15}{7} : \frac{9}{7} = (\frac{17 \cdot 3}{6 \cdot 3} + \frac{20 \cdot 2}{9 \cdot 2}) : \frac{13}{4} - \frac{15}{7} \cdot \frac{7}{9} = (\frac{51}{18} + \frac{40}{18}) : \frac{13}{4} - \frac{15 \cdot 7}{7 \cdot 9} = \frac{51 + 40}{18} : \frac{13}{4} - \frac{15}{9} = \frac{91}{18} : \frac{13}{4} - \frac{15}{9} = \frac{91}{18} \cdot \frac{4}{13} - \frac{15}{9} = \frac{91 \cdot 4}{18 \cdot 13} - \frac{15}{9} = \frac{7 \cdot 13 \cdot 2 \cdot 2}{2 \cdot 9 \cdot 13} - \frac{15}{9} = \frac{7 \cdot 2}{9} - \frac{15}{9} = \frac{14}{9} - \frac{15}{9} = \frac{14 - 15}{9} = \frac{-1}{9} = -\frac{1}{9}\)

Ответ: 1) 18; 2) 2; 3) \(-1\frac{15}{133}\); 4) \(-\frac{1}{9}\)