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

1) \(5\frac{1}{3}:\frac{8}{9}:1\frac{1}{3} = \frac{5 \cdot 3 + 1}{3} : \frac{8}{9} : \frac{1 \cdot 3 + 1}{3} = \frac{16}{3} : \frac{8}{9} : \frac{4}{3} = \frac{16}{3} \cdot \frac{9}{8} \cdot \frac{3}{4} = \frac{16 \cdot 9 \cdot 3}{3 \cdot 8 \cdot 4} = \frac{2 \cdot 8 \cdot 3 \cdot 3 \cdot 3}{3 \cdot 8 \cdot 4} = \frac{2 \cdot 3 \cdot 3}{4} = \frac{18}{4} = \frac{9}{2} = 4\frac{1}{2}\)

3) \((8\frac{5}{7}-6\frac{5}{6}):1\frac{1}{36}:4\frac{3}{4} = (\frac{8 \cdot 7 + 5}{7} - \frac{6 \cdot 6 + 5}{6}) : \frac{1 \cdot 36 + 1}{36} : \frac{4 \cdot 4 + 3}{4} = (\frac{61}{7} - \frac{41}{6}) : \frac{37}{36} : \frac{19}{4} = (\frac{61 \cdot 6 - 41 \cdot 7}{42}) : \frac{37}{36} : \frac{19}{4} = (\frac{366 - 287}{42}) : \frac{37}{36} : \frac{19}{4} = \frac{79}{42} \cdot \frac{36}{37} \cdot \frac{4}{19} = \frac{79 \cdot 36 \cdot 4}{42 \cdot 37 \cdot 19} = \frac{79 \cdot 6 \cdot 6 \cdot 4}{6 \cdot 7 \cdot 37 \cdot 19} = \frac{79 \cdot 6 \cdot 4}{7 \cdot 37 \cdot 19} = \frac{1896}{4907}\)

2) \(5\frac{1}{3}:(\frac{8}{9}:1\frac{1}{3}) = \frac{5 \cdot 3 + 1}{3} : (\frac{8}{9} : \frac{1 \cdot 3 + 1}{3}) = \frac{16}{3} : (\frac{8}{9} : \frac{4}{3}) = \frac{16}{3} : (\frac{8}{9} \cdot \frac{3}{4}) = \frac{16}{3} : \frac{8 \cdot 3}{9 \cdot 4} = \frac{16}{3} : \frac{24}{36} = \frac{16}{3} : \frac{2}{3} = \frac{16}{3} \cdot \frac{3}{2} = \frac{16 \cdot 3}{3 \cdot 2} = \frac{16}{2} = 8\)

4) \((2\frac{5}{6}+2\frac{2}{9}):3\frac{1}{4}-\frac{2}{7}:1\frac{1}{7} = (\frac{2 \cdot 6 + 5}{6} + \frac{2 \cdot 9 + 2}{9}) : \frac{3 \cdot 4 + 1}{4} - \frac{2}{7} : \frac{1 \cdot 7 + 1}{7} = (\frac{17}{6} + \frac{20}{9}) : \frac{13}{4} - \frac{2}{7} : \frac{8}{7} = (\frac{17 \cdot 3 + 20 \cdot 2}{18}) : \frac{13}{4} - \frac{2}{7} \cdot \frac{7}{8} = (\frac{51 + 40}{18}) : \frac{13}{4} - \frac{2 \cdot 7}{7 \cdot 8} = \frac{91}{18} \cdot \frac{4}{13} - \frac{2}{8} = \frac{91 \cdot 4}{18 \cdot 13} - \frac{1}{4} = \frac{7 \cdot 13 \cdot 2 \cdot 2}{2 \cdot 9 \cdot 13} - \frac{1}{4} = \frac{7 \cdot 2}{9} - \frac{1}{4} = \frac{14}{9} - \frac{1}{4} = \frac{14 \cdot 4 - 1 \cdot 9}{36} = \frac{56 - 9}{36} = \frac{47}{36} = 1\frac{11}{36}\)

Ответ: 1) \(4\frac{1}{2}\); 3) \(\frac{1896}{4907}\); 2) \(8\); 4) \(1\frac{11}{36}\)