83. Вычислите значение выражения: 1) (5\frac{3}{5}-1\frac{1}{3}):(7\frac{7}{12}-2\frac{1}{4}); 2) (3\frac{3}{4} \cdot \frac{3}{5}-7\frac{1}{2}:27+1\frac{1}{9}):(3\frac{1}{6}-1\frac{1}{4}).

83. Вычислите значение выражения:

1) $$(5\frac{3}{5}-1\frac{1}{3}):(7\frac{7}{12}-2\frac{1}{4}) = (\frac{5 \cdot 5 + 3}{5} - \frac{1 \cdot 3 + 1}{3}):(\frac{7 \cdot 12 + 7}{12} - \frac{2 \cdot 4 + 1}{4}) = (\frac{25+3}{5} - \frac{3+1}{3}):(\frac{84+7}{12} - \frac{8+1}{4}) = (\frac{28}{5} - \frac{4}{3}):(\frac{91}{12} - \frac{9}{4}) = (\frac{28 \cdot 3}{5 \cdot 3} - \frac{4 \cdot 5}{3 \cdot 5}):(\frac{91}{12} - \frac{9 \cdot 3}{4 \cdot 3}) = (\frac{84}{15} - \frac{20}{15}):(\frac{91}{12} - \frac{27}{12}) = \frac{84-20}{15}:\frac{91-27}{12} = \frac{64}{15}:\frac{64}{12} = \frac{64}{15} \cdot \frac{12}{64} = \frac{64 \cdot 12}{15 \cdot 64} = \frac{12}{15} = \frac{4}{5} $$

2) $$(3\frac{3}{4} \cdot \frac{3}{5}-7\frac{1}{2}:27+1\frac{1}{9}):(3\frac{1}{6}-1\frac{1}{4}) = (\frac{3 \cdot 4 + 3}{4} \cdot \frac{3}{5} - \frac{7 \cdot 2 + 1}{2}:\frac{27}{1} + \frac{1 \cdot 9 + 1}{9}):(\frac{3 \cdot 6 + 1}{6} - \frac{1 \cdot 4 + 1}{4}) = (\frac{12+3}{4} \cdot \frac{3}{5} - \frac{14+1}{2}:\frac{27}{1} + \frac{9+1}{9}):(\frac{18+1}{6} - \frac{4+1}{4}) = (\frac{15}{4} \cdot \frac{3}{5} - \frac{15}{2}:\frac{27}{1} + \frac{10}{9}):(\frac{19}{6} - \frac{5}{4}) = (\frac{15 \cdot 3}{4 \cdot 5} - \frac{15}{2} \cdot \frac{1}{27} + \frac{10}{9}):(\frac{19 \cdot 2}{6 \cdot 2} - \frac{5 \cdot 3}{4 \cdot 3}) = (\frac{45}{20} - \frac{15}{54} + \frac{10}{9}):(\frac{38}{12} - \frac{15}{12}) = (\frac{9}{4} - \frac{5}{18} + \frac{10}{9}):\frac{38-15}{12} = (\frac{9 \cdot 9}{4 \cdot 9} - \frac{5 \cdot 2}{18 \cdot 2} + \frac{10 \cdot 4}{9 \cdot 4}):\frac{23}{12} = (\frac{81}{36} - \frac{10}{36} + \frac{40}{36}):\frac{23}{12} = \frac{81-10+40}{36}:\frac{23}{12} = \frac{111}{36}:\frac{23}{12} = \frac{37}{12} \cdot \frac{12}{23} = \frac{37}{23} = 1\frac{14}{23} $$

Ответ: 1) $$\frac{4}{5}$$; 2) $$1\frac{14}{23}$$