Найдите значение выражения:
а) \(3\frac{3}{5} \cdot \frac{1}{3} + 6\frac{4}{9} : 2 = 4\frac{19}{45}\)
1) \(3\frac{3}{5} \cdot \frac{1}{3} = \frac{18}{5} \cdot \frac{1}{3} = \frac{18 \cdot 1}{5  \cdot 3} = \frac{6 \cdot 1}{5  \cdot 1} =  \frac{6}{5} = 1\frac{1}{5} = 1,2\);
2) \(6\frac{4}{9} : 2 = \frac{58}{9} : 2 = \frac{58}{9} \cdot \frac{1}{2} = \frac{58 \cdot 1}{9 \cdot 2} = \frac{29 \cdot 1}{9 \cdot 1} = \frac{29}{9} = 3\frac{2}{9}\);
3) \(1,2 + 3\frac{2}{9} = 1\frac{1}{5} + 3\frac{2}{9} = 1\frac{9}{45} + 3\frac{10}{45} = 4\frac{19}{45}\).

б) \(\frac{2}{3} - \frac{8}{23} \cdot (\frac{3}{4} + 1\frac{1}{6}) = 0\)
1) \(\frac{3}{4} + 1\frac{1}{6} = \frac{9}{12} + 1 + \frac{2}{12} = 1 + \frac{11}{12} = 1\frac{11}{12}\);
2) \(\frac{8}{23} \cdot 1\frac{11}{12} = \frac{8}{23} \cdot \frac{23}{12} = \frac{8 \cdot 23}{23  \cdot 12} = \frac{2 \cdot 1}{1 \cdot 3} =  \frac{2}{3}\);
3) \(\frac{2}{3} - \frac{2}{3} = 0\).

в) \(2\frac{5}{6} - 1\frac{1}{5} \cdot 1\frac{1}{9} + 1\frac{5}{7} : 1\frac{1}{7} = 3\)
1) \(1\frac{1}{5} \cdot 1\frac{1}{9} = \frac{6}{5} \cdot \frac{10}{9} = \frac{6 \cdot 10}{5 \cdot 9} = \frac{2 \cdot 2}{1 \cdot 3} = \frac{4}{3} = 1\frac{1}{3}\);
2) \(1\frac{5}{7} : 1\frac{1}{7} = \frac{12}{7} : \frac{8}{7} = \frac{12}{7} \cdot \frac{7}{8} = \frac{12 \cdot 7}{7 \cdot 8} = \frac{3 \cdot 1}{1 \cdot 2} = 1\frac{1}{2}\);
3) \(2\frac{5}{6} - 1\frac{1}{3} = 2\frac{5}{6} - 1\frac{2}{6} = 1\frac{3}{6} = 1\frac{1}{2}\);
4) \(1\frac{1}{2} + 1\frac{1}{2} = 2 + \frac{2}{2} = 2 + 1 = 3\).

г) \(5\frac{2}{9} : (3 - 1\frac{1}{9} \cdot 2\frac{2}{5}) + \frac{4}{5} = 4\frac{19}{45}\)
1) \(1\frac{1}{9} \cdot 2\frac{2}{5} = \frac{10}{9} \cdot \frac{12}{5} = \frac{10 \cdot 12}{9 \cdot 5} = \frac{2 \cdot 4}{3 \cdot 1} = \frac{8}{3} = 2\frac{2}{3}\);
2) \(3 - 2\frac{2}{3} = 2\frac{3}{3} - 2\frac{2}{3} = \frac{1}{3}\);
3) \(5\frac{2}{9} : \frac{1}{3} = \frac{47}{9} \cdot \frac{3}{1} = \frac{47 \cdot 3}{9 \cdot 1} = \frac{47 \cdot 1}{3 \cdot 1} = \frac{47}{3} = 15\frac{2}{3}\);
4) \(15\frac{2}{3} + \frac{4}{5} = 15\frac{10}{15} + \frac{12}{15} = 15\frac{22}{15} = 15 + 1 + \frac{7}{15} = 16\frac{7}{15}\).

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