2. Найдите значение выражений. a) \(1\frac{1}{9} - \frac{2}{3}\); б) \(12\frac{3}{8} - 6\frac{7}{20}\); в) \(4\frac{5}{21} + 5\frac{3}{14}\); д) \(\frac{3}{10} \cdot \frac{20}{21}\); e) \(9\frac{1}{3} \cdot 1\frac{1}{8}\); ж) \(\frac{9}{14} : \frac{18}{35}\); з) \(3\frac{1}{5} : 2\frac{2}{15}\)

Давай найдем значения выражений по порядку: a) \(1\frac{1}{9} - \frac{2}{3} = \frac{10}{9} - \frac{2}{3} = \frac{10}{9} - \frac{2 \times 3}{3 \times 3} = \frac{10}{9} - \frac{6}{9} = \frac{10-6}{9} = \frac{4}{9}\) б) \(12\frac{3}{8} - 6\frac{7}{20} = 12\frac{15}{40} - 6\frac{14}{40} = (12-6) + (\frac{15}{40} - \frac{14}{40}) = 6 + \frac{1}{40} = 6\frac{1}{40}\) в) \(4\frac{5}{21} + 5\frac{3}{14} = 4\frac{10}{42} + 5\frac{9}{42} = (4+5) + (\frac{10}{42} + \frac{9}{42}) = 9 + \frac{19}{42} = 9\frac{19}{42}\) д) \(\frac{3}{10} \cdot \frac{20}{21} = \frac{3 \times 20}{10 \times 21} = \frac{60}{210} = \frac{6}{21} = \frac{2}{7}\) e) \(9\frac{1}{3} \cdot 1\frac{1}{8} = \frac{28}{3} \cdot \frac{9}{8} = \frac{28 \times 9}{3 \times 8} = \frac{252}{24} = \frac{63}{6} = 10\frac{3}{6} = 10\frac{1}{2}\) ж) \(\frac{9}{14} : \frac{18}{35} = \frac{9}{14} \cdot \frac{35}{18} = \frac{9 \times 35}{14 \times 18} = \frac{315}{252} = \frac{5}{4} = 1\frac{1}{4}\) з) \(3\frac{1}{5} : 2\frac{2}{15} = \frac{16}{5} : \frac{32}{15} = \frac{16}{5} \cdot \frac{15}{32} = \frac{16 \times 15}{5 \times 32} = \frac{240}{160} = \frac{3}{2} = 1\frac{1}{2}\)

Ответ: a) \(\frac{4}{9}\); б) \(6\frac{1}{40}\); в) \(9\frac{19}{42}\); д) \(\frac{2}{7}\); e) \(10\frac{1}{2}\); ж) \(1\frac{1}{4}\); з) \(1\frac{1}{2}\)

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