5.359 Выполните действие и сократите дробную часть полученного результата: a) \(\frac{14}{18} - \frac{5}{18}\); б) \(\frac{5}{22} + \frac{6}{22}\); в) 6 \(\frac{7}{12}\) - 1 \(\frac{3}{12}\); г) 7 \(\frac{5}{27}\) + 3 \(\frac{4}{27}\)

a) \(\frac{14}{18} - \frac{5}{18} = \frac{14 - 5}{18} = \frac{9}{18} = \frac{9 \cdot 1}{9 \cdot 2} = \frac{1}{2}\)

б) \(\frac{5}{22} + \frac{6}{22} = \frac{5 + 6}{22} = \frac{11}{22} = \frac{11 \cdot 1}{11 \cdot 2} = \frac{1}{2}\)

в) \(6 \frac{7}{12} - 1 \frac{3}{12} = (6 - 1) + (\frac{7}{12} - \frac{3}{12}) = 5 + \frac{7 - 3}{12} = 5 + \frac{4}{12} = 5 + \frac{4 \cdot 1}{4 \cdot 3} = 5 + \frac{1}{3} = 5\frac{1}{3}\)

г) \(7 \frac{5}{27} + 3 \frac{4}{27} = (7 + 3) + (\frac{5}{27} + \frac{4}{27}) = 10 + \frac{5 + 4}{27} = 10 + \frac{9}{27} = 10 + \frac{9 \cdot 1}{9 \cdot 3} = 10 + \frac{1}{3} = 10\frac{1}{3}\)

Ответ: а) \(\frac{1}{2}\); б) \(\frac{1}{2}\); в) \(5\frac{1}{3}\); г) \(10\frac{1}{3}\)