2.193 Выполните действие: а) \(\frac{1}{5}+\frac{1}{7}\); б) \(\frac{1}{3}+\frac{2}{7}\); в) \(\frac{3}{5}+\frac{5}{6}\); г) \(\frac{8}{9}-\frac{2}{5}\); д) \(\frac{5}{12}+\frac{1}{6}\); е) \(\frac{3}{5}-\frac{4}{15}\); ж) \(\frac{19}{21}-\frac{11}{15}\); з) \(\frac{5}{42}+\frac{10}{63}\);

Выполним действия:

1. а) \(\frac{1}{5}+\frac{1}{7} = \frac{7}{35} + \frac{5}{35} = \frac{12}{35}\).
2. б) \(\frac{1}{3}+\frac{2}{7} = \frac{7}{21} + \frac{6}{21} = \frac{13}{21}\).
3. в) \(\frac{3}{5}+\frac{5}{6} = \frac{18}{30} + \frac{25}{30} = \frac{43}{30} = 1\frac{13}{30}\).
4. г) \(\frac{8}{9}-\frac{2}{5} = \frac{40}{45} - \frac{18}{45} = \frac{22}{45}\).
5. д) \(\frac{5}{12}+\frac{1}{6} = \frac{5}{12} + \frac{2}{12} = \frac{7}{12}\).
6. е) \(\frac{3}{5}-\frac{4}{15} = \frac{9}{15} - \frac{4}{15} = \frac{5}{15} = \frac{1}{3}\).
7. ж) \(\frac{19}{21}-\frac{11}{15} = \frac{95}{105} - \frac{77}{105} = \frac{18}{105} = \frac{6}{35}\).
8. з) \(\frac{5}{42}+\frac{10}{63} = \frac{15}{126} + \frac{20}{126} = \frac{35}{252} = \frac{5}{36}\).

Ответ: а) \(\frac{12}{35}\); б) \(\frac{13}{21}\); в) \(1\frac{13}{30}\); г) \(\frac{22}{45}\); д) \(\frac{7}{12}\); е) \(\frac{1}{3}\); ж) \(\frac{6}{35}\); з) \(\frac{5}{36}\).