835. a) \frac{1}{6} + \frac{1}{9}; б) \frac{2}{9} + \frac{5}{6}; в) \frac{2}{3} + \frac{3}{8}; г) \frac{1}{3} + \frac{2}{10}; д) \frac{1}{2} + \frac{3}{12}; е) \frac{5}{12} + \frac{4}{15}.

a) \(\frac{1}{6} + \frac{1}{9} = \frac{1 \cdot 3}{6 \cdot 3} + \frac{1 \cdot 2}{9 \cdot 2} = \frac{3}{18} + \frac{2}{18} = \frac{3+2}{18} = \frac{5}{18}\)

б) \(\frac{2}{9} + \frac{5}{6} = \frac{2 \cdot 2}{9 \cdot 2} + \frac{5 \cdot 3}{6 \cdot 3} = \frac{4}{18} + \frac{15}{18} = \frac{4+15}{18} = \frac{19}{18} = 1\frac{1}{18}\)

в) \(\frac{2}{3} + \frac{3}{8} = \frac{2 \cdot 8}{3 \cdot 8} + \frac{3 \cdot 3}{8 \cdot 3} = \frac{16}{24} + \frac{9}{24} = \frac{16+9}{24} = \frac{25}{24} = 1\frac{1}{24}\)

г) \(\frac{1}{3} + \frac{2}{10} = \frac{1 \cdot 10}{3 \cdot 10} + \frac{2 \cdot 3}{10 \cdot 3} = \frac{10}{30} + \frac{6}{30} = \frac{10+6}{30} = \frac{16}{30} = \frac{8}{15}\)

д) \(\frac{1}{2} + \frac{3}{12} = \frac{1 \cdot 6}{2 \cdot 6} + \frac{3}{12} = \frac{6}{12} + \frac{3}{12} = \frac{6+3}{12} = \frac{9}{12} = \frac{3}{4}\)

е) \(\frac{5}{12} + \frac{4}{15} = \frac{5 \cdot 5}{12 \cdot 5} + \frac{4 \cdot 4}{15 \cdot 4} = \frac{25}{60} + \frac{16}{60} = \frac{25+16}{60} = \frac{41}{60}\)

Ответ: a) \(\frac{5}{18}\); б) \(1\frac{1}{18}\); в) \(1\frac{1}{24}\); г) \(\frac{8}{15}\); д) \(\frac{3}{4}\); е) \(\frac{41}{60}\)