832. Сложите дроби: a) \frac{1}{2} + \frac{1}{3}; б) \frac{1}{2} + \frac{1}{5}; в) \frac{1}{3} + \frac{1}{4}; г) \frac{1}{4} + \frac{1}{5}; д) \frac{1}{2} + \frac{1}{4}; е) \frac{1}{3} + \frac{1}{6}; ж) \frac{1}{2} + \frac{1}{6}; з) \frac{1}{4} + \frac{1}{8}.

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

б) \(\frac{1}{2} + \frac{1}{5} = \frac{1 \cdot 5}{2 \cdot 5} + \frac{1 \cdot 2}{5 \cdot 2} = \frac{5}{10} + \frac{2}{10} = \frac{5+2}{10} = \frac{7}{10}\)

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

г) \(\frac{1}{4} + \frac{1}{5} = \frac{1 \cdot 5}{4 \cdot 5} + \frac{1 \cdot 4}{5 \cdot 4} = \frac{5}{20} + \frac{4}{20} = \frac{5+4}{20} = \frac{9}{20}\)

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

е) \(\frac{1}{3} + \frac{1}{6} = \frac{1 \cdot 2}{3 \cdot 2} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{2+1}{6} = \frac{3}{6} = \frac{1}{2}\)

ж) \(\frac{1}{2} + \frac{1}{6} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{3+1}{6} = \frac{4}{6} = \frac{2}{3}\)

з) \(\frac{1}{4} + \frac{1}{8} = \frac{1 \cdot 2}{4 \cdot 2} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{2+1}{8} = \frac{3}{8}\)

Ответ: a) \(\frac{5}{6}\); б) \(\frac{7}{10}\); в) \(\frac{7}{12}\); г) \(\frac{9}{20}\); д) \(\frac{3}{4}\); е) \(\frac{1}{2}\); ж) \(\frac{2}{3}\); з) \(\frac{3}{8}\)