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) \(\frac{1}{4} + \frac{1}{8}\).

Решение:

1. a) \(\frac{1}{2} + \frac{1}{3} = \frac{1\cdot3}{2\cdot3} + \frac{1\cdot2}{3\cdot2} = \frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6}\)
   Ответ: \(\frac{5}{6}\)
2. б) \(\frac{1}{2} + \frac{1}{5} = \frac{1\cdot5}{2\cdot5} + \frac{1\cdot2}{5\cdot2} = \frac{5}{10} + \frac{2}{10} = \frac{5+2}{10} = \frac{7}{10}\)
   Ответ: \(\frac{7}{10}\)
3. в) \(\frac{1}{3} + \frac{1}{4} = \frac{1\cdot4}{3\cdot4} + \frac{1\cdot3}{4\cdot3} = \frac{4}{12} + \frac{3}{12} = \frac{4+3}{12} = \frac{7}{12}\)
   Ответ: \(\frac{7}{12}\)
4. г) \(\frac{1}{4} + \frac{1}{5} = \frac{1\cdot5}{4\cdot5} + \frac{1\cdot4}{5\cdot4} = \frac{5}{20} + \frac{4}{20} = \frac{5+4}{20} = \frac{9}{20}\)
   Ответ: \(\frac{9}{20}\)
5. д) \(\frac{1}{2} + \frac{1}{4} = \frac{1\cdot2}{2\cdot2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}\)
   Ответ: \(\frac{3}{4}\)
6. е) \(\frac{1}{3} + \frac{1}{6} = \frac{1\cdot2}{3\cdot2} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{2+1}{6} = \frac{3}{6} = \frac{1}{2}\)
   Ответ: \(\frac{1}{2}\)
7. ж) \(\frac{1}{2} + \frac{1}{6} = \frac{1\cdot3}{2\cdot3} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{3+1}{6} = \frac{4}{6} = \frac{2}{3}\)
   Ответ: \(\frac{2}{3}\)
8. з) \(\frac{1}{4} + \frac{1}{8} = \frac{1\cdot2}{4\cdot2} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{2+1}{8} = \frac{3}{8}\)
   Ответ: \(\frac{3}{8}\)