П.17 Выполните действие: а) 1/3 + 1/2 б) 2/5 + 3/10 в) 7/12 - 3/12 г) 11/12 - 3/4 д) 4/15 + 3/12 е) 2/9 + 1/3

Решение:

а) \(\frac{1}{3} + \frac{1}{2} = \frac{1 × 2}{3 × 2} + \frac{1 × 3}{2 × 3} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}\)

б) \(\frac{2}{5} + \frac{3}{10} = \frac{2 × 2}{5 × 2} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}\)

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

г) \(\frac{11}{12} - \frac{3}{4} = \frac{11}{12} - \frac{3 × 3}{4 × 3} = \frac{11}{12} - \frac{9}{12} = \frac{2}{12} = \frac{1}{6}\)

д) \(\frac{4}{15} + \frac{3}{12}\). Общий знаменатель 60: \(\frac{4 × 4}{15 × 4} + \frac{3 × 5}{12 × 5} = \frac{16}{60} + \frac{15}{60} = \frac{31}{60}\)

е) \(\frac{2}{9} + \frac{1}{3} = \frac{2}{9} + \frac{1 × 3}{3 × 3} = \frac{2}{9} + \frac{3}{9} = \frac{5}{9}\)

Ответ: а) \(\frac{5}{6}\); б) \(\frac{7}{10}\); в) \(\frac{1}{3}\); г) \(\frac{1}{6}\); д) \(\frac{31}{60}\); е) \(\frac{5}{9}\).