5.411 Вычислите: a) \(\frac{1}{3} + \frac{5}{6};\) б) \(\frac{5}{6} - \frac{1}{2};\) г) \(\frac{5}{6} - \frac{5}{12};\) в) \(\frac{9}{10} - \frac{4}{5};\) д) \(\frac{11}{18} + \frac{1}{6};\) ж) \(\frac{4}{5} - \frac{7}{15};\) е) \(\frac{5}{12} + \frac{3}{4};\) з) \(\frac{11}{21} + \frac{3}{7}.\)

a) \(\frac{1}{3} + \frac{5}{6} = \frac{1*2}{3*2} + \frac{5}{6} = \frac{2}{6} + \frac{5}{6} = \frac{2+5}{6} = \frac{7}{6} = 1\frac{1}{6}\)

Ответ: \(1\frac{1}{6}\)

б) \(\frac{5}{6} - \frac{1}{2} = \frac{5}{6} - \frac{1*3}{2*3} = \frac{5}{6} - \frac{3}{6} = \frac{5-3}{6} = \frac{2}{6} = \frac{1}{3}\)

Ответ: \(\frac{1}{3}\)

г) \(\frac{5}{6} - \frac{5}{12} = \frac{5*2}{6*2} - \frac{5}{12} = \frac{10}{12} - \frac{5}{12} = \frac{10-5}{12} = \frac{5}{12}\)

Ответ: \(\frac{5}{12}\)

в) \(\frac{9}{10} - \frac{4}{5} = \frac{9}{10} - \frac{4*2}{5*2} = \frac{9}{10} - \frac{8}{10} = \frac{9-8}{10} = \frac{1}{10}\)

Ответ: \(\frac{1}{10}\)

д) \(\frac{11}{18} + \frac{1}{6} = \frac{11}{18} + \frac{1*3}{6*3} = \frac{11}{18} + \frac{3}{18} = \frac{11+3}{18} = \frac{14}{18} = \frac{7}{9}\)

Ответ: \(\frac{7}{9}\)

ж) \(\frac{4}{5} - \frac{7}{15} = \frac{4*3}{5*3} - \frac{7}{15} = \frac{12}{15} - \frac{7}{15} = \frac{12-7}{15} = \frac{5}{15} = \frac{1}{3}\)

Ответ: \(\frac{1}{3}\)

е) \(\frac{5}{12} + \frac{3}{4} = \frac{5}{12} + \frac{3*3}{4*3} = \frac{5}{12} + \frac{9}{12} = \frac{5+9}{12} = \frac{14}{12} = \frac{7}{6} = 1\frac{1}{6}\)

Ответ: \(1\frac{1}{6}\)

з) \(\frac{11}{21} + \frac{3}{7} = \frac{11}{21} + \frac{3*3}{7*3} = \frac{11}{21} + \frac{9}{21} = \frac{11+9}{21} = \frac{20}{21}\)

Ответ: \(\frac{20}{21}\)