6.59 Найдите разность: a) 7\(\frac{3}{5}\) – 1\(\frac{2}{5}\); б) 6 – \(\frac{2}{5}\); в) 6 – 2\(\frac{1}{5}\); г) 21 – \(\frac{5}{9}\); д) 4\(\frac{1}{7}\) – 1\(\frac{4}{7}\); e) 12\(\frac{2}{5}\) – 1\(\frac{4}{5}\); ж) 4\(\frac{1}{2}\) – 3\(\frac{1}{4}\); з) 5\(\frac{1}{7}\) – 3\(\frac{20}{21}\)

Ответ: а) 6\(\frac{1}{5}\); б) 5\(\frac{3}{5}\); в) 3\(\frac{4}{5}\); г) 20\(\frac{4}{9}\); д) 2\(\frac{4}{7}\); е) 10\(\frac{3}{5}\); ж) 1\(\frac{1}{4}\); з) 1\(\frac{4}{21}\)

Решаем:

а) \(7\frac{3}{5} - 1\frac{2}{5} = (7 - 1) + (\frac{3}{5} - \frac{2}{5}) = 6 + \frac{1}{5} = 6\frac{1}{5}\)

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

в) \(6 - 2\frac{1}{5} = 5\frac{5}{5} - 2\frac{1}{5} = (5 - 2) + (\frac{5}{5} - \frac{1}{5}) = 3 + \frac{4}{5} = 3\frac{4}{5}\)

г) \(21 - \frac{5}{9} = 20\frac{9}{9} - \frac{5}{9} = 20\frac{4}{9}\)

д) \(4\frac{1}{7} - 1\frac{4}{7} = 3\frac{8}{7} - 1\frac{4}{7} = (3 - 1) + (\frac{8}{7} - \frac{4}{7}) = 2 + \frac{4}{7} = 2\frac{4}{7}\)

е) \(12\frac{2}{5} - 1\frac{4}{5} = 11\frac{7}{5} - 1\frac{4}{5} = (11 - 1) + (\frac{7}{5} - \frac{4}{5}) = 10 + \frac{3}{5} = 10\frac{3}{5}\)

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

з) \(5\frac{1}{7} - 3\frac{20}{21} = 5\frac{3}{21} - 3\frac{20}{21} = 4\frac{24}{21} - 3\frac{20}{21} = (4 - 3) + (\frac{24}{21} - \frac{20}{21}) = 1 + \frac{4}{21} = 1\frac{4}{21}\)

Ответ: а) 6\(\frac{1}{5}\); б) 5\(\frac{3}{5}\); в) 3\(\frac{4}{5}\); г) 20\(\frac{4}{9}\); д) 2\(\frac{4}{7}\); е) 10\(\frac{3}{5}\); ж) 1\(\frac{1}{4}\); з) 1\(\frac{4}{21}\)