135. Выполните действия: a) (6\(\frac{1}{5}\) - 4\(\frac{3}{5}\)) : \(\frac{1}{3}\) б) (7\(\frac{1}{4}\) + 2\(\frac{1}{4}\)) : 5 в) (3\(\frac{3}{14}\) + \(\frac{11}{14}\)) : \(\frac{1}{6}\) г) (6\(\frac{1}{4}\) - 3\(\frac{1}{4}\)) : 5 д) (5\(\frac{4}{19}\) + 3\(\frac{7}{19}\)) : \(\frac{1}{6}\) е) (6\(\frac{1}{4}\) - 4\(\frac{3}{4}\)) : \(\frac{1}{3}\)

Решение:

• а) \(\left(6\frac{1}{5} - 4\frac{3}{5}\right) : \frac{1}{3} = \left(\frac{31}{5} - \frac{23}{5}\right) : \frac{1}{3} = \frac{8}{5} : \frac{1}{3} = \frac{8}{5} \times 3 = \frac{24}{5} = 4\frac{4}{5}\)
• б) \(\left(7\frac{1}{4} + 2\frac{1}{4}\right) : 5 = \left(\frac{29}{4} + \frac{9}{4}\right) : 5 = \frac{38}{4} : 5 = \frac{19}{2} : 5 = \frac{19}{2} \times \frac{1}{5} = \frac{19}{10} = 1\frac{9}{10}\)
• в) \(\left(3\frac{3}{14} + \frac{11}{14}\right) : \frac{1}{6} = \left(\frac{45}{14} + \frac{11}{14}\right) : \frac{1}{6} = \frac{56}{14} : \frac{1}{6} = 4 : \frac{1}{6} = 4 \times 6 = 24\)
• г) \(\left(6\frac{1}{4} - 3\frac{1}{4}\right) : 5 = \left(\frac{25}{4} - \frac{13}{4}\right) : 5 = \frac{12}{4} : 5 = 3 : 5 = \frac{3}{5}\)
• д) \(\left(5\frac{4}{19} + 3\frac{7}{19}\right) : \frac{1}{6} = \left(\frac{99}{19} + \frac{64}{19}\right) : \frac{1}{6} = \frac{163}{19} : \frac{1}{6} = \frac{163}{19} \times 6 = \frac{978}{19} = 51\frac{9}{19}\)
• е) \(\left(6\frac{1}{4} - 4\frac{3}{4}\right) : \frac{1}{3} = \left(\frac{25}{4} - \frac{19}{4}\right) : \frac{1}{3} = \frac{6}{4} : \frac{1}{3} = \frac{3}{2} : \frac{1}{3} = \frac{3}{2} \times 3 = \frac{9}{2} = 4\frac{1}{2}\)

Ответ:

• а) \(4\frac{4}{5}\)
• б) \(1\frac{9}{10}\)
• в) 24
• г) \(\frac{3}{5}\)
• д) \(51\frac{9}{19}\)
• е) \(4\frac{1}{2}\)