2.418 Выполните деление: a) \(\frac{5}{9}:5\); б) \(\frac{4}{7}:4\); в) \(1:\frac{5}{13}\); г) \(7:\frac{4}{7}\); д) \(9:\frac{3}{7}\); e) \(4:\frac{8}{9}\)

а) \(\frac{5}{9}:5 = \frac{5}{9}:\frac{5}{1} = \frac{5}{9} \cdot \frac{1}{5} = \frac{5 \cdot 1}{9 \cdot 5} = \frac{1}{9}\)

б) \(\frac{4}{7}:4 = \frac{4}{7}:\frac{4}{1} = \frac{4}{7} \cdot \frac{1}{4} = \frac{4 \cdot 1}{7 \cdot 4} = \frac{1}{7}\)

в) \(1:\frac{5}{13} = \frac{1}{1} : \frac{5}{13} = \frac{1}{1} \cdot \frac{13}{5} = \frac{13}{5} = 2\frac{3}{5}\)

г) \(7:\frac{4}{7} = \frac{7}{1}:\frac{4}{7} = \frac{7}{1} \cdot \frac{7}{4} = \frac{7 \cdot 7}{1 \cdot 4} = \frac{49}{4} = 12\frac{1}{4}\)

д) \(9:\frac{3}{7} = \frac{9}{1}:\frac{3}{7} = \frac{9}{1} \cdot \frac{7}{3} = \frac{9 \cdot 7}{1 \cdot 3} = \frac{3 \cdot 3 \cdot 7}{3} = 21\)

е) \(4:\frac{8}{9} = \frac{4}{1}:\frac{8}{9} = \frac{4}{1} \cdot \frac{9}{8} = \frac{4 \cdot 9}{1 \cdot 8} = \frac{4 \cdot 9}{4 \cdot 2} = \frac{9}{2} = 4\frac{1}{2}\)

Ответ: а) \(\frac{1}{9}\); б) \(\frac{1}{7}\); в) \(2\frac{3}{5}\); г) \(12\frac{1}{4}\); д) 21; е) \(4\frac{1}{2}\)