1. Вычислите: a) \frac{3}{5}: \frac{5}{12}; б) \frac{2}{3}: \frac{2}{5}; в) 7\frac{1}{3}: 1\frac{2}{9}; г) 24:3\frac{1}{5}; д)2\frac{1}{5}: 11

a) \(\frac{3}{5}: \frac{5}{12} = \frac{3}{5} \cdot \frac{12}{5} = \frac{3 \cdot 12}{5 \cdot 5} = \frac{36}{25} = 1\frac{11}{25}\)

б) \(\frac{2}{3}: \frac{2}{5} = \frac{2}{3} \cdot \frac{5}{2} = \frac{2 \cdot 5}{3 \cdot 2} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}\)

в) \(7\frac{1}{3}: 1\frac{2}{9} = \frac{7 \cdot 3 + 1}{3} : \frac{1 \cdot 9 + 2}{9} = \frac{22}{3} : \frac{11}{9} = \frac{22}{3} \cdot \frac{9}{11} = \frac{22 \cdot 9}{3 \cdot 11} = \frac{2 \cdot 3}{1 \cdot 1} = \frac{6}{1} = 6\)

г) \(24:3\frac{1}{5} = 24 : \frac{3 \cdot 5 + 1}{5} = 24 : \frac{16}{5} = 24 \cdot \frac{5}{16} = \frac{24 \cdot 5}{16} = \frac{3 \cdot 5}{2} = \frac{15}{2} = 7\frac{1}{2}\)

д) \(2\frac{1}{5}: 11 = \frac{2 \cdot 5 + 1}{5} : 11 = \frac{11}{5} : 11 = \frac{11}{5} \cdot \frac{1}{11} = \frac{11 \cdot 1}{5 \cdot 11} = \frac{1}{5}\)

Ответ: a) \(1\frac{11}{25}\); б) \(1\frac{2}{3}\); в) 6; г) \(7\frac{1}{2}\); д) \(\frac{1}{5}\)