1. Выполните действие: a)7 8/11 : 5/11; б) 6 6/25 : 5/18; в) 3 3/5 * 1 1/9; г) 1 3/7 * 14; д) 9 5/12 : 27; e) 12/13 : 6.

а) \[\frac{7 \frac{8}{11}}{\frac{5}{11}} = \frac{\frac{7 \cdot 11 + 8}{11}}{\frac{5}{11}} = \frac{\frac{77 + 8}{11}}{\frac{5}{11}} = \frac{\frac{85}{11}}{\frac{5}{11}} = \frac{85}{11} \cdot \frac{11}{5} = \frac{85}{5} = 17\]

б) \[\frac{6 \frac{6}{25}}{\frac{5}{18}} = \frac{\frac{6 \cdot 25 + 6}{25}}{\frac{5}{18}} = \frac{\frac{150 + 6}{25}}{\frac{5}{18}} = \frac{\frac{156}{25}}{\frac{5}{18}} = \frac{156}{25} \cdot \frac{18}{5} = \frac{2808}{125} = 22 \frac{58}{125}\]

в) \(3 \frac{3}{5} \cdot 1 \frac{1}{9} = \frac{3 \cdot 5 + 3}{5} \cdot \frac{1 \cdot 9 + 1}{9} = \frac{15 + 3}{5} \cdot \frac{9 + 1}{9} = \frac{18}{5} \cdot \frac{10}{9} = \frac{18 \cdot 10}{5 \cdot 9} = \frac{180}{45} = 4\)

г) \(1 \frac{3}{7} \cdot 14 = \frac{1 \cdot 7 + 3}{7} \cdot 14 = \frac{7 + 3}{7} \cdot 14 = \frac{10}{7} \cdot 14 = \frac{10 \cdot 14}{7} = \frac{140}{7} = 20\)

д) \(9 \frac{5}{12} : 27 = \frac{9 \cdot 12 + 5}{12} : 27 = \frac{108 + 5}{12} : 27 = \frac{113}{12} : 27 = \frac{113}{12} \cdot \frac{1}{27} = \frac{113}{12 \cdot 27} = \frac{113}{324}\)

е) \(\frac{12}{13} : 6 = \frac{12}{13} \cdot \frac{1}{6} = \frac{12}{13 \cdot 6} = \frac{12}{78} = \frac{2}{13}\)