612. Выполните действия: а) \frac{2}{3} \cdot \frac{6}{7} : \frac{4}{7}; б) \frac{11}{12} : \frac{21}{24} \cdot \frac{7}{22}; в) \frac{15}{16} : \frac{3}{8} \cdot \frac{3}{4}; г) \frac{13}{14} : \frac{7}{25} \cdot \frac{13}{25}; д) 3\frac{3}{4} : (4\frac{1}{2} : 6\frac{3}{4}); е) (2\frac{2}{7} + 1\frac{1}{6}) \cdot 1\frac{1}{16}; ж) (6\frac{1}{2} - 4\frac{1}{4}) : 2\frac{1}{2}; з) (4\frac{8}{15} - 1\frac{1}{3}) \cdot 1\frac{7}{8}; и) (2\frac{2}{3} + 1\frac{5}{6}) : 1\frac{1}{2}; к) (3\frac{1}{6} - 2\frac{7}{15}) : 1\frac{13}{25}; л) (1\frac{2}{3} + 2\frac{4}{9}) : (4\frac{26}{27} - 2\frac{2}{9}); м) (6\frac{1}{24} - 2\frac{1}{3}) : (3\frac{1}{2} + 1\frac{7}{8}).

Выполним действия:

а) $$\frac{2}{3} \cdot \frac{6}{7} : \frac{4}{7} = \frac{2}{3} \cdot \frac{6}{7} \cdot \frac{7}{4} = \frac{2 \cdot 6 \cdot 7}{3 \cdot 7 \cdot 4} = \frac{12}{12} = 1$$

б) $$\frac{11}{12} : \frac{21}{24} \cdot \frac{7}{22} = \frac{11}{12} \cdot \frac{24}{21} \cdot \frac{7}{22} = \frac{11 \cdot 24 \cdot 7}{12 \cdot 21 \cdot 22} = \frac{11 \cdot 2 \cdot 7}{21 \cdot 22} = \frac{2 \cdot 7}{21 \cdot 2} = \frac{14}{42} = \frac{1}{3}$$

в) $$\frac{15}{16} : \frac{3}{8} \cdot \frac{3}{4} = \frac{15}{16} \cdot \frac{8}{3} \cdot \frac{3}{4} = \frac{15 \cdot 8 \cdot 3}{16 \cdot 3 \cdot 4} = \frac{15 \cdot 8}{16 \cdot 4} = \frac{15}{2 \cdot 4} = \frac{15}{8} = 1\frac{7}{8}$$

г) $$\frac{13}{14} : \frac{7}{25} \cdot \frac{13}{25} = \frac{13}{14} \cdot \frac{25}{7} \cdot \frac{13}{25} = \frac{13 \cdot 25 \cdot 13}{14 \cdot 7 \cdot 25} = \frac{13 \cdot 13}{14 \cdot 7} = \frac{169}{98} = 1\frac{71}{98}$$

д) $$3\frac{3}{4} : (4\frac{1}{2} : 6\frac{3}{4}) = \frac{15}{4} : (\frac{9}{2} : \frac{27}{4}) = \frac{15}{4} : (\frac{9}{2} \cdot \frac{4}{27}) = \frac{15}{4} : \frac{36}{54} = \frac{15}{4} : \frac{2}{3} = \frac{15}{4} \cdot \frac{3}{2} = \frac{45}{8} = 5\frac{5}{8}$$

е) $$(2\frac{2}{7} + 1\frac{1}{6}) \cdot 1\frac{1}{16} = (\frac{16}{7} + \frac{7}{6}) \cdot \frac{17}{16} = (\frac{16 \cdot 6 + 7 \cdot 7}{42}) \cdot \frac{17}{16} = (\frac{96 + 49}{42}) \cdot \frac{17}{16} = \frac{145}{42} \cdot \frac{17}{16} = \frac{2465}{672} = 3\frac{449}{672}$$

ж) $$(6\frac{1}{2} - 4\frac{1}{4}) : 2\frac{1}{2} = (\frac{13}{2} - \frac{17}{4}) : \frac{5}{2} = (\frac{26 - 17}{4}) : \frac{5}{2} = \frac{9}{4} : \frac{5}{2} = \frac{9}{4} \cdot \frac{2}{5} = \frac{18}{20} = \frac{9}{10}$$

з) $$(4\frac{8}{15} - 1\frac{1}{3}) \cdot 1\frac{7}{8} = (\frac{68}{15} - \frac{4}{3}) \cdot \frac{15}{8} = (\frac{68 - 20}{15}) \cdot \frac{15}{8} = \frac{48}{15} \cdot \frac{15}{8} = \frac{48}{8} = 6$$

и) $$(2\frac{2}{3} + 1\frac{5}{6}) : 1\frac{1}{2} = (\frac{8}{3} + \frac{11}{6}) : \frac{3}{2} = (\frac{16 + 11}{6}) : \frac{3}{2} = \frac{27}{6} : \frac{3}{2} = \frac{9}{2} \cdot \frac{2}{3} = \frac{9}{3} = 3$$

к) $$(3\frac{1}{6} - 2\frac{7}{15}) : 1\frac{13}{25} = (\frac{19}{6} - \frac{37}{15}) : \frac{38}{25} = (\frac{19 \cdot 5 - 37 \cdot 2}{30}) : \frac{38}{25} = (\frac{95 - 74}{30}) : \frac{38}{25} = \frac{21}{30} : \frac{38}{25} = \frac{7}{10} \cdot \frac{25}{38} = \frac{7 \cdot 5}{2 \cdot 38} = \frac{35}{76}$$

л) $$(1\frac{2}{3} + 2\frac{4}{9}) : (4\frac{26}{27} - 2\frac{2}{9}) = (\frac{5}{3} + \frac{22}{9}) : (\frac{134}{27} - \frac{20}{9}) = (\frac{15 + 22}{9}) : (\frac{134 - 60}{27}) = \frac{37}{9} : \frac{74}{27} = \frac{37}{9} \cdot \frac{27}{74} = \frac{3}{2} = 1\frac{1}{2}$$

м) $$(6\frac{1}{24} - 2\frac{1}{3}) : (3\frac{1}{2} + 1\frac{7}{8}) = (\frac{145}{24} - \frac{7}{3}) : (\frac{7}{2} + \frac{15}{8}) = (\frac{145 - 56}{24}) : (\frac{28 + 15}{8}) = \frac{89}{24} : \frac{43}{8} = \frac{89}{24} \cdot \frac{8}{43} = \frac{89}{3 \cdot 43} = \frac{89}{129}$$

Ответ: а) 1; б) 1/3; в) 1\frac{7}{8}; г) 1\frac{71}{98}; д) 5\frac{5}{8}; е) 3\frac{449}{672}; ж) \frac{9}{10}; з) 6; и) 3; к) \frac{35}{76}; л) 1\frac{1}{2}; м) \frac{89}{129}