444 Вычисли: a) \(\frac{30}{\frac{5}{12} + \frac{1}{4}}\); б) \(\frac{1\frac{3}{8} \cdot 2}{11}\); в) \(\frac{4 - 1\frac{3}{5}}{7\frac{1}{2} \cdot \frac{9}{25}}\); г) \(\frac{8\frac{1}{3} : 2}{1\frac{9}{10} + \frac{7}{20}}\); д) \(\frac{(7\frac{1}{3} : 1\frac{1}{6}) : (8 : 7)}{9 : (1\frac{3}{11} + 2)}\); e) \(\frac{3\frac{4}{7} : (6\frac{1}{28} - 3\frac{3}{4})}{(1\frac{5}{6} \cdot 1\frac{5}{22}) : 18.5}\);

Решение:

a) \(\frac{30}{\frac{5}{12} + \frac{1}{4}} = \frac{30}{\frac{5}{12} + \frac{3}{12}} = \frac{30}{\frac{8}{12}} = \frac{30}{\frac{2}{3}} = 30 \cdot \frac{3}{2} = 15 \cdot 3 = 45\)

б) \(\frac{1\frac{3}{8} \cdot 2}{11} = \frac{\frac{11}{8} \cdot 2}{11} = \frac{\frac{11}{4}}{11} = \frac{11}{4} \cdot \frac{1}{11} = \frac{1}{4}\)

в) \(\frac{4 - 1\frac{3}{5}}{7\frac{1}{2} \cdot \frac{9}{25}} = \frac{4 - \frac{8}{5}}{\frac{15}{2} \cdot \frac{9}{25}} = \frac{\frac{20}{5} - \frac{8}{5}}{\frac{3}{2} \cdot \frac{9}{5}} = \frac{\frac{12}{5}}{\frac{27}{10}} = \frac{12}{5} \cdot \frac{10}{27} = \frac{4}{1} \cdot \frac{2}{9} = \frac{8}{9}\)

г) \(\frac{8\frac{1}{3} : 2}{1\frac{9}{10} + \frac{7}{20}} = \frac{\frac{25}{3} : 2}{\frac{19}{10} + \frac{7}{20}} = \frac{\frac{25}{3} \cdot \frac{1}{2}}{\frac{38}{20} + \frac{7}{20}} = \frac{\frac{25}{6}}{\frac{45}{20}} = \frac{\frac{25}{6}}{\frac{9}{4}} = \frac{25}{6} \cdot \frac{4}{9} = \frac{25}{3} \cdot \frac{2}{9} = \frac{50}{27} = 1\frac{23}{27}\)

д) \(\frac{(7\frac{1}{3} : 1\frac{1}{6}) : (8 : 7)}{9 : (1\frac{3}{11} + 2)} = \frac{(\frac{22}{3} : \frac{7}{6}) : \frac{8}{7}}{9 : (\frac{14}{11} + 2)} = \frac{(\frac{22}{3} \cdot \frac{6}{7}) \cdot \frac{7}{8}}{9 : \frac{36}{11}} = \frac{\frac{44}{7} \cdot \frac{7}{8}}{9 \cdot \frac{11}{36}} = \frac{\frac{11}{2}}{\frac{11}{4}} = \frac{11}{2} \cdot \frac{4}{11} = 2\)

е) \(\frac{3\frac{4}{7} : (6\frac{1}{28} - 3\frac{3}{4})}{(1\frac{5}{6} \cdot 1\frac{5}{22}) : 18.5} = \frac{\frac{25}{7} : (\frac{169}{28} - \frac{15}{4})}{(\frac{11}{6} \cdot \frac{27}{22}) : \frac{37}{2}} = \frac{\frac{25}{7} : (\frac{169}{28} - \frac{105}{28})}{(\frac{1}{2} \cdot \frac{9}{2}) : \frac{37}{2}} = \frac{\frac{25}{7} : \frac{64}{28}}{\frac{9}{4} : \frac{37}{2}} = \frac{\frac{25}{7} \cdot \frac{28}{64}}{\frac{9}{4} \cdot \frac{2}{37}} = \frac{\frac{25}{1} \cdot \frac{4}{64}}{\frac{9}{2} \cdot \frac{1}{37}} = \frac{\frac{25}{1} \cdot \frac{1}{16}}{\frac{9}{2} \cdot \frac{1}{37}} = \frac{\frac{25}{16}}{\frac{9}{74}} = \frac{25}{16} \cdot \frac{74}{9} = \frac{25}{8} \cdot \frac{37}{9} = \frac{925}{72} = 12\frac{61}{72}\)

Ответ: a) 45; б) \(\frac{1}{4}\); в) \(\frac{8}{9}\); г) \(1\frac{23}{27}\); д) 2; е) \(12\frac{61}{72}\)

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