Вычислите:
а) $\frac{7\frac{1}{2} * 2\frac{2}{3} - 12\frac{1}{4} : \frac{7}{2}}{110 * \frac{3}{5}} + \frac{3\frac{3}{8} + 2\frac{3}{4}}{24 : 2\frac{2}{5}}$;
б) $(3\frac{1}{4} + 2\frac{1}{6}) : 2\frac{3}{5} - \frac{2}{3} * 2\frac{1}{4} + 5\frac{1}{6}$;
в) $\frac{(4\frac{2}{5} + 1\frac{1}{7}) * (2\frac{8}{13} + 3\frac{2}{3})}{144 - 256}$;
г) $\frac{5\frac{9}{11} : 1\frac{2}{9} - 7\frac{2}{3} * 1\frac{1}{23}}{\frac{11}{54} - \frac{5}{36}}$.

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Решение

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Решение а

$\frac{7\frac{1}{2} * 2\frac{2}{3} - 12\frac{1}{4} : \frac{7}{2}}{110 * \frac{3}{5}} + \frac{3\frac{3}{8} + 2\frac{3}{4}}{24 : 2\frac{2}{5}} = \frac{\frac{15}{2} * \frac{8}{3} - \frac{49}{4} * \frac{2}{7}}{22 * \frac{3}{1}} + \frac{3\frac{3}{8} + 2\frac{6}{8}}{24 : \frac{12}{5}} = \frac{\frac{5}{1} * \frac{4}{1} - \frac{7}{2} * \frac{1}{1}}{66} + \frac{6\frac{1}{8}}{24 * \frac{5}{12}} = \frac{20 - 3\frac{1}{2}}{66} + \frac{\frac{49}{8}}{2 * \frac{5}{1}} = \frac{16\frac{1}{2}}{66} + \frac{\frac{49}{8}}{10} = \frac{33}{2} * \frac{1}{66} + \frac{49}{8} * \frac{1}{10} = \frac{1}{2} * \frac{1}{2} + \frac{49}{80} = \frac{1}{4} + \frac{49}{80} = \frac{20}{80} + \frac{49}{80} = \frac{69}{80}$

Решение б

$(3\frac{1}{4} + 2\frac{1}{6}) : 2\frac{3}{5} - \frac{2}{3} * 2\frac{1}{4} + 5\frac{1}{6} = (3\frac{3}{12} + 2\frac{2}{12}) : \frac{13}{5} - \frac{2}{3} * \frac{9}{4} + 5\frac{1}{6} = 5\frac{5}{12} * \frac{5}{13} - \frac{1}{1} * \frac{3}{2} + 5\frac{1}{6} = \frac{65}{12} * \frac{5}{13} - 1\frac{1}{2} + 5\frac{1}{6} = \frac{5}{12} * \frac{5}{1} - 1\frac{1}{2} + 5\frac{1}{6} = \frac{25}{12} - 1\frac{1}{2} + 5\frac{1}{6} = 2\frac{1}{12} - 1\frac{6}{12} + 5\frac{2}{12} = 1\frac{13}{12} - 1\frac{6}{12} + 5\frac{2}{12} = \frac{7}{12} + 5\frac{2}{12} = 5\frac{9}{12} = 5\frac{3}{4}$

Решение в

$\frac{(4\frac{2}{5} + 1\frac{1}{7}) * (2\frac{8}{13} + 3\frac{2}{3})}{144 - 256} = \frac{(4\frac{14}{35} + 1\frac{5}{35}) * (2\frac{24}{39} + 3\frac{26}{39})}{-112} = -\frac{5\frac{19}{35} * 5\frac{50}{39}}{112} = -\frac{\frac{194}{35} * \frac{245}{39}}{112} = -\frac{\frac{194}{1} * \frac{7}{39}}{112} = -\frac{\frac{194 * 7}{39}}{112} = -\frac{194 * 7}{39} * \frac{1}{112} = -\frac{194}{39} * \frac{1}{16} = -\frac{97}{39} * \frac{1}{8} = -\frac{97}{312}$

Решение г

$\frac{5\frac{9}{11} : 1\frac{2}{9} - 7\frac{2}{3} * 1\frac{1}{23}}{\frac{11}{54} - \frac{5}{36}} = \frac{\frac{64}{11} : \frac{11}{9} - \frac{23}{3} * \frac{24}{23}}{\frac{22}{108} - \frac{15}{108}} = \frac{\frac{64}{11} * \frac{9}{11} - \frac{1}{1} * \frac{8}{1}}{\frac{7}{108}} = \frac{\frac{576}{121} - 8}{\frac{7}{108}} = \frac{\frac{576 - 968}{121}}{\frac{7}{108}} = -\frac{392}{121} * \frac{108}{7} = -\frac{56}{121} * \frac{108}{1} = -\frac{6048}{121} = -49\frac{119}{121}$