Контрольные задания > 381 Выполни действия: 1) 2\frac{1}{6}-1\frac{2}{9}:3\frac{2}{3}; 2) 4\frac{2}{5}:(\frac{7}{10}+2\frac{3}{5}); 3) 5 \cdot (\frac{2}{3})^{3}:(\frac{4}{9})^{2}; 4) (\frac{5}{6}+2\frac{3}{4}): 4\frac{7}{9} \cdot 2\frac{2}{3}-1\frac{2}{3}: 5) (1\frac{1}{8}+1\frac{1}{2}):3:(5\frac{1}{2}-\frac{9}{20}:1\frac{4}{5}): 6) \frac{9}{10} \cdot 1\frac{1}{14}:2\frac{4}{7} \cdot 24-2\frac{4}{15}:(1\frac{1}{5}-\frac{2}{3}).
Вопрос:

381 Выполни действия: 1) 2\frac{1}{6}-1\frac{2}{9}:3\frac{2}{3}; 2) 4\frac{2}{5}:(\frac{7}{10}+2\frac{3}{5}); 3) 5 \cdot (\frac{2}{3})^{3}:(\frac{4}{9})^{2}; 4) (\frac{5}{6}+2\frac{3}{4}): 4\frac{7}{9} \cdot 2\frac{2}{3}-1\frac{2}{3}: 5) (1\frac{1}{8}+1\frac{1}{2}):3:(5\frac{1}{2}-\frac{9}{20}:1\frac{4}{5}): 6) \frac{9}{10} \cdot 1\frac{1}{14}:2\frac{4}{7} \cdot 24-2\frac{4}{15}:(1\frac{1}{5}-\frac{2}{3}).

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Ответ:

Решим примеры по действиям:

  1. 1) $$2\frac{1}{6}-1\frac{2}{9}:3\frac{2}{3} = \frac{13}{6} - \frac{11}{9} : \frac{11}{3} = \frac{13}{6} - \frac{11}{9} \cdot \frac{3}{11} = \frac{13}{6} - \frac{1}{3} = \frac{13}{6} - \frac{2}{6} = \frac{11}{6} = 1\frac{5}{6}$$.

    Ответ: $$1\frac{5}{6}$$

  2. 2) $$4\frac{2}{5}:(\frac{7}{10}+2\frac{3}{5}) = \frac{22}{5} : (\frac{7}{10} + \frac{13}{5}) = \frac{22}{5} : (\frac{7}{10} + \frac{26}{10}) = \frac{22}{5} : \frac{33}{10} = \frac{22}{5} \cdot \frac{10}{33} = \frac{2}{1} \cdot \frac{2}{3} = \frac{4}{3} = 1\frac{1}{3}$$.

    Ответ: $$1\frac{1}{3}$$

  3. 3) $$5 \cdot (\frac{2}{3})^{3}:(\frac{4}{9})^{2} = 5 \cdot \frac{8}{27} : \frac{16}{81} = 5 \cdot \frac{8}{27} \cdot \frac{81}{16} = 5 \cdot \frac{1}{1} \cdot \frac{3}{2} = \frac{15}{2} = 7\frac{1}{2}$$.

    Ответ: $$7\frac{1}{2}$$

  4. 4) $$( \frac{5}{6}+2\frac{3}{4}): 4\frac{7}{9} \cdot 2\frac{2}{3}-1\frac{2}{3} = (\frac{10}{12} + \frac{33}{12}) : \frac{43}{9} \cdot \frac{8}{3} - \frac{5}{3} = \frac{43}{12} : \frac{43}{9} \cdot \frac{8}{3} - \frac{5}{3} = \frac{43}{12} \cdot \frac{9}{43} \cdot \frac{8}{3} - \frac{5}{3} = \frac{1}{4} \cdot \frac{3}{1} \cdot \frac{2}{1} - \frac{5}{3} = \frac{6}{4} - \frac{5}{3} = \frac{3}{2} - \frac{5}{3} = \frac{9}{6} - \frac{10}{6} = -\frac{1}{6}$$.

    Ответ: $$\frac{-1}{6}$$

  5. 5) $$(1\frac{1}{8}+1\frac{1}{2}):3:(5\frac{1}{2}-\frac{9}{20}:1\frac{4}{5}) = (\frac{9}{8} + \frac{3}{2}) : 3 : (\frac{11}{2} - \frac{9}{20} : \frac{9}{5}) = (\frac{9}{8} + \frac{12}{8}) : 3 : (\frac{11}{2} - \frac{9}{20} \cdot \frac{5}{9}) = \frac{21}{8} : 3 : (\frac{11}{2} - \frac{1}{4}) = \frac{21}{8} : 3 : (\frac{22}{4} - \frac{1}{4}) = \frac{21}{8} : 3 : \frac{21}{4} = \frac{21}{8} \cdot \frac{1}{3} \cdot \frac{4}{21} = \frac{1}{2} \cdot \frac{1}{1} \cdot \frac{1}{3} = \frac{1}{6}$$.

    Ответ: $$\frac{1}{6}$$

  6. 6) $$\frac{9}{10} \cdot 1\frac{1}{14}:2\frac{4}{7} \cdot 24-2\frac{4}{15}:(1\frac{1}{5}-\frac{2}{3}) = \frac{9}{10} \cdot \frac{15}{14} : \frac{18}{7} \cdot 24 - \frac{34}{15} : (\frac{6}{5} - \frac{2}{3}) = \frac{9}{10} \cdot \frac{15}{14} : \frac{18}{7} \cdot 24 - \frac{34}{15} : (\frac{18}{15} - \frac{10}{15}) = \frac{9}{10} \cdot \frac{15}{14} : \frac{18}{7} \cdot 24 - \frac{34}{15} : \frac{8}{15} = \frac{9}{10} \cdot \frac{15}{14} \cdot \frac{7}{18} \cdot 24 - \frac{34}{15} \cdot \frac{15}{8} = \frac{1}{2} \cdot \frac{3}{2} \cdot \frac{1}{2} \cdot 24 - \frac{17}{4} = \frac{72}{8} - \frac{17}{4} = 9 - \frac{17}{4} = \frac{36}{4} - \frac{17}{4} = \frac{19}{4} = 4\frac{3}{4}$$.

    Ответ: $$4\frac{3}{4}$$

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