Решебник по математике 6 класс Виленкин Часть 1, 2 Часть 1. Параграф 2. Действия со смешанными числами Задание 321

\[\boxed{\mathbf{2.}\mathbf{321}}\]

\[\textbf{а)}\ \frac{61}{64} - \left( \frac{7^{\backslash 7}}{12} - \frac{5^{\backslash 6}}{14} \right) \cdot \left( \frac{13}{16} + \frac{1^{\backslash 8}}{2} \right) =\]

\[= \frac{61}{64} - \left( \frac{49}{84} - \frac{30}{84} \right) \cdot \left( \frac{13}{16} + \frac{8}{16} \right) =\]

\[= \frac{61}{64} - \frac{19}{84} \cdot \frac{21}{16} = \frac{61}{64} - \frac{19}{64} =\]

\[= \frac{42}{64} = \frac{21}{32}\]

\[\textbf{б)}\ \left( 1 - \frac{11}{17} \right) \cdot \left( \frac{3^{\backslash 9}}{4} - \frac{5^{\backslash 3}}{12} + \frac{11^{\backslash 2}}{18} \right) =\]

\[= \left( \frac{17}{17} - \frac{11}{17} \right) \cdot \left( \frac{27}{36} - \frac{15}{36} + \frac{22}{36} \right) =\]

\[= \frac{6}{17} \cdot \frac{27 - 15 + 22}{36} = \frac{6}{17} \cdot \frac{34}{36} =\]

\[= \frac{6 \cdot 17}{17 \cdot 18} = \frac{1}{3}\]

\[\textbf{в)}\ (3,5 - 2,9) \cdot \left( 4\frac{1^{\backslash 3}}{22} - 3\frac{7^{\backslash 2}}{33} \right) =\]

\[= 0,6 \cdot \left( 4\frac{3}{66} - 3\frac{14}{66} \right) =\]

\[= \frac{6}{10} \cdot \left( 3\frac{69}{66} - 3\frac{14}{66} \right) =\]

\[= \frac{3}{5} \cdot \frac{55}{66} = \frac{3}{5} \cdot \frac{5}{6} = \frac{1}{2} = 0,5\]

\[\textbf{г)}\ \left( 5\frac{3}{14} - 4\frac{4^{\backslash 2}}{7} \right) \cdot \left( 3\frac{11}{15} - 1\frac{2^{\backslash 3}}{5} \right) =\]

\[= \left( 4\frac{17}{14} - 4\frac{8}{14} \right) \cdot \left( 3\frac{11}{15} - 1\frac{6}{15} \right) =\]

\[= \frac{9}{14} \cdot 2\frac{5}{15} = \frac{9}{14} \cdot 2\frac{1}{3} = \frac{9}{14} \cdot \frac{7}{3} =\]

\[= \frac{3}{2} = 1\frac{1}{2} = 1,5\]