ГДЗ по математике 6 класс Виленкин Часть 1, 2 Часть 1. Параграф 2. Действия со смешанными числами Задание 294

\[\boxed{\mathbf{2.2}\mathbf{94}}\]

\[\textbf{а)}\ \frac{7}{16} \cdot \frac{4}{9} - 1\frac{7}{15} =\]

\[= \frac{7 \cdot 4}{16 \cdot 9} - 1\frac{7}{15} = \frac{7^{\backslash 5}}{36} - 1\frac{7^{\backslash 12}}{15} =\]

\[= \frac{35}{180} - 1\frac{84}{180} =\]

\[= - \left( 1\frac{84}{180} - \frac{35}{180} \right) = - 1\frac{49}{180}\]

\[\textbf{б)}\frac{8}{15} \cdot \left( 2\frac{1}{2} \right)^{2} - \frac{5}{9} =\]

\[= \frac{8}{15} \cdot \left( \frac{5}{2} \right)^{2} - \frac{5}{9} = \frac{8 \cdot 25}{15 \cdot 4} - \frac{5}{9} =\]

\[= \frac{2 \cdot 5}{3} - \frac{5}{9} = \frac{10^{\backslash 3}}{3} - \frac{5}{9} =\]

\[= \frac{30}{9} - \frac{5}{9} = \frac{25}{9} = 2\frac{7}{9}\]

\[\textbf{в)}\ \left( \left( 1\frac{1}{6} \right)^{2} - \frac{7}{18} \right) \cdot 2\frac{4}{7} - 4\frac{2}{5} =\]

\[= \left( \left( \frac{7}{6} \right)^{2} - \frac{7^{\backslash 2}}{18} \right) \cdot \frac{18}{7} - 4\frac{2}{5} =\]

\[= \left( \frac{49}{36} - \frac{14}{36} \right) \cdot \frac{18}{7} - 4\frac{2}{5} =\]

\[= \frac{35 \cdot 18}{36 \cdot 7} - 4\frac{2}{5} = \frac{5}{2} - 4\frac{2}{5} =\]

\[= 2,5 - 4,4 = - 1,9\]

\[\textbf{г)}\ \left( \frac{11^{\backslash 3}}{16} + \frac{7^{\backslash 2}}{24} - \frac{5^{\backslash 4}}{12} \right) + \left( \frac{3}{4} \right)^{2} =\]

\[= \left( \frac{33}{48} + \frac{14}{48} - \frac{20}{48} \right) + \frac{9}{16} =\]

\[= \frac{27}{48} + \frac{9}{16} =\]

\[= \frac{9}{16} + \frac{9}{16} = \frac{18}{16} = \frac{9}{8} = 1\frac{1}{8}\]