Решебник по математике 6 класс Виленкин Часть 1, 2 Часть 1. Параграф 2. Действия со смешанными числами Задание 495

\[\boxed{\mathbf{2.495}}\]

\[\textbf{а)}\ \frac{4}{5}\ :1\frac{1}{3} + 2\frac{1}{3} \cdot \frac{3}{7} - 1\ :1\frac{3}{8} =\]

\[= \frac{4}{5}\ :\frac{4}{3} + \frac{7}{3} \cdot \frac{3}{7} - 1\ :\frac{11}{8} =\]

\[= \frac{4}{5} \cdot \frac{3}{4} + 1 - \frac{8}{11} =\]

\[= \frac{3^{\backslash 5}}{11} + \frac{3^{\backslash 11}}{5} = \frac{15}{55} + \frac{33}{55} = \frac{48}{55}\]

\[= \frac{13}{6}\ :\frac{13}{15} + 2\frac{7}{8} \cdot \frac{4}{23} =\]

\[= \frac{13}{6} \cdot \frac{15}{13} + \frac{23}{8} \cdot \frac{4}{23} = \frac{5}{2} + \frac{1}{2} =\]

\[= \frac{6}{2} = 3\]

\[= 1\frac{29}{28} \cdot \frac{14}{57} - \frac{2 \cdot 6 \cdot 7}{3 \cdot 7 \cdot 32} =\]

\[= \frac{57}{28} \cdot \frac{14}{57} - \frac{1}{8} = \frac{1^{\backslash 4}}{2} - \frac{1}{8} =\]

\[= \frac{4}{8} - \frac{1}{8} = \frac{3}{8}\]

\[\textbf{г)}\ \left( 2\frac{1}{2}\ :3\frac{1}{3} + 3\frac{1}{3}\ :2\frac{1}{2} \right) \cdot 9\frac{3}{5} =\]

\[= \left( \frac{5}{2}\ :\frac{10}{3} + \frac{10}{3}\ :\frac{5}{2} \right) \cdot \frac{48}{5} =\]

\[= \left( \frac{5}{2} \cdot \frac{3}{10} + \frac{10}{3} \cdot \frac{2}{5} \right) \cdot \frac{48}{5} =\]

\[= \left( \frac{3^{\backslash 3}}{4} + \frac{4^{\backslash 4}}{3} \right) \cdot \frac{48}{5} =\]

\[= \left( \frac{9}{12} + \frac{16}{12} \right) \cdot \frac{48}{5} = \frac{25}{12} \cdot \frac{48}{5} = 20\]

\[\textbf{д)}\ \left( 10\frac{5}{13} - 7\frac{23}{26} \right)\ :\frac{5}{6} =\]

\[= \left( 9\frac{18^{\backslash 2}}{13} - 7\frac{23}{26} \right) \cdot \frac{6}{5} =\]

\[= \left( 9\frac{36}{26} - 7\frac{23}{26} \right) \cdot \frac{6}{5} = 2\frac{13}{26} \cdot \frac{6}{5} =\]

\[= 2\frac{1}{2} \cdot \frac{6}{5} = \frac{5}{2} \cdot \frac{6}{5} = 3\]

\[\textbf{е)}\ \left( \left( 1\frac{1}{2} \right)^{3} - \frac{3}{4} \right)\ :\frac{7}{8} =\]

\[= \left( \left( \frac{3}{2} \right)^{3} - \frac{3^{\backslash 2}}{4} \right) \cdot \frac{8}{7} =\]

\[= \left( \frac{27}{8} - \frac{6}{8} \right) \cdot \frac{8}{7} = \frac{21}{8} \cdot \frac{8}{7} = 3\ \ \]