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МатематикаРешебник по математике 6 класс Мерзляк ФГОС Задание 341
Задание 341
\[\boxed{\mathbf{341\ (341).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \left( \frac{11}{18} - \frac{4^{\backslash 2}}{9} \right) \cdot \frac{3}{16} =\]
\[= \left( \frac{11}{18} - \frac{8}{18} \right) \cdot \frac{3}{16} = \frac{3}{18} \cdot \frac{3}{16} =\]
\[= \frac{1}{6} \cdot \frac{3}{16} = \frac{3}{96} = \frac{1}{32}\]
\[3)\ 1\frac{3}{5} \cdot \left( \frac{3}{4} + 1\frac{3}{8} \right) =\]
\[= \frac{8}{5} \cdot \left( \frac{3^{\backslash 2}}{4} + \frac{11}{8} \right) = \frac{8}{5} \cdot \frac{6 + 11}{8} =\]
\[= \frac{8 \cdot 17}{5 \cdot 8} = \frac{17}{5} = 3\frac{2}{5}\]
\[= 13\frac{4}{5} - 12 = 1\frac{4}{5}\]
\[= \frac{12^{\backslash 2}}{5} - \frac{3}{10} = \frac{24 - 3}{10} = \frac{21}{10} =\]
\[= 2\frac{1}{10}\]
\[= \frac{35^{\backslash 2}}{6} + \frac{3^{\backslash 3}}{4} = \frac{70 + 9}{12} = \frac{79}{12} =\]
\[= 6\frac{7}{12}\]
\[8)\ \left( 8 - 2\frac{1}{7} \cdot 3\frac{1}{9} \right) \cdot \frac{27}{44} =\]
\[= \left( 8 - \frac{15}{7} \cdot \frac{28}{9} \right) \cdot \frac{27}{44} =\]
\[= \left( 8 - \frac{15 \cdot 28}{7 \cdot 9} \right) \cdot \frac{27}{44} =\]
\[9)\ \left( \frac{4}{5} + \frac{4}{7} \right) \cdot \left( 7\frac{11^{\backslash 3}}{12} - 5\frac{7^{\backslash 4}}{9} \right) =\]
\[= \frac{28 + 20}{35} \cdot \left( 7\frac{33}{36} - 5\frac{28}{36} \right) =\]
\[= \frac{48}{35} \cdot 2\frac{5}{36} =\]
\[10)\ \frac{4}{5} + \frac{4}{7} \cdot \left( 7\frac{11^{\backslash 3}}{12} - 5\frac{7^{\backslash 4}}{9} \right) =\]
\[= \frac{4}{5} + \frac{4}{7} \cdot \left( 7\frac{33}{36} - 5\frac{28}{36} \right) =\]
\[= \frac{4}{5} + \frac{4}{7} \cdot 2\frac{5}{36} =\]
\[\boxed{\mathbf{341}\mathbf{.}}\]
\[1)\ \frac{4}{15} + \frac{13}{36} + \frac{1}{15} + \frac{5}{36} =\]
\[= \frac{4 + 1}{15} + \frac{13 + 5}{36} =\]
\[= \frac{5}{15} + \frac{18}{36} = \frac{1^{\backslash 2}}{3} + \frac{1^{\backslash 3}}{2} =\]
\[= \frac{2}{6} + \frac{3}{6} = \frac{5}{6}\]
\[2)\ 2\frac{5}{18} + 4\frac{1}{48} + 6\frac{7}{48} + 3\frac{1}{18} =\]
\[= 5\frac{5 + 1}{18} + 10\frac{1 + 7}{48} =\]
\[= 5\frac{6}{18} + 10\frac{8}{48} = 5\frac{1^{\backslash 2}}{3} + 10\frac{1}{6} =\]
\[= 5\frac{2}{6} + 10\frac{1}{6} = 15\frac{3}{6} = 15\frac{1}{2}\]
