Решебник по математике 6 класс Мерзляк ФГОС Задание 356

 

\[\boxed{\mathbf{356\ (356).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

Пояснение.

Решение.

\[1)\ 4\frac{4}{9} \cdot \frac{5}{8} + \frac{5}{8} \cdot 3\frac{5}{9} =\]

\[= \frac{5}{8} \cdot \left( 4\frac{4}{9} + 3\frac{5}{9} \right) = \frac{5}{8} \cdot 8 = 5\]

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

\[= \frac{4}{5} \cdot \left( 3\frac{7}{8} - 1\frac{5}{8} \right) = \frac{4}{5} \cdot 2\frac{2}{8} =\]

\[= \frac{4}{5} \cdot 2\frac{1}{4} = \frac{4}{5} \cdot \frac{9}{4} =\]

\[3)\ 2\frac{11}{15} \cdot 1\frac{1}{19} - 1\frac{1}{19} \cdot \frac{3}{10} - 1\frac{1}{6} \cdot 1\frac{1}{19} =\]

\[= 1\frac{1}{19} \cdot \left( 2\frac{11^{\backslash 2}}{15} - \frac{3^{\backslash 3}}{10} - 1\frac{1^{\backslash 5}}{6} \right) =\]

\[= \frac{20}{19} \cdot \left( 2\frac{22}{30} - \frac{9}{30} - 1\frac{5}{30} \right) =\]

\[= \frac{20}{19} \cdot 1\frac{8}{30} = \frac{20}{19} \cdot 1\frac{4}{15} =\]

\[= \frac{20}{19} \cdot \frac{19}{15} = \frac{20}{15} = \frac{4}{3} = 1\frac{1}{3}\]

\[= 1\frac{13}{14} \cdot \left( 4\frac{7^{\backslash 4}}{9} - 3\frac{7^{\backslash 3}}{12} + 1\frac{13^{\backslash 2}}{18} \right) =\]

\[= \frac{27}{14} \cdot \left( 4\frac{28}{36} - 3\frac{21}{36} + 1\frac{26}{36} \right) =\]

\[= \frac{27}{14} \cdot 2\frac{33}{36} = \frac{27}{14} \cdot 2\frac{11}{12} =\]

\[= \frac{27}{14} \cdot \frac{35}{12} =\]

\[\boxed{\mathbf{356}\mathbf{.}}\]

\[1)\ \frac{1}{3} \rightarrow 3;\]

\[\frac{4}{9} \cdot 3 = \frac{4}{3}.\]

\[2)\ 28 \rightarrow \frac{1}{28};\]

\[7 \cdot \frac{1}{28} = \frac{1}{4}.\]

\[3)\ 1\frac{5}{9} = \frac{14}{9} \rightarrow \frac{9}{14};\]

\[\frac{2}{11} \cdot \frac{9}{14} = \frac{1 \cdot 9}{11 \cdot 7} = \frac{9}{77}.\]