Решебник по математике 6 класс Виленкин Часть 1, 2 Часть 1. Параграф 2. Действия со смешанными числами Задание 559

\[\boxed{\mathbf{2.559}}\]

\[\textbf{а)}\ \frac{\frac{3}{7} \cdot 1,1 \cdot 1\frac{1}{6}\ :0,05}{\frac{1}{7}\ :0,25 \cdot 2\frac{2}{5}} =\]

\[= \frac{\frac{3}{7} \cdot \frac{11}{10} \cdot \frac{7}{6}\ :\frac{1}{20}}{\frac{1}{7}\ :\frac{1}{4} \cdot \frac{12}{5}} =\]

\[= \frac{\frac{3}{7} \cdot \frac{11}{10} \cdot \frac{7}{6} \cdot 20}{\frac{1}{7} \cdot 4 \cdot \frac{12}{5}} = \frac{11}{\frac{48}{35}} =\]

\[= \frac{11 \cdot 35}{48} = \frac{385}{48} = 8\frac{1}{48}\]

\[\textbf{б)}\ \frac{0,3 \cdot 7,4\ :0,37 - 1\frac{11}{14} \cdot 0,7}{1 + 2\frac{1}{8} \cdot 0,16\ :0,01} =\]

\[= \frac{6 - 1,25}{1 + 34} = \frac{4,75}{35} = \frac{475}{3500} =\]

\[= \frac{19}{140}\]

\[\frac{3}{10} \cdot \frac{74}{10}\ :\frac{37}{100} = \frac{3 \cdot 74 \cdot 100}{10 \cdot 10 \cdot 37} =\]

\[= 3 \cdot 2 = 6\]

\[1\frac{11}{14} \cdot 0,7 = \frac{25}{14} \cdot \frac{7}{10} = \frac{5}{4} = 1,25\]

\[\frac{17}{8} \cdot \frac{16}{100}\ :\frac{1}{100} = \frac{17 \cdot 16 \cdot 100}{8 \cdot 100} =\]

\[= 17 \cdot 2 = 34\]

\[\textbf{в)}\ \frac{18,55 \cdot \frac{4}{35} \cdot 4,2}{3\frac{1}{2} \cdot 2,12\ :70} =\]

\[= \frac{\frac{1855}{100} \cdot \frac{4}{35} \cdot \frac{42}{10}}{\frac{7}{2} \cdot \frac{212}{100} \cdot \frac{1}{70}} = \frac{\frac{53 \cdot 1 \cdot 21}{25 \cdot 1 \cdot 5}}{\frac{1 \cdot 53}{2 \cdot 25 \cdot 10}} =\]

\[= \frac{53 \cdot 21}{25 \cdot 5} \cdot \frac{25 \cdot 20}{53} =\]

\[= 21 \cdot 4 = 84\]

\[\textbf{г)}\ \frac{\left( 2,75 \cdot \frac{3}{5} + 2,2\ :1 \right) \cdot 1\frac{1}{11}}{\left( \frac{39}{40} - 0,575 \right)\ :\frac{4}{5} \cdot 0,8} =\]

\[= \frac{4,2}{0,4} = \frac{42}{4} = 10,5\]

\[2,75 \cdot \frac{3}{5} + 2,2\ :1 =\]

\[= \frac{275}{100} \cdot \frac{3}{5} + 2,2 = \frac{11 \cdot 3}{4 \cdot 5} + 2,2 =\]

\[= \frac{33}{20} + 2,2 = \frac{165}{100} + 2,2 =\]

\[= 1,65 + 2,2 = 3,85\]

\[3,85 \cdot \frac{12}{11} = \frac{385}{100} \cdot \frac{12}{11} = \frac{35 \cdot 3}{25} =\]

\[= \frac{7 \cdot 3}{5} = \frac{21}{5} = 4,2\]

\[\frac{39}{40} - \frac{575}{1000} = \frac{39}{40} - \frac{23}{40} = \frac{16}{40} =\]

\[= \frac{4}{10}\]

\[\frac{4}{10}\ :\frac{4}{5} = \frac{4}{10} \cdot \frac{5}{4} = \frac{1}{2}\]

\[\frac{1}{2} \cdot 0,8 = 0,4\]