Решебник по математике 6 класс Ерина Виленкин рабочая тетрадь Часть 1, 2 Часть 1 | Страница 88

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\[\boxed{\mathbf{15.}}\]

\[\textbf{а)}\ \frac{2}{5}x = 5\frac{3}{5}\]

\[x = 5\frac{3}{5}\ :\frac{2}{5} = \frac{28}{5} \cdot \frac{5}{2}\]

\[x = 14.\]

\[Ответ:14.\]

\[\textbf{б)}\ a\ :2\frac{1}{2} = 3\frac{1}{3} \cdot \frac{1}{3}\]

\[a = \frac{10}{3} \cdot \frac{1}{3} \cdot 2\frac{1}{2}\]

\[a = \frac{10}{3} \cdot \frac{1}{3} \cdot \frac{5}{2} = \frac{25}{9}\]

\[a = 2\frac{7}{9}.\]

\[Ответ:2\frac{7}{9}.\]

\[\textbf{в)}\ \frac{2}{9}x + \frac{5}{9}x = 11\frac{2}{3}\]

\[\frac{7}{9}x = 11\frac{2}{3}\]

\[x = \frac{35}{3}\ :\frac{7}{9} = \frac{35 \cdot 9}{3 \cdot 7}\]

\[x = 15.\]

\[Ответ:15.\]

\[\textbf{г)}\ 5\frac{1}{3} \cdot \left( \frac{3}{5}x + \frac{1}{8} \right) = 1\frac{2}{3}\]

\[\frac{3}{5}x + \frac{1}{8} = 1\frac{2}{3}\ :5\frac{1}{3}\]

\[\frac{3}{5}x = \frac{5}{3} \cdot \frac{3}{16} - \frac{1^{\backslash 2}}{8}\]

\[x = \left( \frac{5}{16} - \frac{2}{16} \right)\ :\frac{3}{5}\]

\[x = \frac{3}{16} \cdot \frac{5}{3} = \frac{5}{16}.\]

\[Ответ:\frac{5}{16}.\]

\[\textbf{д)}\ \frac{4}{25}\ :x = \frac{3}{20}\ :\frac{3}{10}\]

\[\frac{3}{20}x = \frac{4}{25} \cdot \frac{3}{10}\]

\[x = \frac{4}{25} \cdot \frac{3}{10}\ :\frac{3}{20} =\]

\[x = \frac{4 \cdot 3 \cdot 20}{25 \cdot 10 \cdot 3} = \frac{4 \cdot 2}{25}\]

\[x = \frac{8}{25}\]

\[Ответ:\frac{8}{25}.\]

\[\textbf{е)}\ \left( 5\frac{7}{18} - 4\frac{23}{30} \right)\ :\left( 1,12 \cdot 1\frac{1}{9} \right) =\]

\[= x\ :\left( 3,2 + 0,8 \cdot \left( 5\frac{1}{2} - 3,25 \right) \right)\]

\[5\frac{7^{\backslash 5}}{18} - 4\frac{23^{\backslash 3}}{30} = 5\frac{35}{90} - 4\frac{69}{90} =\]

\[= 4\frac{125}{90} - 4\frac{69}{90} = \frac{56}{90} = \frac{28}{45}\]

\[1,12 \cdot 1\frac{1}{9} = \frac{112}{100} \cdot \frac{10}{9} = \frac{56}{5 \cdot 9} =\]

\[= \frac{56}{45}\]

\[\frac{28}{45}\ :\frac{56}{45} = \frac{28}{45} \cdot \frac{45}{56} = \frac{1}{2}\]

\[3,2 + 0,8 \cdot \left( 5\frac{1}{2} - 3,25 \right) =\]

\[= 3,2 + 0,8 \cdot (5,5 - 3,25) =\]

\[= 3,2 + 0,8 \cdot 2,25 = 3,2 + 1,8 =\]

\[= 5\]

\[\frac{1}{2} = x\ :5\]

\[x = \frac{1}{2} \cdot 5\]

\[x = \frac{5}{2} = 2,5\]

\[Ответ:2,5.\]

\[10,5 \cdot 0,24 - 15,15\ :7,5 =\]

\[= 2,52 - 2,02 = 0,5\]

\[3\frac{5^{\backslash 5}}{24} - 2\frac{7^{\backslash 4}}{30} = 3\frac{25}{120} - 2\frac{28}{120} =\]

\[= 2\frac{145}{120} - 2\frac{28}{120} = \frac{117}{120} = \frac{39}{40}\]

\[1\frac{11}{15} \cdot \frac{3}{8} = \frac{26}{15} \cdot \frac{3}{8} = \frac{26}{40} = \frac{13}{20}\]

\[\frac{39}{40}\ :\frac{13}{20} = \frac{39}{40} \cdot \frac{20}{13} = \frac{3}{2} = 1,5\]

\[0,5\ :x = 1,5\]

\[x = 0,5\ :1,5\]

\[x = \frac{5}{15} = \frac{1}{3}\ \]

\[Ответ:\frac{1}{3}.\]