Решебник по математике 5 класс Ерина Виленкин рабочая тетрадь Часть 1, 2 Часть 2 | Страница 59

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\[\textbf{а)}\ \frac{2}{4}x = 5\frac{3}{5}\]

\[x = 5\frac{3}{5}\ :\frac{2}{4}\]

\[x = \frac{28}{5}\ :\frac{1}{2}\]

\[x = \frac{28}{5} \cdot 2 = \frac{56}{5}\]

\[x = 11\frac{1}{5}.\]

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

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

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

\[a = \frac{25}{9}\]

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

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

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

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

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

\[x = 15.\]

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

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

\[\frac{3}{5}x + \frac{1}{8} = \frac{5}{3}\ :\frac{26}{5}\]

\[\frac{3}{5}x + \frac{1}{8} = \frac{5}{3} \cdot \frac{5}{26}\]

\[\frac{3}{5}x + \frac{1}{8} = \frac{25}{78}\]

\[\frac{3}{5}x = \frac{25}{78} - \frac{1}{8}\]

\[\frac{3}{5}x = \frac{100 - 39}{312}\]

\[\frac{3}{5}x = \frac{61}{312}\]

\[x = \frac{61}{312}\ :\frac{3}{5}\]

\[x = \frac{61}{312} \cdot \frac{5}{3}\]

\[x = \frac{305}{936}.\]