Решебник по математике 6 класс Ткачева ФГОС рабочая тетрадь | Страница 114

\[Страница\ 114.\]

\[\boxed{\mathbf{10.}}\]

\[\textbf{а)}\ 13\ :x = 17\ :8\]

\[17x = 13 \cdot 8\]

\[x = \frac{13 \cdot 8}{17}\]

\[x = \frac{104}{17} = 6\frac{2}{17}\]

\[Ответ:6\frac{2}{17}.\]

\[\textbf{б)}\ \frac{20}{x} = \frac{190}{114}\]

\[190x = 20 \cdot 114\]

\[x = \frac{20 \cdot 114}{90} = 12\]

\[Ответ:12.\]

\[\textbf{в)}\ \frac{6\frac{1}{3}}{7} = \frac{x}{\frac{7}{38}}\]

\[7x = 6\frac{1}{3} \cdot \frac{7}{38}\]

\[x = \frac{\frac{19}{3} \cdot \frac{7}{38}}{7} = \frac{19 \cdot 7}{3 \cdot 38 \cdot 7} = \frac{1}{6}\]

\[Ответ:\frac{1}{6}.\]

\[\textbf{г)}\ x\ :2\frac{1}{12} = 15\ :4\frac{1}{2}\]

\[4\frac{1}{2}x = 2\frac{1}{12} \cdot 15\]

\[x = \frac{15 \cdot \frac{25}{12}}{\frac{9}{2}} = \frac{15 \cdot 25 \cdot 2}{12 \cdot 9} =\]

\[Ответ:8\frac{1}{3}.\]

\[\textbf{д)}\ 3,75\ :10,4 = 3\frac{11}{13}\ :x\]

\[3,75x = \frac{50}{13} \cdot \frac{104}{10}\]

\[x = \frac{50 \cdot 104 \cdot 100}{13 \cdot 10 \cdot 375} = \frac{160}{15} = \frac{32}{3}\]

\[Ответ:10\frac{2}{3}.\]

\[\textbf{е)}\ 9\frac{1}{6}\ :4\frac{4}{5} = 51\frac{9}{16}\ :x\]

\[9\frac{1}{6}x = 51\frac{9}{16}\ :4\frac{4}{5}\]

\[x = \frac{825 \cdot 24}{16 \cdot 5}\ :9\frac{1}{6} =\]

\[= \frac{325 \cdot 24 \cdot 6}{16 \cdot 5 \cdot 55} = 27\ \]

\[Ответ:27.\ \]