Решебник по математике 6 класс Ерина Никольский рабочая тетрадь Часть 1, 2 Часть 1 | Страница 13

\[\mathbf{Страница\ 13.}\]

\[\boxed{\mathbf{6.}}\]

\[48\ :6 = 56\ :7\]

\[Крайние\ члены:\ \ 48\ и\ 7.\]

\[Их\ произведение:\]

\[48 \cdot 7 = 336.\]

\[Средние\ члены:\ \ 6\ и\ 56.\]

\[Их\ произведение:\]

\[6 \cdot 56 = 336.\ \]

\[\boxed{\mathbf{7.}}\]

\[\textbf{а)}\ 58\ :208 = \frac{1}{2}\ :7\]

\[58 \cdot 7 = 406\]

\[208 \cdot \frac{1}{2} = 104\]

\[406 \neq 104\]

\[Пропорция\ неверна.\]

\[\textbf{б)}\ \frac{116}{12} = \frac{29}{3}\ \]

\[116 \cdot 3 = 348\]

\[29 \cdot 12 = 290 + 58 = 348\]

\[348 = 348\]

\[Пропорция\ верна.\]

\[\boxed{\mathbf{8.}}\]

\[3\ :4 = 9\ :12\]

\[\textbf{а)}\ 3\ :9 = 4\ :12\]

\[\textbf{б)}\ 12\ :4 = 9\ :3\]

\[\textbf{в)}\ 12\ :9 = 4\ :3\]

\[\boxed{\mathbf{9.}}\]

\[\textbf{а)}\ 13\ :x = 17\ :8\]

\[17x = 13 \cdot 8\]

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

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

\[Ответ:\ \ 6\frac{2}{17}.\]

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

\[190x = 20 \cdot 114\]

\[x = \frac{20 \cdot 114}{190} = 2 \cdot 6\]

\[x = 12.\]

\[Ответ:12.\]

\[\textbf{в)}\ 3\frac{3}{4}\ :10\frac{2}{5} = 3\frac{11}{13}\ :x\]

\[\frac{15}{4}\ :\frac{52}{5} = \frac{50}{13}\ :x\]

\[\frac{15}{4}x = \frac{52}{5} \cdot \frac{50}{13}\]

\[\frac{15}{4}x = 40\]

\[x = 40\ :\frac{15}{4}\]

\[x = 40 \cdot \frac{4}{15}\]

\[x = \frac{160}{15} = 10\frac{10}{15}\]

\[x = 10\frac{2}{3}.\]

\[Ответ:10\frac{2}{3}.\]

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

\[\frac{55}{6}\ :\frac{24}{5} = \frac{825}{16}\ :x\]

\[\frac{55}{6}x = \frac{24}{5} \cdot \frac{825}{16}\]

\[\frac{55}{6}x = \frac{495}{2}\]

\[x = \frac{495}{2} \cdot \frac{6}{55} = 9 \cdot 3\]

\[x = 27.\]

\[Ответ:27.\]