Решебник по математике 6 класс Ерина Никольский рабочая тетрадь Часть 1, 2 Часть 1 | Страница 91

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

\[\textbf{а)} - \frac{1}{3}\ :2 = - \frac{1}{3} \cdot \frac{1}{2} = - \frac{1}{6}\]

\[- \frac{1}{4}\ :2 = - \frac{1}{4} \cdot \frac{1}{2} = - \frac{1}{8}\]

\[- \frac{3}{7}\ :( - 4) = \frac{3}{7} \cdot \frac{1}{4} = \frac{3}{28}\]

\[\textbf{б)} - \frac{2}{7}\ :3 = - \frac{2}{7} \cdot \frac{1}{3} = - \frac{2}{21}\]

\[- \frac{1}{11}\ :3 = - \frac{1}{11} \cdot \frac{1}{3} = - \frac{1}{33}\]

\[- \frac{5}{9}\ :( - 5) = \frac{5}{9} \cdot \frac{1}{5} = \frac{1}{9}\]

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

\[\textbf{б)}\ 0,77 \cdot 23 + 0,77 \cdot 77 =\]

\[= 0,77 \cdot (23 + 77) =\]

\[= 0,77 \cdot 100 = 77\]

\[\textbf{в)}\ \frac{16}{27} \cdot \left( - \frac{25}{72} \right) + \frac{16}{27} \cdot \left( - \frac{11}{72} \right) =\]

\[= - \frac{16}{27} \cdot \left( \frac{25}{72} + \frac{11}{72} \right) =\]

\[= - \frac{16}{27} \cdot \frac{36}{72} = - \frac{2 \cdot 4}{3 \cdot 9} = - \frac{8}{27}\]

\[\textbf{г)}\ \frac{19}{20} \cdot \left( \frac{2}{19} - \frac{3}{7} \right) + \frac{19}{20} \cdot \frac{3}{7} =\]

\[= \frac{19}{20} \cdot \left( \frac{2}{19} - \frac{3}{7} + \frac{3}{7} \right) = \frac{19}{20} \cdot \frac{2}{19} =\]

\[= \frac{1}{10} = 0,1\]

\[\textbf{д)}\ \frac{11}{13} \cdot \left( \frac{24}{37} - \frac{13}{11} \right) + \frac{24}{37} \cdot \left( - \frac{11}{13} + \frac{37}{24} \right) =\]

\[= \frac{11}{13} \cdot \frac{24}{37} - \frac{11}{13} \cdot \frac{13}{11} - \frac{24}{37} \cdot \frac{11}{13} + \frac{24}{37} \cdot \frac{37}{24} =\]

\[= - 1 + 1 = 0\]

\[\textbf{е)}\ \frac{3}{5} \cdot \left( \frac{6}{7} - \frac{5}{3} \right) + \frac{6}{5} \cdot \left( \frac{5}{6} - \frac{3}{7} \right) =\]

\[= \ \frac{3}{5} \cdot \frac{6}{7} - \ \frac{3}{5} \cdot \frac{5}{3} + \frac{6}{5} \cdot \frac{5}{6} - \frac{6}{5} \cdot \frac{3}{7} =\]

\[= - 1 + 1 = 0\]

\[\textbf{ж)}\ \frac{11}{13} \cdot \left( - \frac{3}{7} + \frac{13}{22} \right) + \frac{3}{13} \cdot \left( \frac{11}{7} - \frac{13}{3} \right) =\]

\[= - \frac{11}{13} \cdot \frac{3}{7} + \frac{11}{13} \cdot \frac{13}{22} + \frac{3}{13} \cdot \frac{11}{7} - \frac{3}{13} \cdot \frac{13}{3} =\]

\[= \frac{1}{2} - 1 = - \frac{1}{2}\]

\[\boxed{\mathbf{11.}}\]

\[\textbf{а)}\ \left( - \frac{1}{2} \right)^{2} = \frac{1}{4}\]

\[\left( - \frac{1}{3} \right)^{3} = - \frac{1}{27}\]

\[\textbf{б)}\ \left( - \frac{2}{5} \right)^{2} = \frac{4}{25}\]

\[\left( - \frac{3}{5} \right)^{3} = - \frac{27}{125}\]

\[\boxed{\mathbf{12.}}\]

\[\textbf{а)}\ x \cdot \frac{7}{11} = - \frac{3}{22}\]

\[x = - \frac{3}{22}\ :\frac{7}{11}\]

\[x = - \frac{3}{22} \cdot \frac{11}{7}\]

\[x = - \frac{3}{14}.\]

\[Ответ:\ - \frac{3}{14}.\]

\[\textbf{б)}\ \frac{3}{5}\ :x = - \frac{27}{50}\]

\[x = \frac{3}{5}\ :\left( - \frac{27}{50} \right)\]

\[x = - \frac{3}{5} \cdot \frac{50}{27}\]

\[x = - \frac{10}{9}\]

\[x = - 1\frac{1}{9}.\]

\[Ответ:\ - 1\frac{1}{9}.\]

\[\boxed{\mathbf{13.}}\]

\[8 \cdot 2\ :24 = 16\ :24 = \frac{16}{24} =\]

\[= \frac{2}{3}\ (часть) - полного\ \]

\[оборота\ сделала\ первая\]

\[шестерня.\]

\[Ответ:\ \ \frac{2}{3}\ часть.\]