Решебник по математике 6 класс Ерина Никольский рабочая тетрадь Часть 1, 2 Часть 1 | Страница 94

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\[\boxed{\mathbf{5.}}\]

\[\textbf{а)} - \frac{1}{6} + \frac{13}{18} - \frac{7}{18} = - \frac{1}{6} + \frac{6}{18} =\]

\[= - \frac{1}{6} + \frac{2}{6} = \frac{1}{6}\]

\[- \frac{4}{49} - \frac{2}{7} - \frac{3}{47} = - \frac{7}{49} - \frac{2}{7} =\]

\[= - \frac{1}{7} - \frac{2}{7} = - \frac{3}{7}\]

\[- \frac{1}{8} + \frac{5}{24} - \frac{3}{8} = - \frac{4}{8} + \frac{5}{24} =\]

\[= - \frac{12}{24} + \frac{5}{24} = - \frac{7}{24}\]

\[\frac{5}{12} - \frac{7}{8} - \frac{7}{24} = \frac{10}{24} - \frac{21}{24} - \frac{7}{24} =\]

\[= - \frac{18}{24} = - \frac{3}{4}\]

\[\textbf{б)} - \frac{2}{7} + \frac{1}{21} - \frac{2}{21} = - \frac{6}{21} - \frac{1}{21} =\]

\[= - \frac{7}{21} = - \frac{1}{3}\]

\[\frac{25}{48} - \frac{5}{6} - \frac{3}{8} = \frac{25}{48} - \frac{40}{48} - \frac{18}{48} =\]

\[= - \frac{33}{48} = - \frac{11}{16}\]

\[- \frac{5}{169} - \frac{1}{13} - \frac{151}{169} =\]

\[= - \frac{13}{169} - \frac{156}{169} = - \frac{169}{169} = - 1\]

\[\frac{3}{14} - \frac{6}{7} - \frac{1}{42} = \frac{9}{42} - \frac{36}{42} - \frac{1}{42} =\]

\[= - \frac{28}{42} = - \frac{2}{3}\]

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

\[\textbf{а)}\ \frac{1}{2} + \left( \frac{7}{12} - \frac{5}{6} \right) =\]

\[= \frac{6}{12} + \frac{7}{12} - \frac{10}{12} = \frac{3}{12} = \frac{1}{4}\]

\[- \frac{1}{12} + \left( \frac{11}{18} - \frac{4}{9} \right) =\]

\[= - \frac{1}{12} + \frac{11}{18} - \frac{8}{18} =\]

\[= - \frac{1}{12} + \frac{3}{18} = - \frac{1}{12} + \frac{1}{6} =\]

\[= - \frac{1}{12} + \frac{2}{12} = \frac{1}{12}\]

\[\frac{7}{18} + \left( \frac{11}{18} - \frac{1}{6} \right) = \frac{7}{18} + \frac{11}{18} - \frac{1}{6} =\]

\[= \frac{18}{18} - \frac{1}{6} = 1 - \frac{1}{6} = \frac{5}{6}\]

\[\frac{3}{44} + \left( - \frac{11}{44} + \frac{5}{22} \right) =\]

\[= \frac{3}{44} - \frac{11}{44} + \frac{5}{22} =\]

\[= - \frac{8}{44} + \frac{5}{22} = - \frac{4}{22} + \frac{5}{22} = \frac{1}{22}\]

\[- \frac{3}{16} - \left( \frac{5}{16} - \frac{3}{8} \right) =\]

\[= - \frac{3}{16} - \frac{5}{16} + \frac{3}{8} =\]

\[= - \frac{8}{16} + \frac{3}{8} = - \frac{4}{8} + \frac{3}{8} = - \frac{1}{8}\]

\[\textbf{б)} - \frac{1}{48} + \left( \frac{7}{12} - \frac{3}{4} \right) =\]

\[= - \frac{1}{48} + \frac{28}{48} - \frac{36}{48} = - \frac{9}{48}\]

\[\left( - \frac{1}{14} - \frac{3}{7} \right) + \frac{1}{4} =\]

\[= \left( - \frac{1}{14} - \frac{6}{14} \right) + \frac{1}{4} =\]

\[= - \frac{7}{14} + \frac{1}{4} = - \frac{1}{2} + \frac{1}{4} =\]

\[= - \frac{2}{4} + \frac{1}{4} = - \frac{1}{4}\]

\[\left( - \frac{3}{16} + \frac{1}{2} \right) - \frac{3}{8} =\]

\[= - \frac{3}{16} + \frac{8}{16} - \frac{6}{16} = - \frac{1}{16}\]

\[- \left( \frac{3}{8} - \frac{11}{12} \right) + \frac{1}{24} =\]

\[= - \frac{9}{24} + \frac{22}{24} + \frac{1}{24} =\]

\[= - \frac{14}{24} = - \frac{7}{12}\]

\[- \left( \frac{2}{15} + \frac{4}{5} \right) + \frac{3}{10} =\]

\[= - \frac{4}{30} - \frac{24}{30} + \frac{9}{30} = - \frac{19}{30}\]

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

\[\textbf{а)}\ 3 \cdot \left( \frac{1}{9} - \frac{1}{3} \right) = 3 \cdot \left( \frac{1}{9} - \frac{3}{9} \right) =\]

\[= 3 \cdot \left( - \frac{2}{9} \right) = - \frac{2}{3}\]

\[\left( \frac{1}{14} - \frac{1}{7} \right) \cdot ( - 7) =\]

\[= \left( \frac{1}{14} - \frac{2}{14} \right) \cdot ( - 7) =\]

\[= - \frac{1}{14} \cdot ( - 7) = \frac{1}{2}\]

\[\frac{1}{5} \cdot \left( \frac{5}{7} - \frac{5}{8} \right) = \frac{1}{5} \cdot \frac{5}{7} - \frac{1}{5} \cdot \frac{5}{8} =\]

\[= \frac{1}{7} - \frac{1}{8} = \frac{8}{56} - \frac{7}{56} = \frac{1}{56}\]

\[- \frac{1}{4} \cdot \left( \frac{4}{11} - \frac{4}{13} \right) =\]

\[= - \frac{1}{4} \cdot \frac{4}{11} + \frac{1}{4} \cdot \frac{4}{13} =\]

\[= - \frac{1}{11} + \frac{1}{13} = - \frac{13}{143} + \frac{11}{143} =\]

\[= - \frac{2}{143}\]

\[\textbf{б)}\ 5 \cdot \left( \frac{1}{10} - \frac{1}{5} \right) = 5 \cdot \left( \frac{1}{10} - \frac{2}{10} \right) =\]

\[= 5 \cdot \left( - \frac{1}{10} \right) = - \frac{1}{2}\]

\[\left( \frac{1}{18} - \frac{1}{6} \right) \cdot ( - 6) =\]

\[= \left( \frac{1}{18} - \frac{3}{18} \right) \cdot ( - 6) =\]

\[= - \frac{2}{18} \cdot ( - 6) = \frac{2}{3}\]

\[\frac{1}{8} \cdot \left( \frac{8}{13} - \frac{8}{15} \right) = \frac{1}{8} \cdot \frac{8}{13} - \frac{1}{8} \cdot \frac{8}{15} =\]

\[= \frac{1}{13} - \frac{1}{15} = \frac{15}{195} - \frac{13}{195} = \frac{2}{195}\]

\[- \frac{1}{6} \cdot \left( \frac{6}{7} - \frac{6}{11} \right) =\]

\[= - \frac{1}{6} \cdot \frac{6}{7} + \frac{1}{6} \cdot \frac{6}{11} =\]

\[= - \frac{1}{7} + \frac{1}{11} = - \frac{11}{77} + \frac{7}{77} = - \frac{4}{77}\]

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

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