Решебник по математике 6 класс Ткачева ФГОС рабочая тетрадь | Страница 100

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\[\textbf{а)}\ \frac{8\frac{2}{3} + 5 \cdot 1\frac{1}{8} - 10\ :2\frac{2}{3}}{8\frac{1}{2} - 5\frac{3}{4}} =\]

\[= \frac{\frac{26}{3} + \frac{45}{8} - 10 \cdot \frac{3}{8}}{\frac{17}{2} - \frac{23}{4}} = \frac{\frac{208}{24} - \frac{15}{8}}{\frac{34}{4} - \frac{23}{4}} =\]

\[= \frac{\frac{208}{24} - \frac{45}{24}}{\frac{11}{4}} = \frac{\frac{163}{24}}{\frac{11}{4}} = \frac{163 \cdot 4}{24 \cdot 11} =\]

\[= \frac{163}{66} = 2\frac{31}{66}\]

\[Ответ:2\frac{31}{66}.\]

\[49\frac{1}{3}\ :16 - 14\ :8\frac{1}{6} =\]

\[= \frac{148}{3 \cdot 16} - \frac{14 \cdot 6}{49} = \frac{37}{12} - \frac{12}{7} =\]

\[= \frac{259}{84} - \frac{144}{84} = \frac{115}{84} = 1\frac{31}{84}\]

\[14 - 1\frac{31}{84} \cdot 7 = 14 - 9\frac{7}{12} = 4\frac{5}{12}\]

\[1\frac{59}{70} + \frac{37}{42} + 2\frac{19}{30} =\]

\[= \frac{129}{70} + \frac{37}{42} + \frac{79}{30} =\]

\[= \frac{387 + 185 + 553}{210} = \frac{1125}{210} =\]

\[= 5\frac{15}{42} = 5\frac{5}{14}\]

\[1\frac{17}{18} \cdot 5\frac{5}{14} - 10 = \frac{35}{18} \cdot \frac{75}{14} - 10 =\]

\[= \frac{125}{12} - 10 = 10\frac{5}{12} - 10 = \frac{5}{12}\]

\[\frac{115}{84} \cdot \frac{5}{12} = \frac{115 \cdot 12}{84 \cdot 5} = \frac{23}{7} = 3\frac{2}{7}\]

\[Ответ:3\frac{2}{7}.\]

\[\textbf{в)}\ \frac{12\frac{2}{3} - 63\frac{1}{3}\ :5\frac{2}{11}}{2\frac{2}{3}} =\]

\[= \frac{\frac{38}{3} - \frac{190}{3}\ :\frac{57}{11}}{\frac{8}{3}} =\]

\[= \frac{\frac{38}{3} \cdot \left( 1 - 5 \cdot \frac{11}{57} \right)}{\frac{8}{3}} =\]

\[= \frac{38}{3} \cdot \frac{3}{8} \cdot \left( 1 - \frac{55}{57} \right) = \frac{19}{2} \cdot \frac{2}{57} = \frac{1}{3}\]

\[Ответ:\frac{1}{3}.\]

\[\textbf{г)}\ \left( 7\frac{14}{45}\ :7 - \frac{39}{40} \right) \cdot 7,2 =\]

\[= \left( \frac{360}{360} + \frac{16}{360} - \frac{351}{360} \right) \cdot 7,2 =\]

\[= \frac{25}{360} \cdot 7,2 = \frac{180}{360} = \frac{1}{2}\ \]

\[Ответ:\frac{1}{2}.\]

\[\textbf{д)}\ \frac{0,8}{2\ :0,25 - 3,125 \cdot 2,4} =\]

\[= \frac{0,8}{8 - 7,5} = \frac{0,8}{0,5} = \frac{8}{5} = 1\frac{3}{5} = 1,6\]

\[Ответ:1,6.\]