Решебник по математике 6 класс Ткачева ФГОС рабочая тетрадь | Страница 99

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\[\boxed{\mathbf{3.}}\]

\[\textbf{а)}\ \frac{2\frac{1}{4} \cdot 2\frac{2}{3}}{9 \cdot 8} = \frac{\frac{9}{4} \cdot \frac{8}{3}}{72} = \frac{6}{72} = \frac{1}{12}\]

\[\textbf{б)}\ \frac{6\frac{1}{3} \cdot 7\frac{1}{5}}{19 \cdot 36} = \frac{\frac{19}{3} \cdot \frac{36}{5}}{19 \cdot 36} =\]

\[= \frac{19 \cdot 36}{15 \cdot 19 \cdot 36} = \frac{1}{15}\]

\[\textbf{в)}\ \frac{5\frac{3}{8} \cdot 9\frac{1}{3}}{4\frac{2}{3}} = \frac{\frac{43}{8} \cdot \frac{28}{3}}{\frac{14}{3}} =\]

\[= \frac{43 \cdot 28 \cdot 3}{24 \cdot 14} = \frac{86}{8} = 10\frac{3}{4}\]

\[\textbf{г)}\ \frac{6\frac{1}{2} \cdot 3\frac{1}{5}}{1\frac{3}{5}} = \frac{\frac{13}{2} \cdot \frac{16}{5}}{\frac{8}{5}} =\]

\[= \frac{13 \cdot 16 \cdot 5}{10 \cdot 8} = 13\]

\[\textbf{д)}\ \frac{12\frac{1}{2} \cdot 5\frac{1}{3}}{6\frac{1}{4}} = \frac{\frac{25}{2} \cdot \frac{16}{3}}{\frac{25}{4}} =\]

\[= \frac{25 \cdot 16 \cdot 4}{6 \cdot 25} = \frac{32}{3} = 10\frac{2}{3}\]

\[\textbf{е)}\frac{5^{3}}{5^{2}} = 5\ \]

\[\textbf{ж)}\ \frac{6 \cdot 8 \cdot 12}{10 \cdot 8 \cdot 40} = \frac{36}{200} = \frac{9}{50}\]

\[\textbf{з)}\ \frac{2 + \frac{1}{3} + \frac{1}{2}}{2 - \frac{1}{3} - \frac{1}{2}} = \frac{2\frac{5}{6}}{1\frac{1}{6}} = \frac{17 \cdot 6}{6 \cdot 7} =\]

\[= \frac{17}{7} = 2\frac{3}{7}\]

\[\textbf{и)}\ \frac{7}{5 - 0,1}\ :\frac{5 - 0,1}{7} = \frac{7}{4,9} \cdot \frac{7}{4,9} =\]

\[= \frac{10}{7} \cdot \frac{10}{7} = \frac{100}{49} = 2\frac{2}{49}\]

\[к)\frac{3}{5} \cdot \frac{5^{3}}{18} \cdot \frac{3}{5} = \frac{9 \cdot 5³}{5² \cdot 18} = \frac{5}{2} = 2,5\]