Решебник по математике 6 класс Ткачева ФГОС рабочая тетрадь | Страница 75

\[Страница\ 75.\]

\[14.\ Применение\ \]

\[распределительного\ свойства\ \]

\[умножения\]

\[\boxed{\mathbf{1.}}\]

\[\textbf{а)}\ \left( 10 - \frac{1}{3} \right) \cdot 3 = 10 \cdot 3 - \frac{1}{3} \cdot 3 =\]

\[= 30 - 1 = 29\]

\[\textbf{б)}\ \left( \frac{1}{5} + \frac{1}{3} \right) \cdot 15 =\]

\[= \frac{1}{5} \cdot 15 + \frac{1}{3} \cdot 15 = 3 + 5 = 8\]

\[\textbf{в)}\ \left( \frac{7}{8} - \frac{1}{6} \right) \cdot 24 =\]

\[= \frac{7}{8} \cdot 24 - \frac{1}{6} \cdot 24 = 21 - 4 = 17\]

\[\textbf{г)}\ (3 + 9) \cdot \frac{1}{3} = 3 \cdot \frac{1}{3} + 9 \cdot \frac{1}{3} =\]

\[= 1 + 3 = 4\]

\[\textbf{д)}\ \left( 7 - \frac{3}{4} \right) \cdot \frac{1}{3} = 7 \cdot \frac{1}{3} - \frac{3}{4} \cdot \frac{1}{3} =\]

\[= \frac{7}{3} - \frac{1}{4} = \frac{25}{12} = 2\frac{1}{12}\]

\[\textbf{е)}\ \left( \frac{1}{7} + 2 \right) \cdot \frac{7}{9} = \frac{1}{7} \cdot \frac{7}{9} + 2 \cdot \frac{7}{9} =\]

\[= \frac{1}{9} + \frac{14}{9} = \frac{15}{9} = 1\frac{2}{3}\ \]

\[\boxed{\mathbf{2.}}\]

\[\textbf{а)}\ 7\frac{1}{4} \cdot 8 = \frac{29}{4} \cdot 8 = 58\]

\[5\frac{2}{3} \cdot 6 = \frac{17}{3} \cdot 6 = 34\]

\[4 \cdot 1\frac{1}{2} = 4 \cdot \frac{3}{2} = 6\]

\[70 \cdot 2\frac{1}{7} = 70 \cdot \frac{15}{7} = 150\]

\[\textbf{б)}\ 35\frac{2}{5} \cdot 5 = 177\]

\[9 \cdot 1\frac{1}{18} = 9\frac{1}{2}\]

\[2\frac{1}{3} \cdot 2 = 4\frac{2}{3}\]

\[18\frac{1}{4} \cdot \frac{1}{9} = 2\frac{1}{36}\]

\[\textbf{в)}\ 12\frac{1}{5} \cdot \frac{1}{12} = 1\frac{1}{60}\]

\[80\frac{1}{5} \cdot \frac{1}{20} = 4\frac{1}{100}\]

\[16\frac{1}{8} \cdot \frac{1}{4} = 4\frac{1}{32}\]

\[32\frac{1}{9} \cdot \frac{1}{8} = 4\frac{1}{72}\]