Решебник по математике 5 класс Ткачева рабочая тетрадь | Страница 69

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

\[1)\ \frac{14}{21} = \frac{6}{9}\]

\[14 \cdot 9 = 21 \cdot 6\]

\[2)\ \frac{a}{13} = \frac{5}{6}\]

\[a \cdot 6 = 13 \cdot 5\]

\[3)\ 17\ :b = 20\ :19\]

\[17 \cdot 19 = b \cdot 20\]

\[4)\ 5\ :8 = x\ :23\]

\[5 \cdot 23 = 8 \cdot x\]

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

\[1)\ \frac{25}{x} = \frac{35}{8}\]

\[x = (25 \cdot 8)\ :35 = \frac{25 \cdot 8}{35} =\]

\[= \frac{5 \cdot 8}{7} = \frac{40}{7} = 5\frac{5}{7}.\]

\[2)\ \frac{10}{27} = \frac{15}{x}\]

\[x = (27 \cdot 15)\ :10 = \frac{27 \cdot 15}{10} =\]

\[= \frac{27 \cdot 3}{5} = \frac{81}{5} = 16\frac{1}{5}.\]

\[3)\ \frac{9}{14}\ :1\frac{2}{7} = x\ :\frac{2}{5}\]

\[x = \left( \frac{9}{14} \cdot \frac{2}{5} \right)\ :\frac{9}{7} = \frac{9 \cdot 2 \cdot 7}{14 \cdot 5 \cdot 9} =\]

\[= \frac{2}{2 \cdot 5} = \frac{2}{10}.\]

\[4)\ \ x\ :2\frac{1}{4} = \frac{4}{11}\ :\frac{3}{8}\]

\[x = \left( \frac{9}{4} \cdot \frac{4}{11} \right)\ :\frac{3}{8} = \frac{9 \cdot 4 \cdot 8}{4 \cdot 11 \cdot 3} =\]

\[= \frac{3 \cdot 8}{11} = \frac{24}{11} = 2\frac{2}{11}.\]

\[\mathbf{41.\ 2.\ Пропорциональные\ величины}\]

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

\[1)\ 2\ :4 = 5\ :x\]

\[x = (4 \cdot 5)\ :2 = 20\ :2 = 10.\]

\[2)\ 2\ :10 = 5\ :x\]

\[x = (10 \cdot 5)\ :2 = 50\ :2 = 25.\]

\[3)\ \ 2\ :x = 5\ :15\]

\[x = (2 \cdot 15)\ :5 = 30\ :5 = 6.\]

\[4)\ 2\ :x = 5\ :23\]

\[x = (2 \cdot 23)\ :5 = 46\ :5 =\]

\[= \frac{46}{5} = 9\frac{1}{5}.\]