Упражнение 149

\(1)\ \frac{8m}{n}:\frac{4m}{n}=\frac{8m}{n}\cdot\frac{n}{4m}=\frac{8m\cdot{n}}{n\cdot4m}=\frac{2\cdot1}{1\cdot1}=2;\)

\(2)\ \frac{3b}{8}:b=\frac{3b}{8}:\frac{b}{1}=\frac{3b}{8}\cdot\frac{1}{b}=\frac{3b}{8\cdot{b}}=\frac{3}{8\cdot1}=\frac{3}{8};\)

\(3)\ \frac{7c^2}{d}:\frac{c}{d^3}=\frac{7c^2}{d}\cdot\frac{d^3}{c}=\frac{7c^2\cdot{d}^3}{d\cdot{c}}=\frac{7c\cdot{d}^2}{1\cdot1}=7cd^2;\)

\(4)\ \frac{6a}{5b}:\frac{3a^2}{20b^2}=\frac{6a}{5b}\cdot\frac{20b^2}{3a^2}=\frac{6a\cdot20b^2}{5b\cdot3a^2}=\frac{2\cdot4b}{1\cdot{a}}=\frac{8b}{a};\)

\(5)\ {-}\frac{9a}{b^5}:\frac{18a^4}{b^3}={-}\frac{9a}{b^5}\cdot\frac{b^3}{18a^4}={-}\frac{9a\cdot{b}^3}{b^5\cdot18a^4}={-}\frac{1\cdot1}{b^2\cdot2a^3}={-}\frac{1}{2a^3b^2};\)

\(6)\ a^2:\frac{a}{b^2c}=\frac{a^2}{1}:\frac{a}{b^2c}=\frac{a^2}{1}\cdot\frac{b^2c}{a}=\frac{a^2\cdot{b}^2c}{a}=\frac{a\cdot{b}^2c}{1}=ab^2c;\)

\(7)\ 24a^3:\frac{12a^2}{b}=\frac{24a^3}{1}:\frac{12a^2}{b}=\frac{24a^3}{1}\cdot\frac{b}{12a^2}=\frac{24a^3\cdot{b}}{12a^2}=\frac{2a\cdot{b}}{1}=2ab;\)

\(8)\ \frac{36a}{c^3}:(4a^2c)=\frac{36a}{c^3}:\frac{4a^2c}{1}=\frac{36a}{c^3}\cdot\frac{1}{4a^2c}=\frac{36a}{c^3\cdot4a^2c}=\frac{9}{c^3\cdot{ac}}=\frac{9}{ac^4}.\)