212° Вправа 212Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 64

212. Виконайте ділення.

${\displaystyle \frac{A}{B}:\frac{C}{D}=}$${\displaystyle \frac{A}{B}\cdot \frac{D}{C}}$ — ділене множимо на дріб, обернений до дільника.

1) ${\displaystyle \frac{1}{a}:\frac{1}{b}=}$${\displaystyle \frac{1}{a}\cdot \frac{b}{1}=}$${\displaystyle \frac{b}{a}}$;

2) ${\displaystyle \frac{2}{x}:\frac{2}{y}=}$${\displaystyle \frac{2}{x}\cdot \frac{y}{2}=}$${\displaystyle \frac{\stackrel{1}{\cancel{2}}y}{x\cdot \underset{1}{\cancel{2}}}=}$${\displaystyle \frac{y}{x}}$;

3) ${\displaystyle \frac{1}{2x}:\frac{1}{2y}=}$${\displaystyle \frac{1}{2x}\cdot \frac{2y}{1}=}$${\displaystyle \frac{\stackrel{1}{\cancel{2}}y}{\underset{1}{\cancel{2}}x}=}$${\displaystyle \frac{y}{x}}$;

4) ${\displaystyle \frac{1}{2x}:\frac{2}{y}=}$${\displaystyle \frac{1}{2x}\cdot \frac{y}{2}=}$${\displaystyle \frac{y}{4x}}$;

5) ${\displaystyle \frac{2x}{3}:\frac{2y}{5}=}$${\displaystyle \frac{2x}{3}\cdot \frac{5}{2y}=}$${\displaystyle \frac{\stackrel{1}{\cancel{2}}x\cdot 5}{3\cdot \underset{1}{\cancel{2}}y}=}$${\displaystyle \frac{5x}{3y}}$;

6) ${\displaystyle \frac{1}{3xy}:\frac{5}{9x}=}$${\displaystyle \frac{1}{3xy}\cdot \frac{9x}{5}=}$${\displaystyle \frac{\stackrel{3}{\cancel{9}}\cancel{x}}{\underset{1}{\cancel{3}}\cancel{x}y\cdot 5}=}$${\displaystyle \frac{3}{5y}}$;

7) ${\displaystyle \frac{1}{5x}:\frac{2}{15xy}=}$${\displaystyle \frac{1}{5x}\cdot \frac{15xy}{2}=}$${\displaystyle \frac{\cancel{5x}\cdot 3y}{\cancel{5x}\cdot 2}=}$${\displaystyle \frac{3y}{2}}$;

8) ${\displaystyle \frac{7}{2ab}:\frac{14}{4a}=}$${\displaystyle \frac{7}{2ab}\cdot \frac{4a}{14}=}$${\displaystyle \frac{\stackrel{1}{\cancel{7}}\cdot \stackrel{1}{\cancel{4}}\cancel{a}}{\underset{1}{\cancel{4}}\cancel{a}b\cdot \underset{1}{\cancel{7}}}=}$${\displaystyle \frac{1}{b}}$;

9) ${\displaystyle \frac{6x}{5}:\frac{12y}{25}=}$${\displaystyle \frac{6x}{5}\cdot \frac{25}{12y}=}$${\displaystyle \frac{\stackrel{1}{\cancel{6}}x\cdot \stackrel{5}{\cancel{25}}}{\underset{1}{\cancel{5}}\cdot \underset{2}{\cancel{12}}y}=}$${\displaystyle \frac{5x}{2y}}$;

10) ${\displaystyle \frac{7}{3a}:\frac{28}{9b}=}$${\displaystyle \frac{7}{3a}\cdot \frac{9b}{28}=}$${\displaystyle \frac{\stackrel{1}{\cancel{7}}\cdot \stackrel{3}{\cancel{9}}b}{\underset{1}{\cancel{3}}a\cdot \underset{4}{\cancel{28}}}=}$${\displaystyle \frac{3b}{4a}}$;

11) ${\displaystyle \frac{3x}{8y}:\frac{21}{40xy}=}$${\displaystyle \frac{3x}{8y}\cdot \frac{40xy}{21}=}$${\displaystyle \frac{\stackrel{1}{\cancel{3}}x\cdot \stackrel{5}{\cancel{40}}x\cancel{y}}{\underset{1}{\cancel{8}}\cancel{y}\cdot \underset{7}{\cancel{21}}}=}$${\displaystyle \frac{5x^2}{7}}$;

12) ${\displaystyle \frac{9}{2ab}:\frac{63}{16b}=}$${\displaystyle \frac{9}{2ab}\cdot \frac{16b}{63}=}$${\displaystyle \frac{\stackrel{1}{\cancel{9}}\cdot \stackrel{8}{\cancel{16}}\cancel{b}}{\underset{1}{\cancel{2}}a\cancel{b}\cdot \underset{7}{\cancel{63}}}=}$${\displaystyle \frac{8}{7a}}$.