213° Вправа 213Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 64

213. 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^{2}b}:\frac{1}{a{b}^2}=}$${\displaystyle \frac{1}{a^{2}b}\cdot \frac{a{b}^2}{1}=}$${\displaystyle \frac{\cancel{ab}\cdot b}{\cancel{ab}\cdot a}=}$${\displaystyle \frac{b}{a}}$;

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

3) ${\displaystyle \frac{4x^3}{5}:\frac{8x^4}{3}=}$${\displaystyle \frac{4x^3}{5}\cdot \frac{3}{8x^4}=}$${\displaystyle \frac{\cancel{4x^3}\cdot 3}{5\cdot \cancel{4x^3}\cdot 2x}=}$${\displaystyle \frac{3}{10x}}$;

4) ${\displaystyle \frac{3}{2a^{3}b}:\frac{9}{4a^2{b}^2}=}$${\displaystyle \frac{3}{2a^{3}b}\cdot \frac{4a^2{b}^2}{9}=}$${\displaystyle \frac{\stackrel{1}{\cancel{3}}\cdot \cancel{2a^{2}b}\cdot 2b}{\cancel{2a^{2}b}\cdot a\cdot \underset{3}{\cancel{9}}}=}$${\displaystyle \frac{2b}{3a}}$;

5) ${\displaystyle \frac{5x^{3}y}{2}:\frac{15x^2{y}^2}{8}=}$${\displaystyle \frac{5x^{3}y}{2}\cdot \frac{8}{15x^2{y}^2}=}$${\displaystyle \frac{\cancel{5x^{2}y}\cdot x\cdot \stackrel{4}{\cancel{8}}}{\underset{1}{\cancel{2}}\cdot \cancel{5x^{2}y}\cdot 3y}=}$${\displaystyle \frac{4x}{3y}}$;

6) ${\displaystyle \frac{4x^4}{9y}:\frac{16x^2}{3y^2}=}$${\displaystyle \frac{4x^4}{9y}\cdot \frac{3y^2}{16x^2}=}$${\displaystyle \frac{\cancel{4x^2}{x}^2\cdot \cancel{3y}y}{\cancel{3y}\cdot 3\cdot \cancel{4x^2}\cdot 4}=}$${\displaystyle \frac{x^{2}y}{12}}$.