214° Вправа 214Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 64

214. 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{6x}{5}:\frac{3y}{2}=}$${\displaystyle \frac{6x}{5}\cdot \frac{2}{3y}=}$${\displaystyle \frac{\stackrel{2}{\cancel{6}}x\cdot 2}{5\cdot \underset{1}{\cancel{3}}y}=}$${\displaystyle \frac{4x}{5y}}$;

2) ${\displaystyle \frac{1}{3x}:\frac{5}{12x}=}$${\displaystyle \frac{1}{3x}\cdot \frac{12x}{5}=}$${\displaystyle \frac{\cancel{3x}\cdot 4}{\cancel{3x}\cdot 5}=}$${\displaystyle \frac{4}{5}}$;

3) ${\displaystyle \frac{1}{5a}:\frac{3}{35ab}=}$${\displaystyle \frac{1}{5a}\cdot \frac{35ab}{3}=}$${\displaystyle \frac{\cancel{5a}\cdot 7b}{\cancel{5a}\cdot 3}=}$${\displaystyle \frac{7b}{3}}$;

4) ${\displaystyle \frac{7a}{2b}:\frac{14a}{5}=}$${\displaystyle \frac{7a}{2b}\cdot \frac{5}{14a}=}$${\displaystyle \frac{\cancel{7a}\cdot 5}{2b\cdot \cancel{7a}\cdot 2}=}$${\displaystyle \frac{5}{4b}}$;

5) ${\displaystyle \frac{1}{a^3{b}^3}:\frac{1}{a^2{b}^2}=}$${\displaystyle \frac{1}{a^3{b}^3}\cdot \frac{a^2{b}^2}{1}=}$${\displaystyle \frac{\cancel{a^2{b}^2}}{\cancel{a^2{b}^2}\cdot ab}=}$${\displaystyle \frac{1}{ab}}$;

6) ${\displaystyle \frac{6x^2{y}^4}{7}:\frac{18x{y}^5}{35}=}$${\displaystyle \frac{6x^2{y}^4}{7}\cdot \frac{35}{18x{y}^5}=}$${\displaystyle \frac{\cancel{6x{y}^4}\cdot x\cdot \stackrel{5}{\cancel{35}}}{\underset{1}{\cancel{7}}\cdot \cancel{6x{y}^4}\cdot 3y}=}$${\displaystyle \frac{5x}{3y}}$.