217° Вправа 217Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 65

217. Виконайте ділення.

Цілий вираз — це дріб зі знаменником 1, обернений до нього: ${\displaystyle a=}$${\displaystyle \frac{a}{1}}$ → ${\displaystyle \frac{1}{a}}$.

1) ${\displaystyle \frac{x}{5}:x=}$${\displaystyle \frac{x}{5}\cdot \frac{1}{x}=}$${\displaystyle \frac{1}{5}=}$${\displaystyle 0,2}$;

2) ${\displaystyle \frac{12}{y}:6=}$${\displaystyle \frac{12}{y}\cdot \frac{1}{6}=}$${\displaystyle \frac{2}{y}}$;

3) ${\displaystyle \frac{3x^2}{4y^3}:x^2=}$${\displaystyle \frac{3x^2}{4y^3}\cdot \frac{1}{x^2}=}$${\displaystyle \frac{3}{4y^3}}$;

4) ${\displaystyle \frac{6a^3}{b^2}:3a^2=}$${\displaystyle \frac{6a^3}{b^2}\cdot \frac{1}{3a^2}=}$${\displaystyle \frac{2a}{b^2}}$;

5) ${\displaystyle x:\frac{5}{x}=}$${\displaystyle x\cdot \frac{x}{5}=}$${\displaystyle \frac{x^2}{5}}$;

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

7) ${\displaystyle \frac{5}{2x^2}:x^2=}$${\displaystyle \frac{5}{2x^2}\cdot \frac{1}{x^2}=}$${\displaystyle \frac{5}{2x^4}}$;

8) ${\displaystyle \frac{6}{b^2}:3b^2=}$${\displaystyle \frac{6}{b^2}\cdot \frac{1}{3b^2}=}$${\displaystyle \frac{2}{b^4}}$;

9) ${\displaystyle \frac{3y}{7}:(-y)=}$${\displaystyle \frac{3y}{7}\cdot \left(-\frac{1}{y}\right)=}$${\displaystyle -\frac{3}{7}}$;

10) ${\displaystyle \frac{24x^3}{25}:(-4x)=}$${\displaystyle \frac{24x^3}{25}\cdot \left(-\frac{1}{4x}\right)=}$${\displaystyle -\frac{6x^2}{25}}$;

11) ${\displaystyle -\frac{6}{7x}:(-12x)=}$${\displaystyle \frac{6}{7x}\cdot \frac{1}{12x}=}$${\displaystyle \frac{1}{14x^2}}$;

12) ${\displaystyle -4y^3:\frac{5y^2}{16}=}$${\displaystyle -4y^3\cdot \frac{16}{5y^2}=}$${\displaystyle -\frac{64y}{5}}$.