266 Вправа 266Алгебра 8 клас Бевз 2025 · § 6 · стор. 58

266. Виконай ділення.

а) ${\displaystyle \frac{1}{3a{x}^2}:\frac{1}{9a^{2}x}=}$${\displaystyle \frac{1}{3a{x}^2}\cdot 9a^{2}x=}$${\displaystyle \frac{9a^{2}x}{3a{x}^2}=}$${\displaystyle \frac{3\cdot \cancel{3}a\cancel{a}\cancel{x}}{\cancel{3}\cancel{a}x\cancel{x}}=}$${\displaystyle \frac{3a}{x}}$;

б) ${\displaystyle \frac{6x^2}{y}:\frac{1,5x^3}{y^2}=}$${\displaystyle \frac{6x^2}{y}\cdot \frac{y^2}{1,5x^3}=}$${\displaystyle \frac{6x^2\cdot y^2}{y\cdot 1,5x^3}}$=

=${\displaystyle \frac{4\cdot \cancel{1,5}\cancel{x^2}y\cancel{y}}{\cancel{y}\cdot \cancel{1,5}x\cancel{x^2}}=}$${\displaystyle \frac{4y}{x}}$;

в) ${\displaystyle \frac{14}{5x^3}:\frac{7x}{2y^2}=}$${\displaystyle \frac{14}{5x^3}\cdot \frac{2y^2}{7x}=}$${\displaystyle \frac{14\cdot 2y^2}{5x^3\cdot 7x}=}$${\displaystyle \frac{2\cdot \cancel{7}\cdot 2y^2}{5x^3\cdot \cancel{7}x}=}$${\displaystyle \frac{4y^2}{5x^4}}$;

г) ${\displaystyle \frac{2a}{3x}:\frac{4a^2}{9x}=}$${\displaystyle \frac{2a}{3x}\cdot \frac{9x}{4a^2}=}$${\displaystyle \frac{2a\cdot 9x}{3x\cdot 4a^2}=}$${\displaystyle \frac{\cancel{2}\cancel{a}\cdot 3\cdot \cancel{3}\cancel{x}}{\cancel{3}\cancel{x}\cdot 2\cdot \cancel{2}a\cancel{a}}=}$${\displaystyle \frac{3}{2a}}$;

ґ) ${\displaystyle \frac{18c^2}{5xy}:\frac{9c^3}{15x^2}=}$${\displaystyle \frac{18c^2}{5xy}\cdot \frac{15x^2}{9c^3}=}$${\displaystyle \frac{18c^2\cdot 15x^2}{5xy\cdot 9c^3}}$=

=${\displaystyle \frac{2\cdot \cancel{9}\cancel{c^2}\cdot 3\cdot \cancel{5}x\cancel{x}}{\cancel{5}\cancel{x}y\cdot \cancel{9}c\cancel{c^2}}=}$${\displaystyle \frac{6x}{cy}}$;

д) ${\displaystyle \frac{18z^3}{x{y}^2}:\frac{9z^3}{x^{2}y}=}$${\displaystyle \frac{18z^3}{x{y}^2}\cdot \frac{x^{2}y}{9z^3}=}$${\displaystyle \frac{18z^3\cdot x^{2}y}{x{y}^2\cdot 9z^3}}$=

=${\displaystyle \frac{2\cdot \cancel{9}\cancel{z^3}\cdot x\cancel{x}\cancel{y}}{\cancel{x}y\cancel{y}\cdot \cancel{9}\cancel{z^3}}=}$${\displaystyle \frac{2x}{y}}$.