267 Вправа 267Алгебра 8 клас Бевз 2025 · § 6 · стор. 58

267. Виконай ділення.

а) ${\displaystyle \frac{34a{b}^2}{a^2}:\frac{17b^2}{a{c}^2}=}$${\displaystyle \frac{34a{b}^2}{a^2}\cdot \frac{a{c}^2}{17b^2}=}$${\displaystyle \frac{34a{b}^2\cdot a{c}^2}{a^2\cdot 17b^2}}$=

=${\displaystyle \frac{2\cdot \cancel{17}\cancel{a}\cancel{b^2}\cdot \cancel{a}{c}^2}{\cancel{a^2}\cdot \cancel{17}\cancel{b^2}}=}$${\displaystyle 2c^2}$;

б) ${\displaystyle \frac{3m^2{n}^3}{4ap}:9m{n}^4=}$${\displaystyle \frac{3m^2{n}^3}{4ap}\cdot \frac{1}{9m{n}^4}=}$${\displaystyle \frac{3m^2{n}^3}{4ap\cdot 9m{n}^4}}$=

=${\displaystyle \frac{\cancel{3}m\cancel{m}\cancel{n^3}}{4ap\cdot 3\cdot \cancel{3}\cancel{m}n\cancel{n^3}}=}$${\displaystyle \frac{m}{12nap}}$;

в) ${\displaystyle 3x^2:\frac{1}{9x^3}=}$${\displaystyle 3x^2\cdot 9x^3=}$${\displaystyle 27x^5}$;

г) ${\displaystyle -\frac{2ab}{3xy}:\frac{8a^2{b}^2}{9x^2{y}^2}=}$${\displaystyle \frac{-2ab}{3xy}\cdot \frac{9x^2{y}^2}{8a^2{b}^2}=}$${\displaystyle \frac{-2ab\cdot 9x^2{y}^2}{3xy\cdot 8a^2{b}^2}}$=

=${\displaystyle -\frac{\cancel{2}\cancel{a}\cancel{b}\cdot 3\cdot \cancel{3}x\cancel{x}y\cancel{y}}{\cancel{3}\cancel{x}\cancel{y}\cdot 4\cdot \cancel{2}a\cancel{a}b\cancel{b}}=}$${\displaystyle -\frac{3xy}{4ab}}$;

ґ) ${\displaystyle \frac{x}{5cz}:(-\frac{1}{15z^3})=}$${\displaystyle \frac{x}{5cz}\cdot \frac{15z^3}{-1}=}$${\displaystyle \frac{x\cdot 15z^3}{5cz\cdot (-1)}}$=

=${\displaystyle -\frac{x\cdot 3\cdot \cancel{5}{z}^2\cancel{z}}{\cancel{5}c\cancel{z}}=}$${\displaystyle -\frac{3x{z}^2}{c}}$;

д) ${\displaystyle 1:\frac{2xy}{z^2}=}$${\displaystyle 1\cdot \frac{z^2}{2xy}=}$${\displaystyle \frac{z^2}{2xy}}$.