265 Вправа 265Алгебра 8 клас Бевз 2025 · § 6 · стор. 57

265. Виконай ділення.

а) ${\displaystyle \frac{4}{7}:\frac{2}{21}=}$${\displaystyle \frac{4}{7}\cdot \frac{21}{2}=}$${\displaystyle \frac{4\cdot 21}{7\cdot 2}=}$${\displaystyle \frac{2\cdot \cancel{2}\cdot 3\cdot \cancel{7}}{\cancel{7}\cdot \cancel{2}}=}$${\displaystyle 6}$;

б) ${\displaystyle -15:\frac{5}{7}=}$${\displaystyle -15\cdot \frac{7}{5}=}$${\displaystyle \frac{-15\cdot 7}{5}}$=

=${\displaystyle -\frac{3\cdot \cancel{5}\cdot 7}{\cancel{5}}=}$${\displaystyle -21}$;

в) ${\displaystyle \frac{35}{4}:\frac{-7}{16}=}$${\displaystyle \frac{35}{4}\cdot \frac{16}{-7}=}$${\displaystyle \frac{35\cdot 16}{4\cdot (-7)}}$=

=${\displaystyle -\frac{5\cdot \cancel{7}\cdot 4\cdot \cancel{4}}{\cancel{4}\cdot \cancel{7}}=}$${\displaystyle -20}$;

г) ${\displaystyle \frac{5x}{3y}:\frac{10x}{6y}=}$${\displaystyle \frac{5x}{3y}\cdot \frac{6y}{10x}=}$${\displaystyle \frac{5x\cdot 6y}{3y\cdot 10x}=}$${\displaystyle \frac{\cancel{5}\cancel{x}\cdot \cancel{3}\cdot \cancel{2}\cancel{y}}{\cancel{3}\cancel{y}\cdot \cancel{5}\cdot \cancel{2}\cancel{x}}=}$${\displaystyle 1}$;

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

д) ${\displaystyle \frac{4m^2}{n^3}:\frac{12m^3}{n^4}=}$${\displaystyle \frac{4m^2}{n^3}\cdot \frac{n^4}{12m^3}=}$${\displaystyle \frac{4m^2\cdot n^4}{n^3\cdot 12m^3}}$=

=${\displaystyle \frac{\cancel{4}\cancel{m^2}\cdot n\cancel{n^3}}{\cancel{n^3}\cdot 3\cdot \cancel{4}m\cancel{m^2}}=}$${\displaystyle \frac{n}{3m}}$.