183° Вправа 183Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 56

183. Виконайте множення.

Перемножуємо чисельники і знаменники: ${\displaystyle \frac{A}{B}\cdot \frac{C}{D}=}$${\displaystyle \frac{A\cdot C}{B\cdot D}}$, потім скорочуємо.

1) ${\displaystyle \frac{x}{8}\cdot \frac{a}{5}=}$${\displaystyle \frac{x\cdot a}{8\cdot 5}=}$${\displaystyle \frac{ax}{40}}$;

2) ${\displaystyle \frac{3}{y}\cdot \frac{4}{c}=}$${\displaystyle \frac{3\cdot 4}{y\cdot c}=}$${\displaystyle \frac{12}{cy}}$;

3) ${\displaystyle \frac{x}{2y}\cdot \frac{a}{2c}=}$${\displaystyle \frac{x\cdot a}{2y\cdot 2c}=}$${\displaystyle \frac{ax}{4cy}}$;

4) ${\displaystyle \frac{5a}{b}\cdot \frac{3x}{y}=}$${\displaystyle \frac{5a\cdot 3x}{b\cdot y}=}$${\displaystyle \frac{15ax}{by}}$;

5) ${\displaystyle \frac{3x}{7y}\cdot \frac{2a}{5b}=}$${\displaystyle \frac{3x\cdot 2a}{7y\cdot 5b}=}$${\displaystyle \frac{6ax}{35by}}$;

6) ${\displaystyle \frac{3x}{4y}\cdot \frac{b}{4c}=}$${\displaystyle \frac{3x\cdot b}{4y\cdot 4c}=}$${\displaystyle \frac{3bx}{16cy}}$;

7) ${\displaystyle \frac{3x}{5y}\cdot \frac{2a}{6c}=}$${\displaystyle \frac{\stackrel{1}{\cancel{3}}x\cdot \stackrel{1}{\cancel{2}}a}{5y\cdot \underset{1}{\cancel{3}}\cdot \underset{1}{\cancel{2}}c}=}$${\displaystyle \frac{ax}{5cy}}$;

8) ${\displaystyle \frac{15a}{16b}\cdot \frac{4x}{5y}=}$${\displaystyle \frac{\stackrel{3}{\cancel{15}}a\cdot \stackrel{1}{\cancel{4}}x}{\underset{4}{\cancel{16}}b\cdot \underset{1}{\cancel{5}}y}=}$${\displaystyle \frac{3ax}{4by}}$;

9) ${\displaystyle \frac{2x}{3y}\cdot \frac{4y^2}{5b}=}$${\displaystyle \frac{2x\cdot 4\cancel{y}y}{3\cancel{y}\cdot 5b}=}$${\displaystyle \frac{8xy}{15b}}$;

10) ${\displaystyle \frac{3x}{7y}\cdot \frac{14a}{5x}=}$${\displaystyle \frac{3\cancel{x}\cdot \stackrel{2}{\cancel{14}}a}{\underset{1}{\cancel{7}}y\cdot 5\cancel{x}}=}$${\displaystyle \frac{6a}{5y}}$;

11) ${\displaystyle \frac{3b}{5y}\cdot \frac{10a}{9b}=}$${\displaystyle \frac{\stackrel{1}{\cancel{3}}\cancel{b}\cdot \stackrel{2}{\cancel{10}}a}{\underset{1}{\cancel{5}}y\cdot \underset{3}{\cancel{9}}\cancel{b}}=}$${\displaystyle \frac{2a}{3y}}$;

12) ${\displaystyle \frac{3x}{5a}\cdot \frac{2a^2}{3b}=}$${\displaystyle \frac{\stackrel{1}{\cancel{3}}x\cdot 2\cancel{a}a}{5\cancel{a}\cdot \underset{1}{\cancel{3}}b}=}$${\displaystyle \frac{2ax}{5b}}$.