№ 5.5 Алгебра = № 10.5 Математика
Виконайте дію:
1. $\frac{5a}{7}\cdot\frac{21}{20a^2};$
2. $\frac{3,5}{14a^2}\cdot\frac{4a^3}{5b};$
3. $\frac{c^2}{30}\cdot\frac{20}{cm};$
4. $-\frac{3m}{5a^2}\cdot\frac{a}{9m^2};$
5. $\frac{4x^2}{7p}\cdot\left(-\frac{21p}{8x^3}\right);$
6. $-\frac{5x^2}{7y^3}\cdot\left(-\frac{21y^2}{25x}\right).$
Розв'язок:
1. $\frac{5a}{7}\cdot\frac{21}{20a^2}=\frac{5a\cdot21}{7\cdot20a^2}=$
$= \frac{105a}{140a^2}=\frac{3}{4a};$
2. $\frac{3,5}{14a^2}\cdot\frac{4a^3}{5b}=\frac{3,5\cdot4a^3}{14a^2\cdot5b}=$
$= \frac{14a}{14\cdot5b}=\frac{a}{5b};$
3. $\frac{c^2}{30}\cdot\frac{20}{cm}=\frac{c^2\cdot20}{30cm}=\frac{2c}{3m};$
4. $-\frac{3m}{5a^2}\cdot\frac{a}{9m^2}=-\frac{3am}{5a^2\cdot9m^2}=$
$= -\frac{3a}{45a^2m}=-\frac{1}{15am};$
5. $\frac{4x^2}{7p}\cdot\left(-\frac{21p}{8x^3}\right)=-\frac{4x^2\cdot21p}{7p{\cdot8x}^3}=$
$= -\frac{84x^2p}{56px^3}=-\frac{3}{2x};$
6. $-\frac{5x^2}{7y^3}\cdot\left(-\frac{21y^2}{25x}\right)=\frac{5x^2\cdot21y^2}{7y^3\cdot25x}=$
$= \frac{105xy^2}{175y^3}=\frac{3x}{5y}.$