№ 5.31 Алгебра = № 10.31 Математика
Обчисліть:
1. $\frac{26}{45}:\frac{91}{135};$
2. $2\frac{1}{2}:\frac{15}{16};$
3. $-3\frac{1}{7}:2\frac{5}{14};$
4. $-5\frac{13}{15}:\left(-1\frac{8}{25}\right).$
Розв'язок:
1. $\frac{26}{45}:\frac{91}{135}=\frac{2\cdot13\cdot9\cdot15}{5\cdot9\cdot7\cdot13}=\frac{6}{7};$
2. $2\frac{1}{2}:\frac{15}{16}=\frac{5\cdot16}{2\cdot15}=\frac{8}{3}=2\frac{2}{3};$
3. $-3\frac{1}{7}:2\frac{5}{14}=-\frac{22}{7}\cdot\frac{33}{14}=$
$= -\frac{22\cdot14}{7\cdot33}=-\frac{4}{3}=-1\frac{1}{3};$
4. $-5\frac{13}{15}:\left(-1\frac{8}{25}\right)=$
$= -\frac{88}{15}:\left(-\frac{33}{25}\right)=$
$= \frac{88\cdot25}{15\cdot33}=\frac{40}{9}=4\frac{4}{9}.$