04. Упростите выражение:

Решение:

1. \( \frac{2}{3}a \cdot \frac{7}{12}b = \frac{2 \cdot 7}{3 \cdot 12}ab = \frac{14}{36}ab = \frac{7}{18}ab \)
2. \( \frac{8}{9}x \cdot \frac{4}{5}y = \frac{8 \cdot 4}{9 \cdot 5}xy = \frac{32}{45}xy \)
3. \( 5m \cdot \frac{6}{11}n \cdot 2 \frac{5}{14}k = 5m \cdot \frac{6}{11}n \cdot \frac{33}{14}k = \frac{5 \cdot 6 \cdot 33}{11 \cdot 14}mnk = \frac{5 \cdot 6 \cdot 3}{1 \cdot 14}mnk = \frac{90}{14}mnk = \frac{45}{7}mnk \)
4. \( \frac{5}{8}x \cdot 2y \cdot 2 \frac{2}{7}z = \frac{5}{8}x \cdot 2y \cdot \frac{16}{7}z = \frac{5 \cdot 2 \cdot 16}{8 \cdot 7}xyz = \frac{160}{56}xyz = \frac{20}{7}xyz \)

Ответ: а) \( \frac{7}{18}ab \); б) \( \frac{32}{45}xy \); в) \( \frac{45}{7}mnk \); г) \( \frac{20}{7}xyz \).