02 Упростите выражение:

Решение:

• а) \( \frac{2}{3}a \cdot \frac{7}{12}b = \frac{2 \cdot 7}{3 \cdot 12}ab = \frac{14}{36}ab = \frac{7}{18}ab \)
• б) \( \frac{8}{9}x \cdot \frac{4}{5}y = \frac{8 \cdot 4}{9 \cdot 5}xy = \frac{32}{45}xy \)
• в) \( 5m \cdot 2n \cdot \frac{6}{11}k \cdot \frac{5}{14} = (5 \cdot 2 \cdot \frac{6}{11} \cdot \frac{5}{14})mnk = (10 \cdot \frac{30}{154})mnk = (10 \cdot \frac{15}{77})mnk = \frac{150}{77}mnk \)
• г) \( 2 \frac{5}{8}x \cdot 2y \cdot 2 \frac{2}{7}z = \frac{21}{8}x \cdot 2y \cdot \frac{16}{7}z = (\frac{21}{8} \cdot 2 \cdot \frac{16}{7})xyz = (\frac{21 \cdot 2 \cdot 16}{8 \cdot 7})xyz = (\frac{21 \cdot 32}{56})xyz = (\frac{672}{56})xyz = 12xyz \)
• д) \( \frac{5}{7}x \cdot \frac{5}{12}y = \frac{5 \cdot 5}{7 \cdot 12}xy = \frac{25}{84}xy \)

Ответ: а) \( \frac{7}{18}ab \); б) \( \frac{32}{45}xy \); в) \( \frac{150}{77}mnk \); г) \( 12xyz \); д) \( \frac{25}{84}xy \).