Упростите выражение: a) \(\frac{2}{3}a \cdot \frac{7}{12}b\) д) \(\frac{7}{8}p \cdot \frac{4}{9}k\) б) \(\frac{8}{9}x \cdot 1\frac{4}{5}y\) е) \(1\frac{3}{7}x \cdot \frac{5}{12}y\) в) \(5m \cdot 2\frac{6}{11}n \cdot 2\frac{5}{14}k\) г) \(2\frac{5}{8}x \cdot 2y \cdot \frac{2}{7}z\)

Решение:

a) \( \frac{2}{3}a \cdot \frac{7}{12}b = \frac{2 \cdot 7}{3 \cdot 12} ab = \frac{14}{36} ab = \frac{7}{18}ab \)

б) \( \frac{8}{9}x \cdot 1\frac{4}{5}y = \frac{8}{9}x \cdot \frac{9}{5}y = \frac{8 \cdot 9}{9 \cdot 5} xy = \frac{8}{5}xy = 1\frac{3}{5}xy \)

в) \( 5m \cdot 2\frac{6}{11}n \cdot 2\frac{5}{14}k = 5m \cdot \frac{28}{11}n \cdot \frac{33}{14}k = \frac{5 \cdot 28 \cdot 33}{11 \cdot 14} mnk = \frac{5 \cdot (2 \cdot 14) \cdot (3 \cdot 11)}{11 \cdot 14} mnk = 5 \cdot 2 \cdot 3 mnk = 30mnk \)

г) \( 2\frac{5}{8}x \cdot 2y \cdot \frac{2}{7}z = \frac{21}{8}x \cdot 2y \cdot \frac{2}{7}z = \frac{21 \cdot 2 \cdot 2}{8 \cdot 7} xyz = \frac{84}{56} xyz = \frac{3}{2}xyz = 1\frac{1}{2}xyz \)

д) \( \frac{7}{8}p \cdot \frac{4}{9}k = \frac{7 \cdot 4}{8 \cdot 9} pk = \frac{28}{72} pk = \frac{7}{18}pk \)

е) \( 1\frac{3}{7}x \cdot \frac{5}{12}y = \frac{10}{7}x \cdot \frac{5}{12}y = \frac{10 \cdot 5}{7 \cdot 12} xy = \frac{50}{84} xy = \frac{25}{42}xy \)

Ответ: а) \(\frac{7}{18}ab\); б) \(1\frac{3}{5}xy\); в) \(30mnk\); г) \(1\frac{1}{2}xyz\); д) \(\frac{7}{18}pk\); е) \(\frac{25}{42}xy\).