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

Решение:

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

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

6) \(\frac{8}{9}x \cdot 1\frac{1}{4}y = \frac{8}{9}x \cdot \frac{5}{4}y = \frac{8 \cdot 5}{9 \cdot 4}xy = \frac{40}{36}xy = \frac{10}{9}xy\)

e) \( 1\frac{7}{8}x \cdot \frac{5}{12}y = \frac{15}{8}x \cdot \frac{5}{12}y = \frac{15 \cdot 5}{8 \cdot 12}xy = \frac{75}{96}xy = \frac{25}{32}xy \)

в) \( 5m \cdot 2\frac{6}{11}n \cdot 2\frac{5}{14}k = 5m \cdot \frac{28}{11}n \cdot \frac{33}{14}k = \frac{5 \cdot 28 \cdot 33}{11 \cdot 14}mnk = \frac{5 \cdot 2 \cdot 1}{1}mnk = 10mnk \)

г) \( 2\frac{5}{8}x \cdot 2y \cdot 2\frac{7}{9}z = \frac{21}{8}x \cdot 2y \cdot \frac{25}{9}z = \frac{21 \cdot 2 \cdot 25}{8 \cdot 9}xyz = \frac{21 \cdot 25}{4 \cdot 9}xyz = \frac{7 \cdot 25}{4 \cdot 3}xyz = \frac{175}{12}xyz \)

Ответ: a) \(\frac{7}{18}ab\); д) \(\frac{7}{18}pk\); 6) \(\frac{10}{9}xy\); e) \(\frac{25}{32}xy\); в) \(10mnk\); г) \(\frac{175}{12}xyz\).