04 Упростите выражение:

Решение:

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

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

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

e) \( 1\frac{5}{7}x \cdot \frac{5}{12}y = \frac{12}{7}x \cdot \frac{5}{12}y = \frac{12 \cdot 5}{7 \cdot 12}xy = \frac{5}{7}xy \)

в) \( 5m \cdot \frac{6}{11}n \cdot 2\frac{5}{14}k = 5m \cdot \frac{6}{11}n \cdot \frac{33}{14}k = \frac{5 \cdot 6 \cdot 33}{11 \cdot 14}mnk = \frac{5 \cdot 6 \cdot 3 \cdot 11}{11 \cdot 2 \cdot 7}mnk = \frac{5 \cdot 3 \cdot 3}{7}mnk = \frac{45}{7}mnk = 6\frac{3}{7}mnk \)

г) \( 2\frac{5}{8}x \cdot 2y \cdot 2\frac{7}{12}z = \frac{21}{8}x \cdot 2y \cdot \frac{31}{12}z = \frac{21 \cdot 2 \cdot 31}{8 \cdot 12}xyz = \frac{21 \cdot 2 \cdot 31}{8 \cdot 12}xyz = \frac{7 \cdot 3 \cdot 2 \cdot 31}{8 \cdot 4 \cdot 3}xyz = \frac{7 \cdot 31}{4 \cdot 4}xyz = \frac{217}{16}xyz = 13\frac{9}{16}xyz \)

Ответ: а) \(\frac{7}{18}ab\), г) \(\frac{7}{18}pk\), б) \(1\frac{3}{5}xy\), е) \(\frac{5}{7}xy\), в) \(6\frac{3}{7}mnk\), г) \(13\frac{9}{16}xyz\).