04 Упростите выражение: a) 2/3 a * 7/12 b = 6) 8/9 x * 1 1/4 y = в) 5m * 2 6/11 n * 2 5/14 k = r) 2 5/8 x * 2 y * 2 2/7 z =

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. \( \frac{8}{9}x \cdot 1\frac{1}{4}y = \frac{8}{9}x \cdot \frac{5}{4}y = \frac{8 \cdot 5}{9 \cdot 4}xy = \frac{40}{36}xy = \frac{10}{9}xy \)
3. \( 5m \cdot 2\frac{6}{11}n \cdot 2\frac{5}{14}k = 5m \cdot \frac{28}{11}n \cdot \frac{33}{14}k = \frac{5 \cdot 28 \cdot 33}{11 \cdot 14}mnk = \frac{5 \cdot (2 \cdot 14) \cdot (3 \cdot 11)}{11 \cdot 14}mnk = 5 \cdot 2 \cdot 3 mnk = 30mnk \)
4. \( 2\frac{5}{8}x \cdot 2y \cdot 2\frac{2}{7}z = \frac{21}{8}x \cdot 2y \cdot \frac{16}{7}z = \frac{21 \cdot 2 \cdot 16}{8 \cdot 7}xyz = \frac{(3 \cdot 7) \cdot 2 \cdot (2 \cdot 8)}{8 \cdot 7}xyz = 3 \cdot 2 \cdot 2 xyz = 12xyz \)

Ответ: а) \( \frac{7}{18}ab \), б) \( \frac{10}{9}xy \), в) \( 30mnk \), г) \( 12xyz \).