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

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. \(\frac{8}{9}x \cdot 1\frac{4}{5}y = \frac{8}{9}x \cdot \frac{9}{5}y = \frac{8 \cdot 9}{9 \cdot 5}xy = \frac{8}{5}xy\)
3. \(5m \cdot 2\frac{6}{11}n = 5m \cdot \frac{28}{11}n = \frac{5 \cdot 28}{11}mn = \frac{140}{11}mn\)
4. \(\frac{2}{8}x \cdot 2\frac{4}{7}y \cdot 2\frac{2}{7}z = \frac{1}{4}x \cdot \frac{18}{7}y \cdot \frac{16}{7}z = \frac{1 18 16}{4 7 7}xyz = \frac{432}{196}xyz = \frac{108}{49}xyz\)
5. \(1\frac{5}{7}x \cdot \frac{5}{12}y = \frac{12}{7}x \cdot \frac{5}{12}y = \frac{12 5}{7 12}xy = \frac{5}{7}xy\)
6. \(\frac{8}{9}p \cdot \frac{7}{4}k = \frac{8 7}{9 4}pk = \frac{56}{36}pk = \frac{14}{9}pk\)

Ответ: 1. \(\frac{7}{18}ab\) 2. \(\frac{8}{5}xy\) 3. \(\frac{140}{11}mn\) 4. \(\frac{108}{49}xyz\) 5. \(\frac{5}{7}xy\) 6. \(\frac{14}{9}pk\)