5.36 Найдите коэффициент выражения: a) $$\frac{44}{18}s \cdot \left( -\frac{9}{11}n \right)$$; б) -1 $$\frac{2}{5}a \cdot \left( -1 \frac{3}{7} \right)$$; в) $$\frac{2}{5}z \cdot \left( -\frac{5}{6}x \right) \cdot \left( -\frac{5}{6} \right)$$; г) -1 $$\frac{3}{7} \cdot (-n) \cdot \left( -2 \frac{1}{3} \right)$$

Решение:

1. $$\frac{44}{18}s \cdot \left( -\frac{9}{11}n \right) = \left( \frac{44}{18} \cdot \left( -\frac{9}{11} \right) \right) sn = \left( \frac{2 × 2}{2 × 9} \cdot \left( -\frac{9}{11} \right) \right) sn = \left( \frac{2}{9} \cdot \left( -\frac{9}{11} \right) \right) sn = \left( -\frac{2}{11} \right) sn \). Коэффициент: -$$\(\frac{2}{11}\)$$.
2. \( -1 \frac{2}{5}a \cdot \left( -1 \frac{3}{7} \right) = \left( -\frac{7}{5} \right) a \cdot \left( -\frac{10}{7} \right) = \left( -\frac{7}{5} \cdot \left( -\frac{10}{7} \right) \right) a = \left( \frac{7 × 10}{5 × 7} \right) a = \frac{10}{5} a = 2a \). Коэффициент: 2.
3. $$\(\frac{2}{5}\)z \(\cdot\) \(\left\)\(-\frac{5}{6}x \right\) \(\cdot\) \(\left\)\(-\frac{5}{6} \right\) = \(\left\)( \(\frac{2}{5}\) \(\cdot\) \(\left\)\(-\frac{5}{6} \right\) \(\cdot\) \(\left\)\(-\frac{5}{6} \right\) \(\right\)) zx = \(\left\)( \(\frac{2 × (-5) × (-5)}{5 × 6 × 6}\) \(\right\)) zx = \(\frac{50}{180}\) zx = \(\frac{5}{18}\) zx \). Коэффициент: $$\frac{5}{18}$$.
4. \( -1 \frac{3}{7} \cdot (-n) \cdot \left( -2 \frac{1}{3} \right) = \left( -\frac{10}{7} \right) \cdot (-n) \cdot \left( -\frac{7}{3} \right) = \left( -\frac{10}{7} \cdot (-1) \cdot \left( -\frac{7}{3} \right) \right) n = \left( -\frac{10}{3} \right) n \). Коэффициент: -$$\frac{10}{3}$$.