Вычислите: 2) $$\frac{-5}{6} + \frac{9}{11} =$$ 3) $$\frac{-5}{9} \cdot \frac{36}{55} =$$ 4) $$-3\frac{1}{2} : \left(-2\frac{3}{4}\right) =$$

Решение:

1. 2) $$\frac{-5}{6} + \frac{9}{11} = \frac{-5 \cdot 11}{6 \cdot 11} + \frac{9 \cdot 6}{11 \cdot 6} = \frac{-55}{66} + \frac{54}{66} = \frac{-55+54}{66} = \frac{-1}{66} = -\frac{1}{66}$$

2. 3) $$\frac{-5}{9} \cdot \frac{36}{55} = \frac{-5 \cdot 36}{9 \cdot 55} = \frac{-5 \cdot 4 \cdot 9}{9 \cdot 5 \cdot 11} = \frac{-4}{11} = -\frac{4}{11}$$

3. 4) $$-3\frac{1}{2} : \left(-2\frac{3}{4}\right) = -\frac{3 \cdot 2 + 1}{2} : \left(-\frac{2 \cdot 4 + 3}{4}\right) = -\frac{7}{2} : \left(-\frac{11}{4}\right) = -\frac{7}{2} \cdot \left(-\frac{4}{11}\right) = \frac{7 \cdot 4}{2 \cdot 11} = \frac{7 \cdot 2 \cdot 2}{2 \cdot 11} = \frac{14}{11} = 1\frac{3}{11}$$

Ответ:

• $$-\frac{1}{66}$$
• $$-\frac{4}{11}$$
• $$1\frac{3}{11}$$