Решение:

1. $$\frac{1}{4} \text{ и } \frac{3}{6}$$

НОЗ = 12

$$\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}$$

$$\frac{3}{6} = \frac{3 \cdot 2}{6 \cdot 2} = \frac{6}{12}$$

$$\frac{3}{12} < \frac{6}{12}$$

2. $$\frac{2}{5} \text{ и } \frac{4}{10}$$

НОЗ = 10

$$\frac{2}{5} = \frac{2 \cdot 2}{5 \cdot 2} = \frac{4}{10}$$

$$\frac{4}{10} = \frac{4}{10}$$

$$\frac{4}{10} = \frac{4}{10}$$

3. $$\frac{3}{4} \text{ и } \frac{4}{12}$$

НОЗ = 12

$$\frac{3}{4} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{9}{12}$$

$$\frac{4}{12} = \frac{4}{12}$$

$$\frac{9}{12} > \frac{4}{12}$$

4. $$\frac{1}{2} \text{ и } \frac{3}{2}$$

НОЗ = 2

$$\frac{1}{2} = \frac{1}{2}$$

$$\frac{3}{2} = \frac{3}{2}$$

$$\frac{1}{2} < \frac{3}{2}$$

5. $$\frac{1}{2} \text{ и } \frac{1}{3} + \frac{1}{6}$$

$$\frac{1}{3} + \frac{1}{6} = \frac{1 \cdot 2}{3 \cdot 2} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$$

$$\frac{1}{2} = \frac{1}{2}$$

$$\frac{1}{2} = \frac{1}{2}$$

6. $$\frac{3}{4} \text{ и } -(\frac{2}{5} + \frac{1}{10})$$

$$\frac{2}{5} + \frac{1}{10} = \frac{2 \cdot 2}{5 \cdot 2} + \frac{1}{10} = \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$$

$$\frac{3}{4} \text{ и } -\frac{1}{2}$$

$$\frac{3}{4} > -\frac{1}{2}$$