- \(\frac{3}{5}\) + \(\frac{1}{7}\); - \(\frac{4}{15}\) - \(\frac{8}{25}\); \(\frac{14}{25}\) \(\cdot\) \(\frac{15}{21}\); \(\frac{18}{25}\) : \(\frac{42}{55}\)

Решение:

1. \( -\frac{3}{5} + \frac{1}{7} = -\frac{3 \cdot 7}{5 \cdot 7} + \frac{1 \cdot 5}{7 \cdot 5} = -\frac{21}{35} + \frac{5}{35} = \frac{-21+5}{35} = -\frac{16}{35} \)
2. \( -\frac{4}{15} - \frac{8}{25} = -\frac{4 \cdot 5}{15 \cdot 5} - \frac{8 \cdot 3}{25 \cdot 3} = -\frac{20}{75} - \frac{24}{75} = \frac{-20-24}{75} = -\frac{44}{75} \)
3. \( \frac{14}{25} \cdot \frac{15}{21} = \frac{14 \cdot 15}{25 \cdot 21} = \frac{(2 \cdot 7) \cdot (3 \cdot 5)}{(5 \cdot 5) \cdot (3 \cdot 7)} = \frac{2 \cdot 3 \cdot 5 \cdot 7}{3 \cdot 5 \cdot 5 \cdot 7} = \frac{2}{5} \)
4. \( \frac{18}{25} : \frac{42}{55} = \frac{18}{25} \cdot \frac{55}{42} = \frac{18 \cdot 55}{25 \cdot 42} = \frac{(2 \cdot 3 \cdot 3) \cdot (5 \cdot 11)}{(5 \cdot 5) \cdot (2 \cdot 3 \cdot 7)} = \frac{2 \cdot 3 \cdot 3 \cdot 5 \cdot 11}{2 \cdot 3 \cdot 5 \cdot 5 \cdot 7} = \frac{3 \cdot 11}{5 \cdot 7} = \frac{33}{35} \)

Ответ: 1) \( -\frac{16}{35} \); 2) \( -\frac{44}{75} \); 3) \( \frac{2}{5} \); 4) \( \frac{33}{35} \).