Solve the following arithmetic problems: 1. \(\frac{29}{15} + \frac{1}{15}\) 2. \(\frac{11}{3} + \frac{5}{6}\) 3. \(\frac{15}{15} + \frac{1}{13}\) 4. \(\frac{40}{8} + \frac{5}{16}\) 5. \(\frac{65}{7} - \frac{23}{7}\) 6. \(\frac{2}{7} - \frac{1}{7}\)

Решение:

Выполним сложение и вычитание дробей.

1. \(\frac{29}{15} + \frac{1}{15} = \frac{29+1}{15} = \frac{30}{15} = 2\)
2. \(\frac{11}{3} + \frac{5}{6} = \frac{11 \times 2}{3 \times 2} + \frac{5}{6} = \frac{22}{6} + \frac{5}{6} = \frac{22+5}{6} = \frac{27}{6} = \frac{9}{2} = 4.5\)
3. \(\frac{15}{15} + \frac{1}{13} = 1 + \frac{1}{13} = \frac{13}{13} + \frac{1}{13} = \frac{14}{13}\)
4. \(\frac{40}{8} + \frac{5}{16} = 5 + \frac{5}{16} = \frac{5 \times 16}{16} + \frac{5}{16} = \frac{80}{16} + \frac{5}{16} = \frac{85}{16}\)
5. \(\frac{65}{7} - \frac{23}{7} = \frac{65-23}{7} = \frac{42}{7} = 6\)
6. \(\frac{2}{7} - \frac{1}{7} = \frac{2-1}{7} = \frac{1}{7}\)

Ответ: 2; \(\frac{9}{2}\); \(\frac{14}{13}\); \(\frac{85}{16}\); 6; \(\frac{1}{7}\).