32. Вычислите.

Решение:

1. \( \frac{3}{4} + \frac{1}{4} = \frac{3+1}{4} = \frac{4}{4} = 1 \)
2. \( \frac{2}{3} + \frac{1}{2} = \frac{2 + 2}{3 + 2} + \frac{1 + 3}{2 + 3} = \frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1 \frac{1}{6} \)
3. \( \frac{4}{9} - \frac{3}{9} = \frac{4-3}{9} = \frac{1}{9} \)
4. \( 1 \frac{2}{3} + 2 \frac{3}{4} = \frac{5}{3} + \frac{11}{4} = \frac{5 + 4}{3 + 4} + \frac{11 + 3}{4 + 3} = \frac{20}{12} + \frac{33}{12} = \frac{53}{12} = 4 \frac{5}{12} \)
5. \( 1 \frac{1}{2} + 1 \frac{1}{2} = \frac{3}{2} + \frac{3}{2} = \frac{6}{2} = 3 \)
6. \( \frac{1}{2} - \frac{2}{5} = \frac{1 + 5}{2 + 5} - \frac{2 + 2}{5 + 2} = \frac{5}{10} - \frac{4}{10} = \frac{1}{10} \)
7. \( 1 - \frac{1}{7} = \frac{7}{7} - \frac{1}{7} = \frac{6}{7} \)
8. \( 2 \frac{7}{9} - 1 \frac{1}{2} = \frac{25}{9} - \frac{3}{2} = \frac{25 + 2}{9 + 2} - \frac{3 + 9}{2 + 9} = \frac{50}{18} - \frac{27}{18} = \frac{23}{18} = 1 \frac{5}{18} \)
9. \( \frac{8}{9} + \frac{3}{4} = \frac{8 + 4}{9 + 4} + \frac{3 + 9}{4 + 9} = \frac{32}{36} + \frac{27}{36} = \frac{59}{36} = 1 \frac{23}{36} \)
10. \( 1 \frac{1}{4} - \frac{1}{2} = \frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \)

Ответ: a) 1, б) \(1 \frac{1}{6}\), в) \(\frac{1}{9}\), г) \(4 \frac{5}{12}\), д) 3, е) \(\frac{1}{10}\), ж) \(\frac{6}{7}\), з) \(1 \frac{5}{18}\), и) \(1 \frac{23}{36}\), к) \(\frac{3}{4}\).