Вычислите: 1) $$3\frac{3}{4} + \frac{5}{7}$$; 2) $$9\frac{9}{14} - 3\frac{3}{4}$$; 3) $$11\frac{11}{12} - 2\frac{2}{3}$$; 4) $$\frac{7}{25} + \frac{1}{4}$$; 5) $$\frac{11}{18} - \frac{1}{18}$$; 6) $$\frac{13}{18} + \frac{1}{18}$$

Выполним вычисления по порядку:

1. $$3\frac{3}{4} + \frac{5}{7} = \frac{3*4+3}{4} + \frac{5}{7} = \frac{15}{4} + \frac{5}{7} = \frac{15*7 + 5*4}{4*7} = \frac{105 + 20}{28} = \frac{125}{28} = 4\frac{13}{28}$$ Ответ: $$4\frac{13}{28}$$
2. $$9\frac{9}{14} - 3\frac{3}{4} = \frac{9*14+9}{14} - \frac{3*4+3}{4} = \frac{135}{14} - \frac{15}{4} = \frac{135*2 - 15*7}{28} = \frac{270 - 105}{28} = \frac{165}{28} = 5\frac{25}{28}$$ Ответ: $$5\frac{25}{28}$$
3. $$11\frac{11}{12} - 2\frac{2}{3} = \frac{11*12+11}{12} - \frac{2*3+2}{3} = \frac{143}{12} - \frac{8}{3} = \frac{143 - 8*4}{12} = \frac{143 - 32}{12} = \frac{111}{12} = 9\frac{3}{12} = 9\frac{1}{4}$$ Ответ: $$9\frac{1}{4}$$
4. $$\frac{7}{25} + \frac{1}{4} = \frac{7*4 + 1*25}{25*4} = \frac{28 + 25}{100} = \frac{53}{100}$$ Ответ: $$\frac{53}{100}$$
5. $$\frac{11}{18} - \frac{1}{18} = \frac{11-1}{18} = \frac{10}{18} = \frac{5}{9}$$ Ответ: $$\frac{5}{9}$$
6. $$\frac{13}{18} + \frac{1}{18} = \frac{13+1}{18} = \frac{14}{18} = \frac{7}{9}$$ Ответ: $$\frac{7}{9}$$