5.445 Вычислите: a) 1/2 + 1/3; б) 1/3 + 2/7; г) 3/7 + 4/9; д) 5/9 - 1/6; ж) 1/6 + 1/3; к) 7/15 - 3/10; е) 5/11 + 3/5; з) 9/5 - 7/10; л) 3/8 + 5/12; о) 17/30 - 3/6;

Выполним вычисления:

1. a) $$\frac{1}{2} + \frac{1}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}$$
2. б) $$\frac{1}{3} + \frac{2}{7} = \frac{1 \cdot 7}{3 \cdot 7} + \frac{2 \cdot 3}{7 \cdot 3} = \frac{7}{21} + \frac{6}{21} = \frac{7 + 6}{21} = \frac{13}{21}$$
3. г) $$\frac{3}{7} + \frac{4}{9} = \frac{3 \cdot 9}{7 \cdot 9} + \frac{4 \cdot 7}{9 \cdot 7} = \frac{27}{63} + \frac{28}{63} = \frac{27 + 28}{63} = \frac{55}{63}$$
4. д) $$\frac{5}{9} - \frac{1}{6} = \frac{5 \cdot 2}{9 \cdot 2} - \frac{1 \cdot 3}{6 \cdot 3} = \frac{10}{18} - \frac{3}{18} = \frac{10 - 3}{18} = \frac{7}{18}$$
5. ж) $$\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{1}{6} + \frac{2}{6} = \frac{1 + 2}{6} = \frac{3}{6} = \frac{1}{2}$$
6. к) $$\frac{7}{15} - \frac{3}{10} = \frac{7 \cdot 2}{15 \cdot 2} - \frac{3 \cdot 3}{10 \cdot 3} = \frac{14}{30} - \frac{9}{30} = \frac{14 - 9}{30} = \frac{5}{30} = \frac{1}{6}$$
7. е) $$\frac{5}{11} + \frac{3}{5} = \frac{5 \cdot 5}{11 \cdot 5} + \frac{3 \cdot 11}{5 \cdot 11} = \frac{25}{55} + \frac{33}{55} = \frac{25 + 33}{55} = \frac{58}{55}$$
8. з) $$\frac{9}{5} - \frac{7}{10} = \frac{9 \cdot 2}{5 \cdot 2} - \frac{7}{10} = \frac{18}{10} - \frac{7}{10} = \frac{18 - 7}{10} = \frac{11}{10}$$
9. л) $$\frac{3}{8} + \frac{5}{12} = \frac{3 \cdot 3}{8 \cdot 3} + \frac{5 \cdot 2}{12 \cdot 2} = \frac{9}{24} + \frac{10}{24} = \frac{9 + 10}{24} = \frac{19}{24}$$
10. о) $$\frac{17}{30} - \frac{3}{6} = \frac{17}{30} - \frac{3 \cdot 5}{6 \cdot 5} = \frac{17}{30} - \frac{15}{30} = \frac{17 - 15}{30} = \frac{2}{30} = \frac{1}{15}$$

Ответ: a) 5/6; б) 13/21; г) 55/63; д) 7/18; ж) 1/2; к) 1/6; е) 58/55; з) 11/10; л) 19/24; о) 1/15.