№2. Выполните сложение: a) 4/9 + 3/5 г) 11/25 + 13/30 ж) 5/38 + 7/19 б) 7/18 + 7/12 д) 5/42 + 1/7 з) 11/21 + 3/14 в) 2/9 + 5/18 е) 17/20 + 5/12 и) 1/45 +0,3+ 11/50

a) \(\frac{4}{9} + \frac{3}{5}\). НОЗ (9, 5) = 45

$$\frac{4}{9} + \frac{3}{5} = \frac{4\cdot 5}{9\cdot 5} + \frac{3\cdot 9}{5\cdot 9} = \frac{20}{45} + \frac{27}{45} = \frac{20+27}{45} = \frac{47}{45} = 1\frac{2}{45}$$

Ответ: $$1\frac{2}{45}$$

г) \(\frac{11}{25} + \frac{13}{30}\). НОЗ (25, 30) = 150

$$\frac{11}{25} + \frac{13}{30} = \frac{11\cdot 6}{25\cdot 6} + \frac{13\cdot 5}{30\cdot 5} = \frac{66}{150} + \frac{65}{150} = \frac{66+65}{150} = \frac{131}{150}$$

Ответ: $$\frac{131}{150}$$

ж) \(\frac{5}{38} + \frac{7}{19}\). НОЗ (38, 19) = 38

$$\frac{5}{38} + \frac{7}{19} = \frac{5}{38} + \frac{7\cdot 2}{19\cdot 2} = \frac{5}{38} + \frac{14}{38} = \frac{5+14}{38} = \frac{19}{38} = \frac{1}{2}$$

Ответ: $$\frac{1}{2}$$

б) \(\frac{7}{18} + \frac{7}{12}\). НОЗ (18, 12) = 36

$$\frac{7}{18} + \frac{7}{12} = \frac{7\cdot 2}{18\cdot 2} + \frac{7\cdot 3}{12\cdot 3} = \frac{14}{36} + \frac{21}{36} = \frac{14+21}{36} = \frac{35}{36}$$

Ответ: $$\frac{35}{36}$$

д) \(\frac{5}{42} + \frac{1}{7}\). НОЗ (42, 7) = 42

$$\frac{5}{42} + \frac{1}{7} = \frac{5}{42} + \frac{1\cdot 6}{7\cdot 6} = \frac{5}{42} + \frac{6}{42} = \frac{5+6}{42} = \frac{11}{42}$$

Ответ: $$\frac{11}{42}$$

з) \(\frac{11}{21} + \frac{3}{14}\). НОЗ (21, 14) = 42

$$\frac{11}{21} + \frac{3}{14} = \frac{11\cdot 2}{21\cdot 2} + \frac{3\cdot 3}{14\cdot 3} = \frac{22}{42} + \frac{9}{42} = \frac{22+9}{42} = \frac{31}{42}$$

Ответ: $$\frac{31}{42}$$

в) \(\frac{2}{9} + \frac{5}{18}\). НОЗ (9, 18) = 18

$$\frac{2}{9} + \frac{5}{18} = \frac{2\cdot 2}{9\cdot 2} + \frac{5}{18} = \frac{4}{18} + \frac{5}{18} = \frac{4+5}{18} = \frac{9}{18} = \frac{1}{2}$$

Ответ: $$\frac{1}{2}$$

е) \(\frac{17}{20} + \frac{5}{12}\). НОЗ (20, 12) = 60

$$\frac{17}{20} + \frac{5}{12} = \frac{17\cdot 3}{20\cdot 3} + \frac{5\cdot 5}{12\cdot 5} = \frac{51}{60} + \frac{25}{60} = \frac{51+25}{60} = \frac{76}{60} = \frac{19}{15} = 1\frac{4}{15}$$

Ответ: $$1\frac{4}{15}$$

и) \(\frac{1}{45} +0,3+ \frac{11}{50}\). НОЗ (45, 50) = 450

$$0,3 = \frac{3}{10} = \frac{3 \cdot 45}{10 \cdot 45} = \frac{135}{450}$$ $$\frac{1}{45} = \frac{1 \cdot 10}{45 \cdot 10} = \frac{10}{450}$$ $$\frac{11}{50} = \frac{11 \cdot 9}{50 \cdot 9} = \frac{99}{450}$$ $$\frac{1}{45} +0,3+ \frac{11}{50} = \frac{10}{450} + \frac{135}{450} + \frac{99}{450} = \frac{10+135+99}{450} = \frac{244}{450} = \frac{122}{225}$$

Ответ: $$\frac{122}{225}$$