2. Выполните действия: a) 2/7 + 3/5 ; 2/3 + 3/4 б) 5/6 - 1/3 ; 12-4/19 в) 18/25 : 5/9 ; 8/14 : 5/13 г) 2/7 : 5/14 ; 15/13 : 8/9

Решение:

1. a) 2/7 + 3/5 ; 2/3 + 3/4
   • \( \frac{2}{7} + \frac{3}{5} = \frac{2 \times 5}{7 \times 5} + \frac{3 \times 7}{5 \times 7} = \frac{10}{35} + \frac{21}{35} = \frac{10 + 21}{35} = \frac{31}{35} \)
   • \( \frac{2}{3} + \frac{3}{4} = \frac{2 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3} = \frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12} = 1 \frac{5}{12} \)
2. б) 5/6 - 1/3 ; 12-4/19
   • \( \frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{1 \times 2}{3 \times 2} = \frac{5}{6} - \frac{2}{6} = \frac{5 - 2}{6} = \frac{3}{6} = \frac{1}{2} \)
   • \( 12 - \frac{4}{19} = \frac{12 \times 19}{19} - \frac{4}{19} = \frac{228}{19} - \frac{4}{19} = \frac{224}{19} = 11 \frac{15}{19} \)
3. в) 18/25 : 5/9 ; 8/14 : 5/13
   • \( \frac{18}{25} : \frac{5}{9} = \frac{18}{25} \times \frac{9}{5} = \frac{18 \times 9}{25 \times 5} = \frac{162}{125} = 1 \frac{37}{125} \)
   • \( \frac{8}{14} : \frac{5}{13} = \frac{4}{7} : \frac{5}{13} = \frac{4}{7} \times \frac{13}{5} = \frac{4 \times 13}{7 \times 5} = \frac{52}{35} = 1 \frac{17}{35} \)
4. г) 2/7 : 5/14 ; 15/13 : 8/9
   • \( \frac{2}{7} : \frac{5}{14} = \frac{2}{7} \times \frac{14}{5} = \frac{2 \times 14}{7 \times 5} = \frac{2 \times 2}{5} = \frac{4}{5} \)
   • \( \frac{15}{13} : \frac{8}{9} = \frac{15}{13} \times \frac{9}{8} = \frac{15 \times 9}{13 \times 8} = \frac{135}{104} = 1 \frac{31}{104} \)

Ответ: а) 31/35; 1 5/12; б) 1/2; 11 15/19; в) 1 37/125; 1 17/35; г) 4/5; 1 31/104.