Вычислите: a) 3/4 + 4/5 ; б) 2/3 + 1/7 ; в) 2/13 + 0; г) 5/9 + 2/11 ; д) 5/12 + 3/4; e) 5/6 + 7/8.

Решение:

a) $$ \frac{3}{4} + \frac{4}{5} = \frac{3 \cdot 5}{4 \cdot 5} + \frac{4 \cdot 4}{5 \cdot 4} = \frac{15}{20} + \frac{16}{20} = \frac{15+16}{20} = \frac{31}{20} = 1 \frac{11}{20} $$

б) $$ \frac{2}{3} + \frac{1}{7} = \frac{2 \cdot 7}{3 \cdot 7} + \frac{1 \cdot 3}{7 \cdot 3} = \frac{14}{21} + \frac{3}{21} = \frac{14+3}{21} = \frac{17}{21} $$

в) $$ \frac{2}{13} + 0 = \frac{2}{13} $$

г) $$ \frac{5}{9} + \frac{2}{11} = \frac{5 \cdot 11}{9 \cdot 11} + \frac{2 \cdot 9}{11 \cdot 9} = \frac{55}{99} + \frac{18}{99} = \frac{55+18}{99} = \frac{73}{99} $$

д) $$ \frac{5}{12} + \frac{3}{4} = \frac{5}{12} + \frac{3 \cdot 3}{4 \cdot 3} = \frac{5}{12} + \frac{9}{12} = \frac{5+9}{12} = \frac{14}{12} = \frac{7}{6} = 1 \frac{1}{6} $$

e) $$ \frac{5}{6} + \frac{7}{8} = \frac{5 \cdot 4}{6 \cdot 4} + \frac{7 \cdot 3}{8 \cdot 3} = \frac{20}{24} + \frac{21}{24} = \frac{20+21}{24} = \frac{41}{24} = 1 \frac{17}{24} $$

Ответ: a) 31/20 = 1 11/20; б) 17/21; в) 2/13; г) 73/99; д) 14/12 = 7/6 = 1 1/6; e) 41/24 = 1 17/24