Вариант 3. Выполните сложение: a) 4/7 + 5/6 б) 5/12 + 2/15 в) 3/7 + 5/14 г) 5/18 + 7/30 д) 13/25 + 7/10 е) 8/9 + 7/12 ж) 15/19 + 27/37 з) 4/21 + 5/7 и) 3/25 + 1/20

a) $$ \frac{4}{7} + \frac{5}{6} = \frac{4 \cdot 6}{7 \cdot 6} + \frac{5 \cdot 7}{6 \cdot 7} = \frac{24}{42} + \frac{35}{42} = \frac{24+35}{42} = \frac{59}{42} = 1 \frac{17}{42} $$

б) $$ \frac{5}{12} + \frac{2}{15} = \frac{5 \cdot 5}{12 \cdot 5} + \frac{2 \cdot 4}{15 \cdot 4} = \frac{25}{60} + \frac{8}{60} = \frac{25+8}{60} = \frac{33}{60} = \frac{11}{20} $$

в) $$ \frac{3}{7} + \frac{5}{14} = \frac{3 \cdot 2}{7 \cdot 2} + \frac{5}{14} = \frac{6}{14} + \frac{5}{14} = \frac{6+5}{14} = \frac{11}{14} $$

г) $$ \frac{5}{18} + \frac{7}{30} = \frac{5 \cdot 5}{18 \cdot 5} + \frac{7 \cdot 3}{30 \cdot 3} = \frac{25}{90} + \frac{21}{90} = \frac{25+21}{90} = \frac{46}{90} = \frac{23}{45} $$

д) $$ \frac{13}{25} + \frac{7}{10} = \frac{13 \cdot 2}{25 \cdot 2} + \frac{7 \cdot 5}{10 \cdot 5} = \frac{26}{50} + \frac{35}{50} = \frac{26+35}{50} = \frac{61}{50} = 1 \frac{11}{50} $$

е) $$ \frac{8}{9} + \frac{7}{12} = \frac{8 \cdot 4}{9 \cdot 4} + \frac{7 \cdot 3}{12 \cdot 3} = \frac{32}{36} + \frac{21}{36} = \frac{32+21}{36} = \frac{53}{36} = 1 \frac{17}{36} $$

ж) $$ \frac{15}{19} + \frac{27}{37} = \frac{15 \cdot 37}{19 \cdot 37} + \frac{27 \cdot 19}{37 \cdot 19} = \frac{555}{703} + \frac{513}{703} = \frac{555+513}{703} = \frac{1068}{703} = 1 \frac{365}{703} $$

з) $$ \frac{4}{21} + \frac{5}{7} = \frac{4}{21} + \frac{5 \cdot 3}{7 \cdot 3} = \frac{4}{21} + \frac{15}{21} = \frac{4+15}{21} = \frac{19}{21} $$

и) $$ \frac{3}{25} + \frac{1}{20} = \frac{3 \cdot 4}{25 \cdot 4} + \frac{1 \cdot 5}{20 \cdot 5} = \frac{12}{100} + \frac{5}{100} = \frac{12+5}{100} = \frac{17}{100} $$

Ответ: a) $$1 \frac{17}{42}$$, б) $$\frac{11}{20}$$, в) $$\frac{11}{14}$$, г) $$\frac{23}{45}$$, д) $$1 \frac{11}{50}$$, е) $$1 \frac{17}{36}$$, ж) $$1 \frac{365}{703}$$, з) $$\frac{19}{21}$$, и) $$\frac{17}{100}$$