№1. Выполните действия: a) 5/6 + 2/3 б) 1/2 + 2/5 в) 5/8 + 7/10 г) 3/8 + 10/11 д) 10 6/5 е) 18/25 : 12/35 ж) 4/7 : 28;

a) \[\frac{5}{6} + \frac{2}{3} = \frac{5}{6} + \frac{2 \cdot 2}{3 \cdot 2} = \frac{5}{6} + \frac{4}{6} = \frac{5+4}{6} = \frac{9}{6} = \frac{3}{2} = 1\frac{1}{2}\]

б) \[\frac{1}{2} + \frac{2}{5} = \frac{1 \cdot 5}{2 \cdot 5} + \frac{2 \cdot 2}{5 \cdot 2} = \frac{5}{10} + \frac{4}{10} = \frac{5+4}{10} = \frac{9}{10}\]

в) \[\frac{5}{8} + \frac{7}{10} = \frac{5 \cdot 5}{8 \cdot 5} + \frac{7 \cdot 4}{10 \cdot 4} = \frac{25}{40} + \frac{28}{40} = \frac{25+28}{40} = \frac{53}{40} = 1\frac{13}{40}\]

г) \[\frac{3}{8} + \frac{10}{11} = \frac{3 \cdot 11}{8 \cdot 11} + \frac{10 \cdot 8}{11 \cdot 8} = \frac{33}{88} + \frac{80}{88} = \frac{33+80}{88} = \frac{113}{88} = 1\frac{25}{88}\]

д) \[10 \cdot \frac{6}{5} = \frac{10 \cdot 6}{5} = \frac{60}{5} = 12\]

е) \[\frac{18}{25} : \frac{12}{35} = \frac{18}{25} \cdot \frac{35}{12} = \frac{18 \cdot 35}{25 \cdot 12} = \frac{6 \cdot 3 \cdot 5 \cdot 7}{5 \cdot 5 \cdot 6 \cdot 2} = \frac{3 \cdot 7}{5 \cdot 2} = \frac{21}{10} = 2\frac{1}{10}\]

ж) \[\frac{4}{7} : 28 = \frac{4}{7} : \frac{28}{1} = \frac{4}{7} \cdot \frac{1}{28} = \frac{4 \cdot 1}{7 \cdot 28} = \frac{4}{7 \cdot 4 \cdot 7} = \frac{1}{7 \cdot 7} = \frac{1}{49}\]