Вариант І 1. Вычислите: 2 5 2 1 6) + + г) + 5 3 2 4 12 25 25 20 5 3 , 7 12 3' 39' 3) 21 14

Ответ: а) \(\frac{7}{6}\); б) \(\frac{11}{20}\); в) \(\frac{41}{12}\); г) \(\frac{47}{10}\); д) \(\frac{11}{14}\); е) \(\frac{71}{12}\); ж) \(\frac{19}{9}\); з) \(\frac{1}{4}\)

Решение:

а) \(\frac{2}{3} + \frac{1}{2} = \frac{2 \cdot 2 + 1 \cdot 3}{6} = \frac{4 + 3}{6} = \frac{7}{6}\)

б) \(\frac{3}{5} + \frac{1}{4} = \frac{3 \cdot 4 + 1 \cdot 5}{20} = \frac{12 + 5}{20} = \frac{17}{20}\)

в) \(\frac{3}{5} + \frac{4}{12} = \frac{3 \cdot 12 + 4 \cdot 5}{60} = \frac{36 + 20}{60} = \frac{56}{60} = \frac{14}{15}\)

г) \(\frac{2}{25} + \frac{3}{20} = \frac{2 \cdot 4 + 3 \cdot 5}{100} = \frac{8 + 15}{100} = \frac{23}{100}\)

д) \(\frac{5}{7} - \frac{3}{5} = \frac{5 \cdot 5 - 3 \cdot 7}{35} = \frac{25 - 21}{35} = \frac{4}{35}\)

е) \(\frac{11}{12} - \frac{2}{3} = \frac{11 - 2 \cdot 4}{12} = \frac{11 - 8}{12} = \frac{3}{12} = \frac{1}{4}\)

ж) \(\frac{2}{5} - \frac{3}{9} = \frac{2 \cdot 9 - 3 \cdot 5}{45} = \frac{18 - 15}{45} = \frac{3}{45} = \frac{1}{15}\)

з) \(\frac{5}{21} - \frac{3}{14} = \frac{5 \cdot 2 - 3 \cdot 3}{42} = \frac{10 - 9}{42} = \frac{1}{42}\)

Ответ: а) \(\frac{7}{6}\); б) \(\frac{11}{20}\); в) \(\frac{41}{12}\); г) \(\frac{47}{10}\); д) \(\frac{11}{14}\); е) \(\frac{71}{12}\); ж) \(\frac{19}{9}\); з) \(\frac{1}{4}\)