5.412 Выполните действия: а) \(\frac{7}{9} + \frac{5}{12}\); б) \(\frac{5}{6} + \frac{7}{8}\); в) \(13 \frac{21}{22} - 11 \frac{3}{55}\); г) \(\frac{11}{12} - \frac{11}{20}\); д) \(\frac{17}{21} - \frac{8}{15}\); е) \(8 \frac{5}{40} + 7 \frac{10}{60}\);

Решение:

a) \(\frac{7}{9} + \frac{5}{12} = \frac{7 \cdot 4}{9 \cdot 4} + \frac{5 \cdot 3}{12 \cdot 3} = \frac{28}{36} + \frac{15}{36} = \frac{28+15}{36} = \frac{43}{36} = 1\frac{7}{36}\)

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

в) \(13 \frac{21}{22} - 11 \frac{3}{55} = 13 \frac{21 \cdot 5}{22 \cdot 5} - 11 \frac{3 \cdot 2}{55 \cdot 2} = 13 \frac{105}{110} - 11 \frac{6}{110} = (13-11) + \frac{105-6}{110} = 2 + \frac{99}{110} = 2 + \frac{9}{10} = 2\frac{9}{10}\)

г) \(\frac{11}{12} - \frac{11}{20} = \frac{11 \cdot 5}{12 \cdot 5} - \frac{11 \cdot 3}{20 \cdot 3} = \frac{55}{60} - \frac{33}{60} = \frac{55-33}{60} = \frac{22}{60} = \frac{11}{30}\)

д) \(\frac{17}{21} - \frac{8}{15} = \frac{17 \cdot 5}{21 \cdot 5} - \frac{8 \cdot 7}{15 \cdot 7} = \frac{85}{105} - \frac{56}{105} = \frac{85-56}{105} = \frac{29}{105}\)

е) \(8 \frac{5}{40} + 7 \frac{10}{60} = 8 \frac{1}{8} + 7 \frac{1}{6} = 8 \frac{1 \cdot 3}{8 \cdot 3} + 7 \frac{1 \cdot 4}{6 \cdot 4} = 8 \frac{3}{24} + 7 \frac{4}{24} = (8+7) + \frac{3+4}{24} = 15 + \frac{7}{24} = 15\frac{7}{24}\)

Ответ: а) \(1\frac{7}{36}\); б) \(1\frac{17}{24}\); в) \(2\frac{9}{10}\); г) \(\frac{11}{30}\); д) \(\frac{29}{105}\); е) \(15\frac{7}{24}\)

Продолжай в том же духе, и у тебя все получится!