5.409 Найдите сумму или разность: a) \(\frac{1}{5} + \frac{1}{7};\) б) \(\frac{1}{4} + \frac{1}{9};\) г) \(\frac{1}{2} + \frac{5}{7};\) д) \(\frac{9}{11} + 0;\) е) \(\frac{3}{4} - \frac{3}{5};\) ж) \(\frac{1}{3} - \frac{1}{4};\) з) \(\frac{3}{7} - \frac{2}{9};\) и) \(\frac{4}{9} - \frac{2}{5};\) к) \(\frac{11}{13} - 0;\) л) \(2\frac{2}{3} + 1\frac{1}{2};\) м) \(2\frac{2}{3} + \frac{1}{4}\)

a) \(\frac{1}{5} + \frac{1}{7} = \frac{1*7}{5*7} + \frac{1*5}{7*5} = \frac{7}{35} + \frac{5}{35} = \frac{7+5}{35} = \frac{12}{35}\)

Ответ: \(\frac{12}{35}\)

б) \(\frac{1}{4} + \frac{1}{9} = \frac{1*9}{4*9} + \frac{1*4}{9*4} = \frac{9}{36} + \frac{4}{36} = \frac{9+4}{36} = \frac{13}{36}\)

Ответ: \(\frac{13}{36}\)

г) \(\frac{1}{2} + \frac{5}{7} = \frac{1*7}{2*7} + \frac{5*2}{7*2} = \frac{7}{14} + \frac{10}{14} = \frac{7+10}{14} = \frac{17}{14} = 1\frac{3}{14}\)

Ответ: \(1\frac{3}{14}\)

д) \(\frac{9}{11} + 0 = \frac{9}{11}\)

Ответ: \(\frac{9}{11}\)

е) \(\frac{3}{4} - \frac{3}{5} = \frac{3*5}{4*5} - \frac{3*4}{5*4} = \frac{15}{20} - \frac{12}{20} = \frac{15-12}{20} = \frac{3}{20}\)

Ответ: \(\frac{3}{20}\)

ж) \(\frac{1}{3} - \frac{1}{4} = \frac{1*4}{3*4} - \frac{1*3}{4*3} = \frac{4}{12} - \frac{3}{12} = \frac{4-3}{12} = \frac{1}{12}\)

Ответ: \(\frac{1}{12}\)

з) \(\frac{3}{7} - \frac{2}{9} = \frac{3*9}{7*9} - \frac{2*7}{9*7} = \frac{27}{63} - \frac{14}{63} = \frac{27-14}{63} = \frac{13}{63}\)

Ответ: \(\frac{13}{63}\)

и) \(\frac{4}{9} - \frac{2}{5} = \frac{4*5}{9*5} - \frac{2*9}{5*9} = \frac{20}{45} - \frac{18}{45} = \frac{20-18}{45} = \frac{2}{45}\)

Ответ: \(\frac{2}{45}\)

к) \(\frac{11}{13} - 0 = \frac{11}{13}\)

Ответ: \(\frac{11}{13}\)

л) \(2\frac{2}{3} + 1\frac{1}{2} = \frac{2*3+2}{3} + \frac{1*2+1}{2} = \frac{8}{3} + \frac{3}{2} = \frac{8*2}{3*2} + \frac{3*3}{2*3} = \frac{16}{6} + \frac{9}{6} = \frac{16+9}{6} = \frac{25}{6} = 4\frac{1}{6}\)

Ответ: \(4\frac{1}{6}\)

м) \(2\frac{2}{3} + \frac{1}{4} = \frac{2*3+2}{3} + \frac{1}{4} = \frac{8}{3} + \frac{1}{4} = \frac{8*4}{3*4} + \frac{1*3}{4*3} = \frac{32}{12} + \frac{3}{12} = \frac{32+3}{12} = \frac{35}{12} = 2\frac{11}{12}\)

Ответ: \(2\frac{11}{12}\)