Контрольные задания > а) \(\frac{1}{4} + \frac{1}{5};\) б) \(\frac{1}{3} + \frac{1}{7};\) в) \(\frac{3}{5} + \frac{3}{4};\) г) \(\frac{1}{2} + \frac{7}{9};\) д) \(\frac{5}{7} + 0;\) е) \(\frac{2}{3} - \frac{2}{5};\) ж) \(\frac{1}{2} - \frac{1}{3};\) з) \(\frac{3}{5} - \frac{4}{7};\) и) \(\frac{5}{7} - \frac{1}{6};\) к) \(\frac{8}{9} - 0;\) л) \(\frac{3}{4} + \frac{4}{5};\) м) \(\frac{3}{4} + \frac{2}{9}.\)
Вопрос:

а) \(\frac{1}{4} + \frac{1}{5};\) б) \(\frac{1}{3} + \frac{1}{7};\) в) \(\frac{3}{5} + \frac{3}{4};\) г) \(\frac{1}{2} + \frac{7}{9};\) д) \(\frac{5}{7} + 0;\) е) \(\frac{2}{3} - \frac{2}{5};\) ж) \(\frac{1}{2} - \frac{1}{3};\) з) \(\frac{3}{5} - \frac{4}{7};\) и) \(\frac{5}{7} - \frac{1}{6};\) к) \(\frac{8}{9} - 0;\) л) \(\frac{3}{4} + \frac{4}{5};\) м) \(\frac{3}{4} + \frac{2}{9}.\)

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Ответ:

Решение:

  1. a) \(\frac{1}{4} + \frac{1}{5} = \frac{1 * 5}{4 * 5} + \frac{1 * 4}{5 * 4} = \frac{5}{20} + \frac{4}{20} = \frac{5 + 4}{20} = \frac{9}{20}\)
  2. б) \(\frac{1}{3} + \frac{1}{7} = \frac{1 * 7}{3 * 7} + \frac{1 * 3}{7 * 3} = \frac{7}{21} + \frac{3}{21} = \frac{7 + 3}{21} = \frac{10}{21}\)
  3. в) \(\frac{3}{5} + \frac{3}{4} = \frac{3 * 4}{5 * 4} + \frac{3 * 5}{4 * 5} = \frac{12}{20} + \frac{15}{20} = \frac{12 + 15}{20} = \frac{27}{20} = 1 \frac{7}{20}\)
  4. г) \(\frac{1}{2} + \frac{7}{9} = \frac{1 * 9}{2 * 9} + \frac{7 * 2}{9 * 2} = \frac{9}{18} + \frac{14}{18} = \frac{9 + 14}{18} = \frac{23}{18} = 1 \frac{5}{18}\)
  5. д) \(\frac{5}{7} + 0 = \frac{5}{7}\)
  6. е) \(\frac{2}{3} - \frac{2}{5} = \frac{2 * 5}{3 * 5} - \frac{2 * 3}{5 * 3} = \frac{10}{15} - \frac{6}{15} = \frac{10 - 6}{15} = \frac{4}{15}\)
  7. ж) \(\frac{1}{2} - \frac{1}{3} = \frac{1 * 3}{2 * 3} - \frac{1 * 2}{3 * 2} = \frac{3}{6} - \frac{2}{6} = \frac{3 - 2}{6} = \frac{1}{6}\)
  8. з) \(\frac{3}{5} - \frac{4}{7} = \frac{3 * 7}{5 * 7} - \frac{4 * 5}{7 * 5} = \frac{21}{35} - \frac{20}{35} = \frac{21 - 20}{35} = \frac{1}{35}\)
  9. и) \(\frac{5}{7} - \frac{1}{6} = \frac{5 * 6}{7 * 6} - \frac{1 * 7}{6 * 7} = \frac{30}{42} - \frac{7}{42} = \frac{30 - 7}{42} = \frac{23}{42}\)
  10. к) \(\frac{8}{9} - 0 = \frac{8}{9}\)
  11. л) \(\frac{3}{4} + \frac{4}{5} = \frac{3 * 5}{4 * 5} + \frac{4 * 4}{5 * 4} = \frac{15}{20} + \frac{16}{20} = \frac{15 + 16}{20} = \frac{31}{20} = 1 \frac{11}{20}\)
  12. м) \(\frac{3}{4} + \frac{2}{9} = \frac{3 * 9}{4 * 9} + \frac{2 * 4}{9 * 4} = \frac{27}{36} + \frac{8}{36} = \frac{27 + 8}{36} = \frac{35}{36}\)

Ответ: а) \(\frac{9}{20}\); б) \(\frac{10}{21}\); в) \(1 \frac{7}{20}\); г) \(1 \frac{5}{18}\); д) \(\frac{5}{7}\); е) \(\frac{4}{15}\); ж) \(\frac{1}{6}\); з) \(\frac{1}{35}\); и) \(\frac{23}{42}\); к) \(\frac{8}{9}\); л) \(1 \frac{11}{20}\); м) \(\frac{35}{36}\)

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