Вопрос:

Найти наименьший общий знаменатель и выполнить сложение и вычитание: 1) 1/3 + 5/6; 2) 3/10 + 2/15; 3) 5/12 + 3/8; 4) 7/18 + 1/6; 5) 4/9 + 5/12; 6) 7/24 + 5/36; 7) 5/8 − 1/4; 8) 7/10 − 2/15; 9) 5/6 − 7/18; 10) 11/12 − 3/8; 11) 13/16 − 5/24; 12) 9/20 − 7/30.

Ответ:

  1. НОЗ = 6: \(\frac{1}{3}+\frac{5}{6}=\frac{2}{6}+\frac{5}{6}=\frac{7}{6}=1\frac{1}{6}\).
  2. НОЗ = 30: \(\frac{3}{10}+\frac{2}{15}=\frac{9}{30}+\frac{4}{30}=\frac{13}{30}\).
  3. НОЗ = 24: \(\frac{5}{12}+\frac{3}{8}=\frac{10}{24}+\frac{9}{24}=\frac{19}{24}\).
  4. НОЗ = 18: \(\frac{7}{18}+\frac{1}{6}=\frac{7}{18}+\frac{3}{18}=\frac{10}{18}=\frac{5}{9}\).
  5. НОЗ = 36: \(\frac{4}{9}+\frac{5}{12}=\frac{16}{36}+\frac{15}{36}=\frac{31}{36}\).
  6. НОЗ = 72: \(\frac{7}{24}+\frac{5}{36}=\frac{21}{72}+\frac{10}{72}=\frac{31}{72}\).
  7. НОЗ = 8: \(\frac{5}{8}-\frac{1}{4}=\frac{5}{8}-\frac{2}{8}=\frac{3}{8}\).
  8. НОЗ = 30: \(\frac{7}{10}-\frac{2}{15}=\frac{21}{30}-\frac{4}{30}=\frac{17}{30}\).
  9. НОЗ = 18: \(\frac{5}{6}-\frac{7}{18}=\frac{15}{18}-\frac{7}{18}=\frac{8}{18}=\frac{4}{9}\).
  10. НОЗ = 24: \(\frac{11}{12}-\frac{3}{8}=\frac{22}{24}-\frac{9}{24}=\frac{13}{24}\).
  11. НОЗ = 48: \(\frac{13}{16}-\frac{5}{24}=\frac{39}{48}-\frac{10}{48}=\frac{29}{48}\).
  12. НОЗ = 60: \(\frac{9}{20}-\frac{7}{30}=\frac{27}{60}-\frac{14}{60}=\frac{13}{60}\).

Ответ: 1) \(1\frac{1}{6}\); 2) \(\frac{13}{30}\); 3) \(\frac{19}{24}\); 4) \(\frac{5}{9}\); 5) \(\frac{31}{36}\); 6) \(\frac{31}{72}\); 7) \(\frac{3}{8}\); 8) \(\frac{17}{30}\); 9) \(\frac{4}{9}\); 10) \(\frac{13}{24}\); 11) \(\frac{29}{48}\); 12) \(\frac{13}{60}\).