Вопрос:

12. Вычислите: А) 1/2 + 1/4 + 1/8 Д) 1/3 + 1/5 + 1/15 3) 2/3 + 1/2 + 1/7 Л) 15/49 - 2 3/14 П) 4 3/14 - 3 2/7 Б) 1/2 + 1/3 + 1/6 Е) 1/2 + 3/7 + 5/14 И) 3/4 + 11/12 + 4/5 М) 5 7/12 - 2 2/15 Р) 3 13/44 - 1 7/33 B) 1/3 + 1/4 + 1/2 Е) 1/3 + 5/4 + 5/7 И) 5/12 + 3/25 + 1/7 Н) 5 2/15 - 2 7/12 С) 9 11/60 - 3 13/80 Г) 1/3 + 1/4 + 1/12 Ж) 1/4 + 1/3 + 1/5 К) 7/8 + 14/15 + 15/16 О) 4 11/14 - 2 3/7 Т) 2 3/5 - 1 6/7

Ответ:

12. Вычисления:

  1. А) \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} = \frac{4}{8} + \frac{2}{8} + \frac{1}{8} = \frac{7}{8} \)
  2. Д) \( \frac{1}{3} + \frac{1}{5} + \frac{1}{15} = \frac{5}{15} + \frac{3}{15} + \frac{1}{15} = \frac{9}{15} = \frac{3}{5} \)
  3. 3) \( \frac{2}{3} + \frac{1}{2} + \frac{1}{7} = \frac{28}{42} + \frac{21}{42} + \frac{6}{42} = \frac{55}{42} = 1 \frac{13}{42} \)
  4. Л) \( \frac{15}{49} - 2 \frac{3}{14} = \frac{15}{49} - \frac{31}{14} = \frac{30}{98} - \frac{217}{98} = -\frac{187}{98} = -1 \frac{89}{98} \)
  5. П) \( 4 \frac{3}{14} - 3 \frac{2}{7} = 4 \frac{3}{14} - 3 \frac{4}{14} = 3 \frac{17}{14} - 3 \frac{4}{14} = \frac{13}{14} \)
  6. Б) \( \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3}{6} + \frac{2}{6} + \frac{1}{6} = \frac{6}{6} = 1 \)
  7. Е) \( \frac{1}{2} + \frac{3}{7} + \frac{5}{14} = \frac{7}{14} + \frac{6}{14} + \frac{5}{14} = \frac{18}{14} = \frac{9}{7} = 1 \frac{2}{7} \)
  8. И) \( \frac{3}{4} + \frac{11}{12} + \frac{4}{5} = \frac{45}{60} + \frac{55}{60} + \frac{48}{60} = \frac{148}{60} = \frac{37}{15} = 2 \frac{7}{15} \)
  9. М) \( 5 \frac{7}{12} - 2 \frac{2}{15} = 5 \frac{35}{60} - 2 \frac{8}{60} = 3 \frac{27}{60} = 3 \frac{9}{20} \)
  10. Р) \( 3 \frac{13}{44} - 1 \frac{7}{33} = 3 \frac{39}{132} - 1 \frac{28}{132} = 2 \frac{111}{132} = 2 \frac{37}{44} \)
  11. В) \( \frac{1}{3} + \frac{1}{4} + \frac{1}{2} = \frac{4}{12} + \frac{3}{12} + \frac{6}{12} = \frac{13}{12} = 1 \frac{1}{12} \)
  12. Е) \( \frac{1}{3} + \frac{3}{4} + \frac{5}{7} = \frac{28}{84} + \frac{63}{84} + \frac{60}{84} = \frac{151}{84} = 1 \frac{67}{84} \)
  13. И) \( \frac{5}{12} + \frac{3}{25} + \frac{1}{7} = \frac{875}{2100} + \frac{252}{2100} + \frac{300}{2100} = \frac{1427}{2100} \)
  14. Н) \( 5 \frac{2}{15} - 2 \frac{7}{12} = 5 \frac{8}{60} - 2 \frac{35}{60} = 4 \frac{68}{60} - 2 \frac{35}{60} = 2 \frac{33}{60} = 2 \frac{11}{20} \)
  15. С) \( 9 \frac{11}{60} - 3 \frac{13}{80} = 9 \frac{44}{240} - 3 \frac{39}{240} = 6 \frac{5}{240} = 6 \frac{1}{48} \)
  16. Г) \( \frac{1}{3} + \frac{1}{4} + \frac{1}{12} = \frac{4}{12} + \frac{3}{12} + \frac{1}{12} = \frac{8}{12} = \frac{2}{3} \)
  17. Ж) \( \frac{1}{4} + \frac{1}{3} + \frac{1}{5} = \frac{15}{60} + \frac{20}{60} + \frac{12}{60} = \frac{47}{60} \)
  18. К) \( \frac{7}{8} + \frac{14}{15} + \frac{15}{16} = \frac{105}{120} + \frac{224}{240} + \frac{225}{240} = \frac{210}{240} + \frac{224}{240} + \frac{225}{240} = \frac{659}{240} = 2 \frac{179}{240} \)
  19. О) \( 4 \frac{11}{14} - 2 \frac{3}{7} = 4 \frac{11}{14} - 2 \frac{6}{14} = 2 \frac{5}{14} \)
  20. Т) \( 2 \frac{3}{5} - 1 \frac{6}{7} = 2 \frac{21}{35} - 1 \frac{30}{35} = 1 \frac{56}{35} - 1 \frac{30}{35} = \frac{26}{35} \)

Ответ: А) 7/8, Д) 3/5, 3) 1 13/42, Л) -1 89/98, П) 13/14, Б) 1, Е) 1 2/7, И) 2 7/15, М) 3 9/20, Р) 2 37/44, В) 1 1/12, Е) 1 67/84, И) 1427/2100, Н) 2 11/20, С) 6 1/48, Г) 2/3, Ж) 47/60, К) 2 179/240, О) 2 5/14, Т) 26/35.

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