П.81 Выполните действия: а) 3 7/9 + 1,95 - 6 1/3 + 5,45; б) 5,1 + 1 5/7 + 1 1/2 + 2,9; в) 7 17/20 + 6,625 + 1 15/40; г) 2,25 + 7 3/4 - 11/28; д) 4,2 + 3 5/26 - (7 - 3,8); е) 33 - (4 1/4 + 2,87 + 7,13); ж) 64 - 7 11/25 + 23,44; з) 3 4/9 - 1,8 - 1 1/3

Решение:

• а) 3 7/9 + 1,95 - 6 1/3 + 5,45
  • \[ 3rac{7}{9} + 1.95 - 6rac{1}{3} + 5.45 = igg(3rac{7}{9} - 6rac{1}{3}igg) + (1.95 + 5.45) \]
  • \[ = igg(rac{31}{9} - rac{19}{3}igg) + 7.4 = igg(rac{31}{9} - rac{57}{9}igg) + 7.4 = -rac{26}{9} + 7.4 \]
  • \[ = -2.888... + 7.4 = 4.511... \]
  • Более точное решение с дробями:
  • \[ 3rac{7}{9} + 1rac{95}{100} - 6rac{1}{3} + 5rac{45}{100} = 3rac{7}{9} + 1rac{19}{20} - 6rac{1}{3} + 5rac{9}{20} \]
  • \[ = igg(3 - 6igg) + igg(rac{7}{9} - rac{1}{3}igg) + igg(1rac{19}{20} + 5rac{9}{20}igg) \]
  • \[ = -3 + igg(rac{7}{9} - rac{3}{9}igg) + 6rac{28}{20} = -3 + rac{4}{9} + 6rac{7}{5} \]
  • \[ = -3 + rac{4}{9} + 7rac{2}{5} = 4 + rac{4}{9} + rac{2}{5} = 4 + rac{20 + 18}{45} = 4 + rac{38}{45} = 4rac{38}{45} \]
• б) 5,1 + 1 5/7 + 1 1/2 + 2,9
  • \[ 5.1 + 1rac{5}{7} + 1rac{1}{2} + 2.9 = (5.1 + 2.9) + 1rac{5}{7} + 1rac{1}{2} \]
  • \[ = 8 + rac{12}{7} + rac{3}{2} = 8 + rac{24 + 21}{14} = 8 + rac{45}{14} = 8 + 3rac{3}{14} = 11rac{3}{14} \]
• в) 7 17/20 + 6,625 + 1 15/40
  • \[ 7rac{17}{20} + 6.625 + 1rac{15}{40} = 7rac{17}{20} + 6rac{625}{1000} + 1rac{3}{8} \]
  • \[ = 7rac{17}{20} + 6rac{5}{8} + 1rac{3}{8} = 7rac{17}{20} + 7rac{8}{8} = 7rac{17}{20} + 8 \]
  • \[ = 15rac{17}{20} = 15.85 \]
• г) 2,25 + 7 3/4 - 11/28
  • \[ 2.25 + 7rac{3}{4} - rac{11}{28} = 2rac{1}{4} + 7rac{3}{4} - rac{11}{28} \]
  • \[ = 9rac{4}{4} - rac{11}{28} = 10 - rac{11}{28} = 9rac{17}{28} \]
• д) 4,2 + 3 5/26 - (7 - 3,8)
  • \[ 4.2 + 3rac{5}{26} - (7 - 3.8) = 4.2 + 3rac{5}{26} - 3.2 \]
  • \[ = (4.2 - 3.2) + 3rac{5}{26} = 1 + 3rac{5}{26} = 4rac{5}{26} \]
• е) 33 - (4 1/4 + 2,87 + 7,13)
  • \[ 33 - (4.25 + 2.87 + 7.13) = 33 - (7.12 + 7.13) \]
  • \[ = 33 - 14.25 = 18.75 \]
• ж) 64 - 7 11/25 + 23,44
  • \[ 64 - 7rac{11}{25} + 23.44 = 64 - 7.44 + 23.44 \]
  • \[ = (64 + 23.44) - 7.44 = 87.44 - 7.44 = 80 \]
• з) 3 4/9 - 1,8 - 1 1/3
  • \[ 3rac{4}{9} - 1.8 - 1rac{1}{3} = 3rac{4}{9} - 1rac{8}{10} - 1rac{1}{3} \]
  • \[ = 3rac{4}{9} - 1rac{4}{5} - 1rac{1}{3} = igg(3 - 1 - 1igg) + igg(rac{4}{9} - rac{4}{5} - rac{1}{3}igg) \]
  • \[ = 1 + igg(rac{20 - 36 - 15}{45}igg) = 1 + rac{-31}{45} = 1 - rac{31}{45} = rac{14}{45} \]

Ответ: а) 4 45 38 ; б) 11 14 3 ; в) 15,85; г) 9 28 17 ; д) 4 26 5 ; е) 18,75; ж) 80; з) 14/45.