Вычислите 1. a) \(\frac{7}{8} + \frac{5}{8}\); б) \(\frac{5}{12} + \frac{7}{12}\); в) \(\frac{3}{10} + \frac{9}{10}\); г) \(\frac{8}{19} + \frac{11}{19}\) 2. a) \(1\frac{1}{18} + 2\frac{5}{18}\); б) \(\frac{5}{12} + \frac{7}{12}\); в) \(\frac{3}{10} + \frac{9}{10}\); г) \(\frac{8}{19} + \frac{11}{19}\) 3. a) \(1\frac{3}{5} + 1\frac{4}{5}\); б) \(1\frac{5}{7} + 2\frac{2}{7}\); в) \(2\frac{3}{4} + 2\frac{3}{4}\); г) \(1\frac{5}{8} + 3\frac{7}{8}\) 4. a) \(1\frac{12}{23} + 2\frac{12}{23}\); б) \(1\frac{11}{15} + 3\frac{7}{15}\); в) \(3\frac{14}{25} + 2\frac{18}{25}\); г) \(3\frac{17}{20} + 1\frac{19}{20}\) 5. a) \(2\frac{13}{14} - 1\frac{9}{14}\); б) \(3\frac{15}{17} - 1\frac{10}{17}\); в) \(5\frac{18}{31} - 2\frac{29}{31}\); г) \(3\frac{4}{19} - 1\frac{14}{19}\) 6. a) \(2\frac{7}{15} - 1\frac{8}{15}\); б) \(5\frac{3}{16} - 2\frac{7}{16}\); в) \(9\frac{1}{20} - 2\frac{10}{20}\); г) \(5\frac{9}{31} - 1\frac{29}{31}\) 7. a) \(7\frac{1}{32} - 2\frac{3}{32}\); б) \(1\frac{5}{18} - \frac{6}{18}\); в) \(6\frac{2}{7} - 1\frac{5}{7}\); г) \(1\frac{9}{20} - \frac{19}{20}\) 8. a) \(2\frac{4}{37} - 1\frac{5}{37}\); б) \(7\frac{8}{41} - \frac{9}{41}\); в) \(10\frac{12}{55} - 5\frac{25}{55}\); г) \(3\frac{8}{43} - \frac{40}{43}\) 9. a) \(2\frac{5}{18} + 3\frac{11}{18} - \frac{5}{18}\); б) \(3\frac{4}{29} + 5\frac{5}{29} + 2\frac{1}{29} - \frac{9}{29}\); в) \(2\frac{9}{26} + 1\frac{8}{26} + 1\frac{17}{26} - \frac{8}{26}\); г) \(8\frac{3}{49} + 1\frac{6}{49} + 2\frac{20}{49} - \frac{9}{49}\) 10. a) \(12\frac{3}{4} - 1\frac{1}{4} - 3\frac{3}{4} + 2\frac{1}{4}\); б) \(5\frac{9}{35} - 2\frac{22}{35} - 1\frac{12}{35} + 10\frac{26}{35}\); в) \(10\frac{7}{13} - 4\frac{4}{13} - 5\frac{9}{13} + 2\frac{6}{13}\); г) \(8\frac{13}{31} - 2\frac{20}{31} - 2\frac{11}{31} + 6\frac{18}{31}\) 11. a) \(5\frac{15}{28} + 9\frac{7}{18} - 1\frac{1}{28} + 3\frac{2}{18}\); б) \(6\frac{18}{37} + 5\frac{11}{20} - 2\frac{18}{37} + 5\frac{9}{20}\); в) \(4\frac{7}{17} + 1\frac{3}{16} + 2\frac{13}{16} + 5\frac{10}{17}\); г) \(14\frac{6}{19} + 1\frac{7}{8} + 2\frac{5}{8} - 4\frac{6}{19}\) 12. a) \((3\frac{16}{27} + 1\frac{17}{27}) - (2\frac{25}{36} + 1\frac{7}{36})\); б) \((3\frac{25}{48} - 1\frac{35}{48}) + (4\frac{65}{72} - 2\frac{68}{72})\); в) \((2\frac{8}{35} - 1\frac{13}{35}) + (3\frac{20}{49} - 2\frac{27}{49})\); г) \((4\frac{7}{15} + 2\frac{11}{15}) - (3\frac{7}{30} + 1\frac{29}{30})\)

Задание 1

а) \(\frac{7}{8} + \frac{5}{8} = \frac{7+5}{8} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}\) б) \(\frac{5}{12} + \frac{7}{12} = \frac{5+7}{12} = \frac{12}{12} = 1\) в) \(\frac{3}{10} + \frac{9}{10} = \frac{3+9}{10} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}\) г) \(\frac{8}{19} + \frac{11}{19} = \frac{8+11}{19} = \frac{19}{19} = 1\)

Задание 2

а) \(1\frac{1}{18} + 2\frac{5}{18} = (1+2) + (\frac{1}{18} + \frac{5}{18}) = 3 + \frac{6}{18} = 3 + \frac{1}{3} = 3\frac{1}{3}\) б) \(\frac{5}{12} + \frac{7}{12} = \frac{5+7}{12} = \frac{12}{12} = 1\) в) \(\frac{3}{10} + \frac{9}{10} = \frac{3+9}{10} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}\) г) \(\frac{8}{19} + \frac{11}{19} = \frac{8+11}{19} = \frac{19}{19} = 1\)

Задание 3

а) \(1\frac{3}{5} + 1\frac{4}{5} = (1+1) + (\frac{3}{5} + \frac{4}{5}) = 2 + \frac{7}{5} = 2 + 1\frac{2}{5} = 3\frac{2}{5}\) б) \(1\frac{5}{7} + 2\frac{2}{7} = (1+2) + (\frac{5}{7} + \frac{2}{7}) = 3 + \frac{7}{7} = 3 + 1 = 4\) в) \(2\frac{3}{4} + 2\frac{3}{4} = (2+2) + (\frac{3}{4} + \frac{3}{4}) = 4 + \frac{6}{4} = 4 + 1\frac{2}{4} = 5\frac{1}{2}\) г) \(1\frac{5}{8} + 3\frac{7}{8} = (1+3) + (\frac{5}{8} + \frac{7}{8}) = 4 + \frac{12}{8} = 4 + 1\frac{4}{8} = 5\frac{1}{2}\)

Задание 4

а) \(1\frac{12}{23} + 2\frac{12}{23} = (1+2) + (\frac{12}{23} + \frac{12}{23}) = 3 + \frac{24}{23} = 3 + 1\frac{1}{23} = 4\frac{1}{23}\) б) \(1\frac{11}{15} + 3\frac{7}{15} = (1+3) + (\frac{11}{15} + \frac{7}{15}) = 4 + \frac{18}{15} = 4 + 1\frac{3}{15} = 5\frac{1}{5}\) в) \(3\frac{14}{25} + 2\frac{18}{25} = (3+2) + (\frac{14}{25} + \frac{18}{25}) = 5 + \frac{32}{25} = 5 + 1\frac{7}{25} = 6\frac{7}{25}\) г) \(3\frac{17}{20} + 1\frac{19}{20} = (3+1) + (\frac{17}{20} + \frac{19}{20}) = 4 + \frac{36}{20} = 4 + 1\frac{16}{20} = 5\frac{4}{5}\)

Задание 5

а) \(2\frac{13}{14} - 1\frac{9}{14} = (2-1) + (\frac{13}{14} - \frac{9}{14}) = 1 + \frac{4}{14} = 1\frac{2}{7}\) б) \(3\frac{15}{17} - 1\frac{10}{17} = (3-1) + (\frac{15}{17} - \frac{10}{17}) = 2 + \frac{5}{17} = 2\frac{5}{17}\) в) \(5\frac{18}{31} - 2\frac{29}{31} = (5-2) + (\frac{18}{31} - \frac{29}{31}) = 3 - \frac{11}{31} = 2\frac{31}{31} - \frac{11}{31} = 2\frac{20}{31}\) г) \(3\frac{4}{19} - 1\frac{14}{19} = (3-1) + (\frac{4}{19} - \frac{14}{19}) = 2 - \frac{10}{19} = 1\frac{19}{19} - \frac{10}{19} = 1\frac{9}{19}\)

Задание 6

а) \(2\frac{7}{15} - 1\frac{8}{15} = (2-1) + (\frac{7}{15} - \frac{8}{15}) = 1 - \frac{1}{15} = \frac{15}{15} - \frac{1}{15} = \frac{14}{15}\) б) \(5\frac{3}{16} - 2\frac{7}{16} = (5-2) + (\frac{3}{16} - \frac{7}{16}) = 3 - \frac{4}{16} = 2\frac{16}{16} - \frac{4}{16} = 2\frac{12}{16} = 2\frac{3}{4}\) в) \(9\frac{1}{20} - 2\frac{10}{20} = (9-2) + (\frac{1}{20} - \frac{10}{20}) = 7 - \frac{9}{20} = 6\frac{20}{20} - \frac{9}{20} = 6\frac{11}{20}\) г) \(5\frac{9}{31} - 1\frac{29}{31} = (5-1) + (\frac{9}{31} - \frac{29}{31}) = 4 - \frac{20}{31} = 3\frac{31}{31} - \frac{20}{31} = 3\frac{11}{31}\)

Задание 7

а) \(7\frac{1}{32} - 2\frac{3}{32} = (7-2) + (\frac{1}{32} - \frac{3}{32}) = 5 - \frac{2}{32} = 4\frac{32}{32} - \frac{2}{32} = 4\frac{30}{32} = 4\frac{15}{16}\) б) \(1\frac{5}{18} - \frac{6}{18} = 1 + \frac{5}{18} - \frac{6}{18} = 1 - \frac{1}{18} = \frac{18}{18} - \frac{1}{18} = \frac{17}{18}\) в) \(6\frac{2}{7} - 1\frac{5}{7} = (6-1) + (\frac{2}{7} - \frac{5}{7}) = 5 - \frac{3}{7} = 4\frac{7}{7} - \frac{3}{7} = 4\frac{4}{7}\) г) \(1\frac{9}{20} - \frac{19}{20} = 1 + \frac{9}{20} - \frac{19}{20} = 1 - \frac{10}{20} = \frac{20}{20} - \frac{10}{20} = \frac{10}{20} = \frac{1}{2}\)

Задание 8

а) \(2\frac{4}{37} - 1\frac{5}{37} = (2-1) + (\frac{4}{37} - \frac{5}{37}) = 1 - \frac{1}{37} = \frac{37}{37} - \frac{1}{37} = \frac{36}{37}\) б) \(7\frac{8}{41} - \frac{9}{41} = 7 + \frac{8}{41} - \frac{9}{41} = 7 - \frac{1}{41} = 6\frac{41}{41} - \frac{1}{41} = 6\frac{40}{41}\) в) \(10\frac{12}{55} - 5\frac{25}{55} = (10-5) + (\frac{12}{55} - \frac{25}{55}) = 5 - \frac{13}{55} = 4\frac{55}{55} - \frac{13}{55} = 4\frac{42}{55}\) г) \(3\frac{8}{43} - \frac{40}{43} = 3 + \frac{8}{43} - \frac{40}{43} = 3 - \frac{32}{43} = 2\frac{43}{43} - \frac{32}{43} = 2\frac{11}{43}\)

Задание 9

а) \(2\frac{5}{18} + 3\frac{11}{18} - \frac{5}{18} = (2+3) + (\frac{5}{18} + \frac{11}{18} - \frac{5}{18}) = 5 + \frac{11}{18} = 5\frac{11}{18}\) б) \(3\frac{4}{29} + 5\frac{5}{29} + 2\frac{1}{29} - \frac{9}{29} = (3+5+2) + (\frac{4}{29} + \frac{5}{29} + \frac{1}{29} - \frac{9}{29}) = 10 + \frac{1}{29} = 10\frac{1}{29}\) в) \(2\frac{9}{26} + 1\frac{8}{26} + 1\frac{17}{26} - \frac{8}{26} = (2+1+1) + (\frac{9}{26} + \frac{8}{26} + \frac{17}{26} - \frac{8}{26}) = 4 + \frac{26}{26} = 4 + 1 = 5\) г) \(8\frac{3}{49} + 1\frac{6}{49} + 2\frac{20}{49} - \frac{9}{49} = (8+1+2) + (\frac{3}{49} + \frac{6}{49} + \frac{20}{49} - \frac{9}{49}) = 11 + \frac{20}{49} = 11\frac{20}{49}\)

Задание 10

а) \(12\frac{3}{4} - 1\frac{1}{4} - 3\frac{3}{4} + 2\frac{1}{4} = (12-1-3+2) + (\frac{3}{4} - \frac{1}{4} - \frac{3}{4} + \frac{1}{4}) = 10 + 0 = 10\) б) \(5\frac{9}{35} - 2\frac{22}{35} - 1\frac{12}{35} + 10\frac{26}{35} = (5-2-1+10) + (\frac{9}{35} - \frac{22}{35} - \frac{12}{35} + \frac{26}{35}) = 12 + \frac{1}{35} = 12\frac{1}{35}\) в) \(10\frac{7}{13} - 4\frac{4}{13} - 5\frac{9}{13} + 2\frac{6}{13} = (10-4-5+2) + (\frac{7}{13} - \frac{4}{13} - \frac{9}{13} + \frac{6}{13}) = 3 + 0 = 3\) г) \(8\frac{13}{31} - 2\frac{20}{31} - 2\frac{11}{31} + 6\frac{18}{31} = (8-2-2+6) + (\frac{13}{31} - \frac{20}{31} - \frac{11}{31} + \frac{18}{31}) = 10 + 0 = 10\)

Задание 11

а) \(5\frac{15}{28} + 9\frac{7}{18} - 1\frac{1}{28} + 3\frac{2}{18} = (5-1+9+3) + (\frac{15}{28} - \frac{1}{28} + \frac{7}{18} + \frac{2}{18}) = 16 + (\frac{14}{28} + \frac{9}{18}) = 16 + (\frac{1}{2} + \frac{1}{2}) = 16 + 1 = 17\) б) \(6\frac{18}{37} + 5\frac{11}{20} - 2\frac{18}{37} + 5\frac{9}{20} = (6-2+5+5) + (\frac{18}{37} - \frac{18}{37} + \frac{11}{20} + \frac{9}{20}) = 14 + (0 + \frac{20}{20}) = 14 + 1 = 15\) в) \(4\frac{7}{17} + 1\frac{3}{16} + 2\frac{13}{16} + 5\frac{10}{17} = (4+5+1+2) + (\frac{7}{17} + \frac{10}{17} + \frac{3}{16} + \frac{13}{16}) = 12 + (\frac{17}{17} + \frac{16}{16}) = 12 + 1 + 1 = 14\) г) \(14\frac{6}{19} + 1\frac{7}{8} + 2\frac{5}{8} - 4\frac{6}{19} = (14-4+1+2) + (\frac{6}{19} - \frac{6}{19} + \frac{7}{8} + \frac{5}{8}) = 13 + (0 + \frac{12}{8}) = 13 + \frac{3}{2} = 13 + 1\frac{1}{2} = 14\frac{1}{2}\)

Задание 12

а) \((3\frac{16}{27} + 1\frac{17}{27}) - (2\frac{25}{36} + 1\frac{7}{36}) = (3+1) + (\frac{16}{27} + \frac{17}{27}) - ((2+1) + (\frac{25}{36} + \frac{7}{36})) = 4 + \frac{33}{27} - (3 + \frac{32}{36}) = 4 + 1\frac{6}{27} - (3 + \frac{8}{9}) = 5\frac{2}{9} - 3\frac{8}{9} = 1\frac{11}{9} - \frac{8}{9} = 1\frac{3}{9} = 1\frac{1}{3}\) б) \((3\frac{25}{48} - 1\frac{35}{48}) + (4\frac{65}{72} - 2\frac{68}{72}) = (3-1) + (\frac{25}{48} - \frac{35}{48}) + ((4-2) + (\frac{65}{72} - \frac{68}{72})) = 2 - \frac{10}{48} + 2 - \frac{3}{72} = 4 - (\frac{5}{24} + \frac{1}{24}) = 4 - \frac{6}{24} = 4 - \frac{1}{4} = 3\frac{3}{4}\) в) \((2\frac{8}{35} - 1\frac{13}{35}) + (3\frac{20}{49} - 2\frac{27}{49}) = (2-1) + (\frac{8}{35} - \frac{13}{35}) + ((3-2) + (\frac{20}{49} - \frac{27}{49})) = 1 - \frac{5}{35} + 1 - \frac{7}{49} = 2 - (\frac{1}{7} + \frac{1}{7}) = 2 - \frac{2}{7} = 1\frac{7}{7} - \frac{2}{7} = 1\frac{5}{7}\) г) \((4\frac{7}{15} + 2\frac{11}{15}) - (3\frac{7}{30} + 1\frac{29}{30}) = (4+2) + (\frac{7}{15} + \frac{11}{15}) - ((3+1) + (\frac{7}{30} + \frac{29}{30})) = 6 + \frac{18}{15} - (4 + \frac{36}{30}) = 6 + 1\frac{3}{15} - (4 + 1\frac{6}{30}) = 7\frac{1}{5} - 5\frac{1}{5} = 2\)

Ответ:

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