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{9}{31}; г) 3\frac{19}{19} - 1\frac{4}{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{17}{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})

Решение:

Давай решим эти примеры с дробями по порядку. Будем складывать и вычитать дроби, а также упрощать результаты, если это возможно.

1. a) \(\frac{7}{8} + \frac{5}{8} = \frac{7+5}{8} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}\) b) \(\frac{5}{12} + \frac{7}{12} = \frac{5+7}{12} = \frac{12}{12} = 1\) в) \(\frac{3}{10} + \frac{9}{10} = \frac{3+9}{10} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}\) г) \(\frac{8}{19} + \frac{11}{19} = \frac{8+11}{19} = \frac{19}{19} = 1\) 2. a) \(1\frac{1}{18} + 2\frac{5}{18} = (1+2) + (\frac{1}{18} + \frac{5}{18}) = 3 + \frac{6}{18} = 3 + \frac{1}{3} = 3\frac{1}{3}\) 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) \(\frac{8}{19} + \frac{11}{19} = \frac{8+11}{19} = \frac{19}{19} = 1\) 3. a) \(1\frac{3}{5} + 1\frac{4}{5} = (1+1) + (\frac{3}{5} + \frac{4}{5}) = 2 + \frac{7}{5} = 2 + 1\frac{2}{5} = 3\frac{2}{5}\) 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) \(2\frac{3}{4} + 2\frac{3}{4} = (2+2) + (\frac{3}{4} + \frac{3}{4}) = 4 + \frac{6}{4} = 4 + 1\frac{2}{4} = 4 + 1\frac{1}{2} = 5\frac{1}{2}\) г) \(1\frac{5}{8} + 3\frac{7}{8} = (1+3) + (\frac{5}{8} + \frac{7}{8}) = 4 + \frac{12}{8} = 4 + 1\frac{4}{8} = 4 + 1\frac{1}{2} = 5\frac{1}{2}\) 4. a) \(1\frac{12}{23} + 2\frac{12}{23} = (1+2) + (\frac{12}{23} + \frac{12}{23}) = 3 + \frac{24}{23} = 3 + 1\frac{1}{23} = 4\frac{1}{23}\) б) \(1\frac{11}{15} + 3\frac{7}{15} = (1+3) + (\frac{11}{15} + \frac{7}{15}) = 4 + \frac{18}{15} = 4 + 1\frac{3}{15} = 4 + 1\frac{1}{5} = 5\frac{1}{5}\) 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) \(3\frac{17}{20} + 1\frac{19}{20} = (3+1) + (\frac{17}{20} + \frac{19}{20}) = 4 + \frac{36}{20} = 4 + 1\frac{16}{20} = 4 + 1\frac{4}{5} = 5\frac{4}{5}\) 5. a) \(2\frac{13}{14} - 1\frac{9}{14} = (2-1) + (\frac{13}{14} - \frac{9}{14}) = 1 + \frac{4}{14} = 1 + \frac{2}{7} = 1\frac{2}{7}\) 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) \(5\frac{18}{31} - 2\frac{9}{31} = (5-2) + (\frac{18}{31} - \frac{9}{31}) = 3 + \frac{9}{31} = 3\frac{9}{31}\) г) \(3\frac{19}{19} - 1\frac{4}{19} = 3 + 1 - 1\frac{4}{19} = 4 - 1\frac{4}{19} = 3 - \frac{4}{19} = 2\frac{19}{19} - \frac{4}{19} = 2\frac{15}{19}\) 6. a) \(2\frac{7}{15} - 1\frac{8}{15} = 1\frac{7}{15} - \frac{8}{15} = \frac{22}{15} - \frac{8}{15} = \frac{14}{15}\) б) \(5\frac{3}{16} - 2\frac{7}{16} = 4\frac{19}{16} - 2\frac{7}{16} = 2\frac{12}{16} = 2\frac{3}{4}\) в) \(9\frac{1}{20} - 2\frac{10}{20} = 8\frac{21}{20} - 2\frac{10}{20} = 6\frac{11}{20}\) г) \(5\frac{9}{31} - 1\frac{29}{31} = 4\frac{40}{31} - 1\frac{29}{31} = 3\frac{11}{31}\) 7. a) \(7\frac{1}{32} - 2\frac{3}{32} = 6\frac{33}{32} - 2\frac{3}{32} = 4\frac{30}{32} = 4\frac{15}{16}\) б) \(1\frac{5}{18} - \frac{6}{18} = \frac{23}{18} - \frac{6}{18} = \frac{17}{18}\) в) \(6\frac{2}{7} - 1\frac{5}{7} = 5\frac{9}{7} - 1\frac{5}{7} = 4\frac{4}{7}\) г) \(1\frac{9}{20} - \frac{19}{20} = \frac{29}{20} - \frac{19}{20} = \frac{10}{20} = \frac{1}{2}\) 8. a) \(2\frac{4}{37} - 1\frac{5}{37} = 1\frac{41}{37} - 1\frac{5}{37} = \frac{36}{37}\) б) \(7\frac{8}{41} - \frac{9}{41} = 6\frac{49}{41} - \frac{9}{41} = 6\frac{40}{41}\) в) \(10\frac{12}{55} - 5\frac{25}{55} = 9\frac{67}{55} - 5\frac{25}{55} = 4\frac{42}{55}\) г) \(3\frac{8}{43} - \frac{40}{43} = 2\frac{51}{43} - \frac{40}{43} = 2\frac{11}{43}\) 9. a) \(2\frac{5}{18} + 3\frac{11}{18} - \frac{5}{18} = 5\frac{16}{18} - \frac{5}{18} = 5\frac{11}{18}\) б) \(3\frac{4}{29} + 5\frac{5}{29} + 2\frac{1}{29} - \frac{9}{29} = 10\frac{10}{29} - \frac{9}{29} = 10\frac{1}{29}\) в) \(2\frac{9}{26} + 1\frac{8}{26} + 1\frac{17}{26} - \frac{8}{26} = 4\frac{34}{26} - \frac{8}{26} = 4\frac{26}{26} = 5\) г) \(8\frac{3}{49} + 1\frac{6}{49} + 2\frac{20}{49} - \frac{9}{49} = 11\frac{29}{49} - \frac{9}{49} = 11\frac{20}{49}\) 10. a) \(12\frac{3}{4} - 1\frac{1}{4} - 3\frac{3}{4} + 2\frac{1}{4} = 11\frac{2}{4} - 3\frac{3}{4} + 2\frac{1}{4} = 7\frac{3}{4} + 2\frac{1}{4} = 9\frac{4}{4} = 10\) б) \(5\frac{9}{35} - 2\frac{22}{35} - 1\frac{12}{35} + 10\frac{26}{35} = 3\frac{9}{35} - 1\frac{12}{35} + 10\frac{26}{35} = 2\frac{32}{35} + 10\frac{26}{35} = 12\frac{58}{35} = 13\frac{23}{35}\) в) \(10\frac{7}{13} - 4\frac{4}{13} - 5\frac{9}{13} + 2\frac{6}{13} = 6\frac{3}{13} - 5\frac{9}{13} + 2\frac{6}{13} = 0\frac{7}{13} + 2\frac{6}{13} = 2\frac{13}{13} = 3\) г) \(8\frac{13}{31} - 2\frac{20}{31} - 2\frac{11}{31} + 6\frac{18}{31} = 6\frac{24}{31} - 2\frac{11}{31} + 6\frac{18}{31} = 4\frac{13}{31} + 6\frac{18}{31} = 10\frac{31}{31} = 11\) 11. a) \(5\frac{15}{28} + 9\frac{7}{18} - 1\frac{1}{28} + 3\frac{2}{18} = 14\frac{14}{28} + 12\frac{9}{18} = 14\frac{1}{2} + 12\frac{1}{2} = 27\) б) \(6\frac{18}{37} + 5\frac{11}{20} - 2\frac{18}{37} + 5\frac{9}{20} = 4\frac{0}{37} + 10\frac{20}{20} = 4 + 11 = 15\) в) \(4\frac{17}{17} + 1\frac{3}{16} + 2\frac{13}{16} + 5\frac{10}{17} = 4 + 1 + 1\frac{3}{16} + 2\frac{13}{16} + 5 = 10 + 3\frac{16}{16} = 10 + 4 = 14\) г) \(14\frac{6}{19} + 1\frac{7}{8} + 2\frac{5}{8} - 4\frac{6}{19} = 10\frac{0}{19} + 3\frac{12}{8} = 10 + 4\frac{4}{8} = 14\frac{1}{2}\) 12. a) \((3\frac{16}{27} + 1\frac{17}{27}) - (2\frac{25}{36} + 1\frac{7}{36}) = 4\frac{33}{27} - 3\frac{32}{36} = 5\frac{6}{27} - 3\frac{8}{9} = 5\frac{2}{9} - 3\frac{8}{9} = 4\frac{11}{9} - 3\frac{8}{9} = 1\frac{3}{9} = 1\frac{1}{3}\) б) \((3\frac{25}{48} - 1\frac{35}{48}) + (4\frac{65}{72} - 2\frac{68}{72}) = 1\frac{38}{48} + 1\frac{69}{72} = 1\frac{19}{24} + 1\frac{23}{24} = 2\frac{42}{24} = 3\frac{18}{24} = 3\frac{3}{4}\) в) \((2\frac{8}{35} - 1\frac{13}{35}) + (3\frac{20}{49} - 2\frac{27}{49}) = 0\frac{40}{35} + 0\frac{93}{49} = 1\frac{5}{35} + 1\frac{44}{49} = 1\frac{1}{7} + 1\frac{44}{49} = 2\frac{7+44}{49} = 2\frac{51}{49} = 3\frac{2}{49}\) г) \((4\frac{7}{15} + 2\frac{11}{15}) - (3\frac{7}{30} + 1\frac{29}{30}) = 6\frac{18}{15} - 4\frac{36}{30} = 7\frac{3}{15} - 5\frac{6}{30} = 7\frac{1}{5} - 5\frac{1}{5} = 2\)

Ответ: смотри выше

Ты отлично поработал(а) над этими примерами! Продолжай в том же духе, и у тебя всё получится!