КР Сложение и вычитание дробей с одинаковыми знаменателями ните действия: а) 6/15 + 8/15 - 9/15, б) 11/17 - 8/17 + 7/17, в) (6/16 + 5/16) - 8/16, г) 19/25 - (11/25 + 2/25). е уравнения: a) x+3/13 = 8/13, б) 11/21 - (x-9/21) = 5/21, в) 5/9 + (x-3/9) = 8/9 ните действия: а) 7/29 + 9/29 - 11/29, б) 17/31 - 14/31 + 5/31, в) (9/15 + 5/15) - 12/15, г) 16/18 - (2/18 + 9/18) • уравнения: a) x-5/13 = 7/13, б) 17/26 - (x+7/26) = 5/26, в) (x-2/8) + 3/8 = 7/8 ните действия: а) 8/14 + 5/14 - 9/14, б) 13/21 - 8/21 + 11/21, в) (7/27 + 16/27) - 18/27, г) 16/19 - (9/19 + 3/19) е уравнения: a) x + 6/16 = 8/16, б) 19/25 - (x-7/25) = 6/25, в) 6/11 + (x-5/11) = 10/11 итевия: а) 19/25 + 5/25 - 17/25, б) 17/19 - 9/19 + 7/19, в) (13/21 + 6/21) - 17/21, г) 23/29 - (11/29 + 3/29) увнения: x + 4/11 = 9/11, б) 18/23 - (x-2/23) = 14/23, в) 4/16 + (x-7/16) = 11/16

Действия с дробями

1. а) \[ \frac{6}{15} + \frac{8}{15} - \frac{9}{15} = \frac{6+8-9}{15} = \frac{5}{15} = \frac{1}{3} \]
2. б) \[ \frac{11}{17} - \frac{8}{17} + \frac{7}{17} = \frac{11-8+7}{17} = \frac{10}{17} \]
3. в) \[ (\frac{6}{16} + \frac{5}{16}) - \frac{8}{16} = \frac{6+5}{16} - \frac{8}{16} = \frac{11}{16} - \frac{8}{16} = \frac{3}{16} \]
4. г) \[ \frac{19}{25} - (\frac{11}{25} + \frac{2}{25}) = \frac{19}{25} - \frac{11+2}{25} = \frac{19}{25} - \frac{13}{25} = \frac{6}{25} \]

Решение уравнений

1. а) \[ x + \frac{3}{13} = \frac{8}{13} \] \[ x = \frac{8}{13} - \frac{3}{13} \] \[ x = \frac{5}{13} \]
2. б) \[ \frac{11}{21} - (x - \frac{9}{21}) = \frac{5}{21} \] \[ \frac{11}{21} - x + \frac{9}{21} = \frac{5}{21} \] \[ \frac{20}{21} - x = \frac{5}{21} \] \[ x = \frac{20}{21} - \frac{5}{21} \] \[ x = \frac{15}{21} = \frac{5}{7} \]
3. в) \[ \frac{5}{9} + (x - \frac{3}{9}) = \frac{8}{9} \] \[ \frac{5}{9} + x - \frac{3}{9} = \frac{8}{9} \] \[ x + \frac{2}{9} = \frac{8}{9} \] \[ x = \frac{8}{9} - \frac{2}{9} \] \[ x = \frac{6}{9} = \frac{2}{3} \]

Действия с дробями

1. а) \[ \frac{7}{29} + \frac{9}{29} - \frac{11}{29} = \frac{7+9-11}{29} = \frac{5}{29} \]
2. б) \[ \frac{17}{31} - \frac{14}{31} + \frac{5}{31} = \frac{17-14+5}{31} = \frac{8}{31} \]
3. в) \[ (\frac{9}{15} + \frac{5}{15}) - \frac{12}{15} = \frac{9+5}{15} - \frac{12}{15} = \frac{14}{15} - \frac{12}{15} = \frac{2}{15} \]
4. г) \[ \frac{16}{18} - (\frac{2}{18} + \frac{9}{18}) = \frac{16}{18} - \frac{2+9}{18} = \frac{16}{18} - \frac{11}{18} = \frac{5}{18} \]

Решение уравнений

1. а) \[ x - \frac{5}{13} = \frac{7}{13} \] \[ x = \frac{7}{13} + \frac{5}{13} \] \[ x = \frac{12}{13} \]
2. б) \[ \frac{17}{26} - (x + \frac{7}{26}) = \frac{5}{26} \] \[ \frac{17}{26} - x - \frac{7}{26} = \frac{5}{26} \] \[ \frac{10}{26} - x = \frac{5}{26} \] \[ x = \frac{10}{26} - \frac{5}{26} \] \[ x = \frac{5}{26} \]
3. в) \[ (x - \frac{2}{8}) + \frac{3}{8} = \frac{7}{8} \] \[ x - \frac{2}{8} + \frac{3}{8} = \frac{7}{8} \] \[ x + \frac{1}{8} = \frac{7}{8} \] \[ x = \frac{7}{8} - \frac{1}{8} \] \[ x = \frac{6}{8} = \frac{3}{4} \]

Действия с дробями

1. а) \[ \frac{8}{14} + \frac{5}{14} - \frac{9}{14} = \frac{8+5-9}{14} = \frac{4}{14} = \frac{2}{7} \]
2. б) \[ \frac{13}{21} - \frac{8}{21} + \frac{11}{21} = \frac{13-8+11}{21} = \frac{16}{21} \]
3. в) \[ (\frac{7}{27} + \frac{16}{27}) - \frac{18}{27} = \frac{7+16}{27} - \frac{18}{27} = \frac{23}{27} - \frac{18}{27} = \frac{5}{27} \]
4. г) \[ \frac{16}{19} - (\frac{9}{19} + \frac{3}{19}) = \frac{16}{19} - \frac{9+3}{19} = \frac{16}{19} - \frac{12}{19} = \frac{4}{19} \]

Решение уравнений

1. а) \[ x + \frac{6}{16} = \frac{8}{16} \] \[ x = \frac{8}{16} - \frac{6}{16} \] \[ x = \frac{2}{16} = \frac{1}{8} \]
2. б) \[ \frac{19}{25} - (x - \frac{7}{25}) = \frac{6}{25} \] \[ \frac{19}{25} - x + \frac{7}{25} = \frac{6}{25} \] \[ \frac{26}{25} - x = \frac{6}{25} \] \[ x = \frac{26}{25} - \frac{6}{25} \] \[ x = \frac{20}{25} = \frac{4}{5} \]
3. в) \[ \frac{6}{11} + (x - \frac{5}{11}) = \frac{10}{11} \] \[ \frac{6}{11} + x - \frac{5}{11} = \frac{10}{11} \] \[ x + \frac{1}{11} = \frac{10}{11} \] \[ x = \frac{10}{11} - \frac{1}{11} \] \[ x = \frac{9}{11} \]

Действия с дробями

1. а) \[ \frac{19}{25} + \frac{5}{25} - \frac{17}{25} = \frac{19+5-17}{25} = \frac{7}{25} \]
2. б) \[ \frac{17}{19} - \frac{9}{19} + \frac{7}{19} = \frac{17-9+7}{19} = \frac{15}{19} \]
3. в) \[ (\frac{13}{21} + \frac{6}{21}) - \frac{17}{21} = \frac{13+6}{21} - \frac{17}{21} = \frac{19}{21} - \frac{17}{21} = \frac{2}{21} \]
4. г) \[ \frac{23}{29} - (\frac{11}{29} + \frac{3}{29}) = \frac{23}{29} - \frac{11+3}{29} = \frac{23}{29} - \frac{14}{29} = \frac{9}{29} \]

Решение уравнений

1. а) \[ x + \frac{4}{11} = \frac{9}{11} \] \[ x = \frac{9}{11} - \frac{4}{11} \] \[ x = \frac{5}{11} \]
2. б) \[ \frac{18}{23} - (x - \frac{2}{23}) = \frac{14}{23} \] \[ \frac{18}{23} - x + \frac{2}{23} = \frac{14}{23} \] \[ \frac{20}{23} - x = \frac{14}{23} \] \[ x = \frac{20}{23} - \frac{14}{23} \] \[ x = \frac{6}{23} \]
3. в) \[ \frac{4}{16} + (x - \frac{7}{16}) = \frac{11}{16} \] \[ \frac{4}{16} + x - \frac{7}{16} = \frac{11}{16} \] \[ x - \frac{3}{16} = \frac{11}{16} \] \[ x = \frac{11}{16} + \frac{3}{16} \] \[ x = \frac{14}{16} = \frac{7}{8} \]