5.7 Раскройте скобки и найдите значение суммы: а) 5/9 + (4/9 – 7/11); г) 7/15 – (4/15 – 4/5); д) 6 7/9 – (3 4/9 + 2 1/3); ж) (4 1/4 – 6 8/11) + (6,75 – 3 3/11); б) 5 3/7 + (-3/7 – 8/9); в) 4,32 + (12/13 – 3,32); e) -9 11/12 – (1/4 – 5/12); з) (9 7/18 – 2,7) – (4 1/18 + 2,3).

Ответ:

1. a) \[\frac{5}{9} + (\frac{4}{9} - \frac{7}{11}) = \frac{5}{9} + \frac{4}{9} - \frac{7}{11} = \frac{9}{9} - \frac{7}{11} = 1 - \frac{7}{11} = \frac{11}{11} - \frac{7}{11} = \frac{4}{11}\]
2. б) \[5 \frac{3}{7} + (-\frac{3}{7} - \frac{8}{9}) = 5 \frac{3}{7} - \frac{3}{7} - \frac{8}{9} = 5 - \frac{8}{9} = 4 \frac{9}{9} - \frac{8}{9} = 4 \frac{1}{9}\]
3. в) \[4.32 + (\frac{12}{13} - 3.32) = 4.32 - 3.32 + \frac{12}{13} = 1 + \frac{12}{13} = \frac{13}{13} + \frac{12}{13} = \frac{25}{13} = 1 \frac{12}{13}\]
4. г) \[\frac{7}{15} - (\frac{4}{15} - \frac{4}{5}) = \frac{7}{15} - \frac{4}{15} + \frac{4}{5} = \frac{3}{15} + \frac{12}{15} = \frac{15}{15} = 1\]
5. д) \[6 \frac{7}{9} - (3 \frac{4}{9} + 2 \frac{1}{3}) = 6 \frac{7}{9} - 3 \frac{4}{9} - 2 \frac{1}{3} = 6 \frac{7}{9} - 3 \frac{4}{9} - 2 \frac{3}{9} = 6 \frac{7}{9} - 5 \frac{7}{9} = 1\]
6. e) \[-9 \frac{11}{12} - (\frac{1}{4} - \frac{5}{12}) = -9 \frac{11}{12} - \frac{3}{12} + \frac{5}{12} = -9 \frac{11}{12} - \frac{3}{12} + \frac{5}{12} = -9 \frac{9}{12} = -9 \frac{3}{4}\]
7. ж) \[(4 \frac{1}{4} - 6 \frac{8}{11}) + (6.75 - 3 \frac{3}{11}) = (4.25 - 6 \frac{8}{11}) + (6.75 - 3 \frac{3}{11}) = 4.25 - 6 \frac{8}{11} + 6.75 - 3 \frac{3}{11} = 4.25 + 6.75 - 6 \frac{8}{11} - 3 \frac{3}{11} = 11 - 9 \frac{11}{11} = 11 - 10 = 1\]
8. з) \[(9 \frac{7}{18} - 2.7) - (4 \frac{1}{18} + 2.3) = (9 \frac{7}{18} - 2.7) - (4 \frac{1}{18} + 2.3) = 9 \frac{7}{18} - 2.7 - 4 \frac{1}{18} - 2.3 = 9 \frac{7}{18} - 4 \frac{1}{18} - 2.7 - 2.3 = 5 \frac{6}{18} - 5 = 5 \frac{1}{3} - 5 = \frac{1}{3}\]

Ответ: 4/11; 4 1/9; 1 12/13; 1; 1; -9 3/4; 1; 1/3