5.7 Раскройте скобки и найдите значение суммы: a) \frac{5}{9} + (\frac{4}{9} - \frac{7}{11}); б) 5\frac{3}{7} + (-\frac{3}{7} - \frac{8}{9}); в) 4,32 + (\frac{12}{13} - 3,32); г) 6\frac{7}{9} - (3\frac{4}{21} + 2\frac{1}{3}); д) 6\frac{7}{15} - (\frac{4}{15} - \frac{4}{5}); e) -\frac{9}{12} - (\frac{1}{4} - \frac{11}{12}); ж) (4\frac{1}{4} - 6\frac{8}{11}) + (6,75 - 3\frac{3}{11}); з) (9\frac{7}{18} - 2,7) - (4\frac{1}{18} + 2,3).

Ответ: Результаты ниже

• a) \[ \frac{5}{9} + (\frac{4}{9} - \frac{7}{11}) = \frac{5}{9} + \frac{4}{9} - \frac{7}{11} = \frac{9}{9} - \frac{7}{11} = 1 - \frac{7}{11} = \frac{11}{11} - \frac{7}{11} = \frac{4}{11} \]
• б) \[ 5\frac{3}{7} + (-\frac{3}{7} - \frac{8}{9}) = 5\frac{3}{7} - \frac{3}{7} - \frac{8}{9} = 5 - \frac{8}{9} = 4\frac{9}{9} - \frac{8}{9} = 4\frac{1}{9} \]
• в) \[ 4,32 + (\frac{12}{13} - 3,32) = 4,32 + \frac{12}{13} - 3,32 = 1 + \frac{12}{13} = \frac{13}{13} + \frac{12}{13} = \frac{25}{13} = 1\frac{12}{13} \]
• г) \[ 6\frac{7}{9} - (3\frac{4}{21} + 2\frac{1}{3}) = 6\frac{7}{9} - 3\frac{4}{21} - 2\frac{1}{3} = 6\frac{49}{63} - 3\frac{12}{63} - 2\frac{21}{63} = (6-3-2) + (\frac{49}{63} - \frac{12}{63} - \frac{21}{63}) = 1 + \frac{16}{63} = 1\frac{16}{63} \]
• д) \[ 6\frac{7}{15} - (\frac{4}{15} - \frac{4}{5}) = 6\frac{7}{15} - \frac{4}{15} + \frac{4}{5} = 6\frac{3}{15} + \frac{12}{15} = 6\frac{15}{15} = 7 \]
• е) \[ -\frac{9}{12} - (\frac{1}{4} - \frac{11}{12}) = -\frac{9}{12} - \frac{1}{4} + \frac{11}{12} = -\frac{9}{12} - \frac{3}{12} + \frac{11}{12} = \frac{-9-3+11}{12} = \frac{-1}{12} = -\frac{1}{12} \]
• ж) \[ (4\frac{1}{4} - 6\frac{8}{11}) + (6,75 - 3\frac{3}{11}) = 4,25 - 6\frac{8}{11} + 6,75 - 3\frac{3}{11} = (4,25 + 6,75) + (- 6\frac{8}{11} - 3\frac{3}{11}) = 11 - 9\frac{11}{11} = 11 - 10 = 1 \]
• з) \[ (9\frac{7}{18} - 2,7) - (4\frac{1}{18} + 2,3) = 9\frac{7}{18} - 2,7 - 4\frac{1}{18} - 2,3 = 9\frac{7}{18} - 4\frac{1}{18} - 2,7 - 2,3 = 5\frac{6}{18} - 5 = 5\frac{1}{3} - 5 = \frac{1}{3} \]

Ответ: Результаты выше