\(a,-\dfrac{5}{9}+\dfrac{14}{9}=\dfrac{-5+14}{9}=\dfrac{9}{9}=1\\ b,\dfrac{2}{7}+\dfrac{8}{-3}\\ =\dfrac{2}{7}-\dfrac{8}{3}\\ =\dfrac{2.3-8.7}{21}\\ =\dfrac{6-56}{21}\\ =\dfrac{-50}{21}\\ c,\dfrac{9}{11}+\dfrac{5}{7}+\dfrac{20}{-11}+\dfrac{12}{25}+\dfrac{2}{7}\\ =\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{9}{11}-\dfrac{20}{11}\right)+\dfrac{12}{25}\\ =\dfrac{7}{7}-\dfrac{11}{11}+\dfrac{12}{25}\\ =1-1+\dfrac{12}{25}\\ =\dfrac{12}{25}\)
a) -5/9 + 14/9 = (-5) + 14/9 = 9/9 = 1 b) 2/7 + 8/-3 = 2/7 + -8/3 = 2 . 3/7 .3 + (-8) . 7/3 . 7 = 6/21 + (-56)/21 = 6 + (-56)/21 = (-50)/21 c) 9/11 + 5/7 + 20/-11 + 12/25 + 2/7 = 9/11 + 5/7 + (-20)/11 + 12/25 + 2/7 = [ 9/11 + (-20)/11 ] + ( 5/7 + 2/7) + 12/25 = (-29)/11 + 7/7 + 12/25 = (-29)/11 + 1 + 12/25 = (-29) . 25/11 . 25 + 275/275 + 12 .11/25.11 = (-725)/275 + 275/275 + 132/275 = (-1000)/275 + 132/275 = (-868)/275