a. a = 5/6 + -1/3
a = 5/6-1/3
on met au dénominateur commun 6 (2*3=6 ou * signifie muiltiplié par)
a = 5/6 - (1*2)/(3*2) = 5/6 - 2/6 = (5-2)/6 = 3/6 = (3*1) / (3*2) = 3/3 * 1/2
a = 1/2
b. b = 7/9 - (1/-27) = 7/9 -(-1/27)
Quand on écrit -(-1/27) c'est comme écrire -1*(-1/27) or -1*-1 = +1 donc
b = 7/9 + 1/27
on met au dénominateur commun 27 (9*3=27)
b = (3*7)/(3*9) + 1/27 = 21/27+1/27 = (21+1)/27
b = 22/27
c. c = -8/5 + 23/50
on met au dénominateur commun 50 (5*10=50)
c = (-8*10)/(5*10) +23/50 = -80/50 + 23/50 = (-80+23)/50 = (23-80)/50 =
c = -57/50
d. d = 45/15 - 7/3 = (15*3)/(15*1) -7/3 = 3/1 - 7/3 = (3*3)/(3*1) -7/3
d = 9/3-7/3 = (9-7)/3
d = 2/3
e. e = 14/11+2 = 14/11+2/1 = 14/11 +(11*2)/(11*1) = 14/11+22/11 = (14+22)/11
e = 36/11
f. f= 8/-91+(-1/7) = -8/91-1/7
on met au dénominateur commun 91 (13*7=91)
f = -8/91 - (1*13)/(7*13) = -8/93-13/91 = (-8-13)/91 = -21/91 =(-3*7)/(13*7) =-3/13*7/7
f = -3/13
g. g = 5/2 - (-45)/4 + 2/8 = (5*2)/(2*2) +45/4 + (1*2)/(4*2)
g = 10/4 + 45/4 + 1/4 = (10+45+1) /4 = 56/4 = (14*4)/(1*4)
g = 14
h. h = 4-5/(-49) +(-8/7) = 4 + 5/49 - 8/7
on met au dénominateur commun 49 (7*7=49 et 1*49=49)
h = (4*49)/49 +5/49 + (8*7)/(7*7) = 196/49 +5/49 - 56/49 = (196+5-56)/49
h = 145/49
