a= (3/5 - 1/2) x 5/2 b = 3-2/3 / 4/3 x 7 c = 8/3 - 2/3 : 8/7 d = -2 / 5 + 5/2 / -3/4 + 1/2 1. prouve que a = b 2. calculer c et d et donne les resultat sous la

A= (3/5 - 1/2) x 5/2
a = (6/10-5/10) x5/2
a = 1/10 x5/2
a = 5/20
a = 1/4

b = 3-2/3 / 4/3 x 7
b = 9/3 -2/3  / 28/3
b = 7/3 x 3/28
b = 7/28
b = 1/4

donc a = b


c = 8/3 - 2/3 : 8/7
c= 6/3 : 8/7
c = 2 x 7/8
c = 14/8
c = 7/4

d = -2 / 5 + 5/2 / -3/4 + 1/2
d = -4/10 +25/10  / -3/4 +2/4
d = 21/10 / -1/4
d = 21/10 x -4
d = -44/10
d = -22/5


b = 1/4  donc son inverse b = 4

d = -22 /5  son oppose = + 22/5

b+d = 1/4 -22/5 = 5/20 -88/20 = -83/20


cxd = 7/4 x -22/5 =  -154/20 = -77/10


c/d =  7/4 / -22/5 = 7/4 x -5/22 =-35 /88

1. Prouve que a = b
A = (3/5 - 1/2) x 5/2
A = (3 x 2 / 5 x 2 - 1 x 5 / 2 x 5) x 5/2
A = (6/10 - 5/10) x 5/2
A = 1/10 x 5/2
A = 5/20
A = 5 x 1 / 5 x 4
A = 1/4

B = 3 - 2/3
     4/3 x 7
B = 3 x 3 / 1 x 3 - 2/3
              28/3
B = 9/3 - 2/3
         28/3
B = 7/3 : 28/3
B = 7/3 x 3/28
B = 21/84
B = 21 x 1 / 21 x 4
B = 1/4

1/4 = 1/4, donc A = B

2. Calculer c et d et donne les résultats sous la forme d'une fraction la plus simplifiée possible 
C = 8/3 - 2/3 : 8/7
C = 8/3 - 2/3 x 7/8
C = 8/3 - 14/24
C = 8 x 8 / 3 x 8 - 14/24
C = 64/24 - 14/24
C = 50/24
C = 2 x 25 / 2 x 12
C = 25/12

D = - 2/5 + 5/2
       - 3/4 + 1/2
D = - 2 x 2 / 5 x 2 + 5 x 5 / 2 x 5
           - 3/4 + 1 x 2 / 2 x 2
D = - 4/10 + 25/10
         - 3/4 + 2/4
D = 21/10 : - 1/4
D = 21/10 x - 4
D = - 84/10
D = 2 x - 42 / 2 x 5
D = - 42/5

3 Donne l'inverse de b et l'opposé de d
Inverse de B = inverse de 1/4 = 4

4. Calculer b + d , c x d et c/d
B + D
= 1/4 + (- 42/5)
= 1 x 5 / 4 x 5 - 42 x 4 / 5 x 4
= 5/20 - 168/20
= - 163/20

C x D
= 25/12 x - 42/5
= - 1050/60
= 30 x - 35 / 30 x 2
= - 35/2

C/D
= 25/12 : - 42/5
= 25/12 x - 5/42
= - 125/504