Bonjour , j'ai besoin d'aide pour mon DM de mathématiques sur les fractions niveau 4ème. (Les calculs doivent etres détaillés et les fractions irréductibles) Vo

Bonjour,

Exercice 2 :  

On donne :  

x=2/3 y=-5/6 z=2/5.

Calculer l'expression :

A=z+x/y

A = 2/5 + 2/3 : - 5/6

A = 2/5 + 2/3 x - 6/5

A = 2/5 - 12/15

A = 2/5 - (3 x 4) / (3 x 5)

A = 2/5 - 4/5

A = - 2/5

Exercice 3 :

A= 3/5+6/5*7/18

A = 3/5 + 42/90

A = (3 x 3) / (5 x 3) + (6 x 7) / (6 x 15)

A = 9/15 + 7/15

A = 16/15

B=8:12/5

B = 8 x 5/12

B = 40/12

B = (4 x 10) / (4 x 3)

B = 10/3

C=(2/3+2/5)*(5/4-5/7)

C = [(2 x 5) / (3 x 5) + (2 x 3) / (5 x 3)] x [(5 x 7) / (4 x 7) - (5 x 4) / (7 x 4)]

C = (10/15 + 6/15) x (35/28 - 20/28)

C = 16/15 x 15/28

C = 240/420

C = (60 x 4) / (60 x 7)

C = 4/7

D=-5/3+18/15:27/25

D = - 5/3 + 18/15 x 25/27

D = - 5/3 + 450/405

D = (- 5 x 3) / (3 x 3) + (45 x 10) / (45 x 9)

D = - 15/9 + 10/9

D = - 5/9

E=(5/8+2)*(2-2/7)

E = [5/8 + (2 x 8) / (1 x 8)] x [(2 x 7) / (1 x 7) - 2/7]

E = (5/8 + 16/8) x (14/7 - 2/7)

E = 21/8 x 12/7

E = 252/56

E = (28 x 9) / (28 x 2)

E = 9/2

F=(3/5+1)*(2+3/5)

F = [3/5 + (1 x 5) / (1 x 5)] x [(2 x 5) / (1 x 5) + 3/5]

F = (3/5 + 5/5) x (10/5 + 3/5)

F = 8/5 x 13/5

F = 104/25

Réponse :

Exercice 2 :

A = 2/5 + 2/3 : 5/6 = 2/5 + 2/3 x 6/5 = 2/5 + 4/5 = 6/5

Exercice 3 :

A = 3/5 + 6/5 x 7/18 = 3/5 + 7/15 = 9/15 + 7/15 = 16/15

B = 8 : 12/5 = 8 x 5/12 = 10/3

C = ( 2/3 + 2/5 ) x ( 5/4 - 5/7 ) = ( 10/15 + 6/15 ) x ( 35/28 - 20/28 )

C = 16/15 x 15/28 = 4/7

D = -5/3 + 18/15 : 27/25 = -5/3 + 18/15 x 25/27 =- 5/3 + 10/9 = -15/9 + 10/9

D = -5/9

E = ( 5/8 + 2 ) x ( 2 - 2/7 ) = ( 5/8 + 16/8 ) x ( 14/7 - 2/7 )

E= 21/8 x 12/7 = 9/2

F = ( 3/5 + 1 ) x ( 2 + 3/5 ) = ( 3/5 + 5/5 ) x ( 10/5 + 3/5 )

F = 8/5 x 13/5 = 104/25