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Bonjour
Sachant que ∶ a=-1/2 , b=-2/3 , c= 4/5 et d= -1/6 Calculer:
1°. a+b+c
- 1/2 - 2/3 + 4/5
= (- 1 x 30) / (2 x 30) - (2 x 20) / (3 x 20) + (4 x 12) / (5 x 12)
= - 30/60 - 40/60 + 48/60
= -22/60
= (2 x - 11) / (2 x 30)
= - 11/30
2°.a×b×c×d
- 1/2 * - 2/3 * 4/5* - 1/6
= 2/6 * - 4/30
= - 8/180
= (4 x - 2) / (4 x 45
= - 2/45
3°.(a+c)(a-c)
(- 1/2 + 4/5) (- 1/2 - 4/5)
= [(- 1 x 5) / (2 x 5) + (4 x 2) / (5 x 2)] [(- 1 x 5) / (2 x 5) - (4 x 2) / (5 x 2)]
= (- 5/10 + 8/10) (- 5/10 - 8/10)
= 3/10 / - 13/10
= - 39/100
4°.(1/c+1/d)×b+d
(1 : 4/5 + 1 : - 1/6) / - 2/3 - 1/6
= (1 x 5/4 + 1 x - 6) / - 2/3 - 1/6
= (5/4 - 6) / - 2/3 - 1/6
= [5/4 - (6 x 4) / (1 x 4)] x - 3/2 - 1/6
= (5/4 - 24/4) x - 3/2 - 1/6
= - 19/4 x - 3/2 - 1/6
= 57/8 - 1/6
= (57 x 3) / (8 x 3) - (1 x 4) / (6 x 4)
= 171/24 - 4/24
= 167/24
5°. (a-b)/(a+b)-c
(- 1/2 + 2/3) / (- 1/2 - 2/3) - 4/5
= [(- 1 x 3) / (2 x 3) + (2 x 2) / (3 x 2)] / [(- 1 x 3) / (2 x 3) - (2 x 2) / (3 x 2)] - 4/5
= (- 3/6 + 4/6) / (- 3/6 - 4/6) - 4/5
= 1/6 : - 7/6 - 4/5
= 1/6 x - 6/7 - 4/5
= - 6/42 - 4/5
= (6 x - 1) / (6 x 7) - 4/5
= - 1/7 - 4/5
= (- 1 x 5) / (7 x 5) - (4 x 7) / (5 x 7)
= - 5/35 - 28/35
= - 33/35
6°.d-d÷(a×c)
- 1/6 - 1/6 : (- 1/2 * 4/5)
= 1/6 - 1/6 : -4/10)
= 1/6 - 1/6 x - 10/4
= 1/6 + 10/24
= (1 x 2) / (6 x 2) + (2 x 5) / (2 x 12)
= 2/12 + 5/12
= 7/12
7°. a/(b-c)+d/a
- 1/2 : (- 2/3 - 4/5) - 1/6 : - 1/2
= - 1/2 : [(- 2 x 5) / (3 x 5) - (4 x 3) / (5 x 3)] - 1/6 x - 2
= - 1/2 : (- 10/15 - 12/15) + 2/6
= - 1/2 : - 22/15 + 2/6
= - 1/2 x - 15/22 + 2/6
= 12/44 + 2/6
= (4 x 3) / (4 x 11) + (2 x 1) / (2 x 3)
= 3/11 + 1/3
= (3 x 3) / (11 x 3) + (1 x 11) / (3 x 11)
= 9/33 + 11/33
= 20/33.
