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Sagot :
Calculer chaque expression sachant que :
M = 1/9 ; N = 2/3 ; P = 5/18
a) m + n
1/9 + 5/18
= 1 x 2 / 9 x 2 + 5/18
= 2/18 + 5/18
= 7/18
b) p - m
5/18 - 1/9
= 5/18 - 1 x 2 / 9 x 2
= 5/18 - 2/18
= 3/18
= 3 x 1 / 3 x 6
= 1/6
c) np
2/3 x 5/18
= 2 x 5
3 x 18
= 10/54
= 2 x 5 / 2 x 27
= 5/27
----------------------------------------------
Exercice 2 ;
A = 3/8 x (4/9 + 2/3)
A = 3/8 x (4/9 + 2 x 3 / 3 x 3)
A = 3/8 x (4/9 + 6/9)
A = 3/8 x 10/9
A = 3 x 10
8 x 9
A = 30/72
A = 6 x 5 / 6 x 12
A = 5/12
B = 3/8 x 4/9 + 2/3
B = 3 x 4 + 2/3
8 x 9
B = 12/72 + 2/3
B = 12/72 + 2 x 24 / 3 x 24
B = 12/72 + 48/72
B = 60/72
B = 12 x 5 / 12 x 6
B = 5/6
C = 7/5 x (3/10 + 1/5)
C = 7/5 x (3/10 + 1 x 2 / 5 x 2)
C = 7/5 x (3/10 + 2/10)
C = 7/5 x 5/10
C = 7 x 5
5 x 10
C = 35/50
C = 5 x 7 / 5 x 10
C = 7/10
D = 7/5 x 3/10 + 1/5
D = 7 x 3 + 1/5
5 x 10
D = 21/50 + 1 x 10 / 5 x 10
D = 21/50 + 10/50
D = 31/50
M = 1/9 ; N = 2/3 ; P = 5/18
a) m + n
1/9 + 5/18
= 1 x 2 / 9 x 2 + 5/18
= 2/18 + 5/18
= 7/18
b) p - m
5/18 - 1/9
= 5/18 - 1 x 2 / 9 x 2
= 5/18 - 2/18
= 3/18
= 3 x 1 / 3 x 6
= 1/6
c) np
2/3 x 5/18
= 2 x 5
3 x 18
= 10/54
= 2 x 5 / 2 x 27
= 5/27
----------------------------------------------
Exercice 2 ;
A = 3/8 x (4/9 + 2/3)
A = 3/8 x (4/9 + 2 x 3 / 3 x 3)
A = 3/8 x (4/9 + 6/9)
A = 3/8 x 10/9
A = 3 x 10
8 x 9
A = 30/72
A = 6 x 5 / 6 x 12
A = 5/12
B = 3/8 x 4/9 + 2/3
B = 3 x 4 + 2/3
8 x 9
B = 12/72 + 2/3
B = 12/72 + 2 x 24 / 3 x 24
B = 12/72 + 48/72
B = 60/72
B = 12 x 5 / 12 x 6
B = 5/6
C = 7/5 x (3/10 + 1/5)
C = 7/5 x (3/10 + 1 x 2 / 5 x 2)
C = 7/5 x (3/10 + 2/10)
C = 7/5 x 5/10
C = 7 x 5
5 x 10
C = 35/50
C = 5 x 7 / 5 x 10
C = 7/10
D = 7/5 x 3/10 + 1/5
D = 7 x 3 + 1/5
5 x 10
D = 21/50 + 1 x 10 / 5 x 10
D = 21/50 + 10/50
D = 31/50
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