Exercices sur le chapitre 7 : calcul littéral

Exercices sur le chapitre 7 : calcul littéral

4ème9
2010-2011
Exercices sur le chapitre 7 : calcul littéral
Calcul mental
6/
– 7×8=– 56
1/ – 5– 8=– 13
7/ 9 – 18=– 9
2/ – 9×– 5=45
8/ – 1 – 1= – 2
3/ – 38=5
9/ – 12×3=– 36
4/ 6× – 7= – 42
10/ – 1 – 2 – 3= – 6
5/ 8 – 14=– 6
Exercice 1 page 114
a/
A=6 x3 x
A=9 x
B=82 x
B=on ne peut pas !
C=4 x 5 x
C=9 x
D=5 x3
D=impossible
E=4 x 2 2 x 2
E=6 x 2
F =5 x4 x 2
F=impossible
G=9 x 2 4 x 2
G=13 x 2
H =7 x 2 3 x 2
H =10 x 2
I =9 x 2  x 2
I =10 x 2
b/
J =5 – 9 x
J=pas possible
K =5 x – 7 x
K=– 2 x
L= – 3 x – 6 x
L= – 9 x
M = – 8 x2 x
M =– 6 x
N =– 8 x 2 – 6 x 2
N =– 14 x 2
P=43 x 2
P=pas possible
S =4 x 2 – 6 x 2
S =– 2 x 2
T = – 5 x2 – x2
T =– 6 x 2
2
R= – 5 x – 7 x
R=pas possible
Exercice 2 page 114
A=5 a29 a
A=14 a2
B=8 a6 a3a
B=17 a
C =73 a4 a
C =77 a
4ème9
D=6 a 2 8 a 2 3 a 2
D=17 a 2
E=5 a 246 a 2
E=11 a 2 4
F =5 a4 a 25 a2
F =5 a9 a 2
G=8 m – 10 m4 m
G=12 m – 10 m
G=2 m
H =5 m – 4 m8 m
H =9 m
I=– 8 m – 2 m – 5 m
I = – 15 m
J =6 m2 5 m2 – 8 m2
J =11 m 2 – 8 m2
J =3 m2
K =2 m – 7 m 24 m2
K =2m – 3 m2
L= – 7 m25 m2 – 3 m2
L= – 10 m2
M =2 n 25 n – 46 n 227
M =2 n 26 n2 27 – 4 5 n
M =8 n 2 5 5 n
N =– 8 n 27 – 3 n4 n2 – 2 n – 5
N =– 8 n 24 n2 – 3 n – 2 n 7 – 5
N =– 4 n 2 – 5 n 2
R=– 9 n2 – 54 – 7 n2 2 n – 8 n
R=– 9 n2 – 7 n 2 2 n – 8 n – 54
R=– 16 n 2 – 6 n – 1
S=53 n – 4n 2 8 n 24 n – 5
S= – 4 n 28 n 2 3 n4n 5 – 5
S=4 n 2 7 n
2010-2011
4ème9
2010-2011
Exercice 4 page 114
a/
A=7×3 x
A=21 x
B=5 x ×2 x
B=10 x 2
C =6×3 x 2
C =18 x 2
E=2 x 2×4
E=8 x 2
F =6 x ×2 x
F =12 x 2
b/
G= – 3 x ×5 x
G= – 15 x 2
H = – 7×2 x
H = – 14 x
I =3 x – 4 x 
I = – 12 x 2
J =– 2 x  – 8 x
J =16 x 2
K =2 – 5 x 2 
K =– 10 x 2
L= – 6 x 2×2
L= – 12 x 2
M = – 4  – 3 x 2
M =12 x 2
N =4 x 2 – 5
N =– 20 x 2
P =– 2 x×8 x
P =– 16 x 2
D=4 x×3
D=12 x
Exercice 5 page 114
a/
A=73 x
A=pas possible
B=7×3 x
B=21 x
C =7 x×3 x
2
C =21 x
D=7 x3 x
D=10 x
b/
E= – 5×2 x
E= – 10 x
F =– 6 x – 2 x
F =– 8 x
G= – 3 x  – 2 x 
G=6 x 2
H = – 82 x
H=pas possible
Exercice 6 page 114
2
• 5 x=9 x ; 6×=– 12 x
2
2
5 x4 x=9 x ; 6×– 2 x =– 12 x
2
• … . – 4 x=7 x ; – 3 x = – 18 x
2
11 x – 4 x=7 x ; – 3 x6 x =– 18 x
2
• 7 = – 28 x ;  – 8 x= – 12 x
7  – 4 x 2 = – 28 x 2 ; – 4 x – 8 x= – 12 x
4ème9
2010-2011
Correction n°9 a/ page 114
A=5 2 x 7
A=5×2 x5×7
A=10 x 35
B=52 x ×3
B=3×53×2 x
B=156 x
C = x 3 x7
C = x×3 x  x×7
2
C =3 x 7 x
D=4 x 2 x6
D=4 x×2 x4 x×6
2
D=8 x 24 x
Exercices donnés en classe : développement simple
A=– 3 x 4 x – 2
B=4 x – 5 x9
C =– 7 x – 3 x – 40
D=– 4 x 6 ×– 5
E=8 – 9 x×3 x
F = – 9 x – 8×– 7 x 
F =– 7 x× – 9 x  – 7 x× – 8
F =63 x 256 x
G= – x 5 x – 6
G= – x×5 x – x × – 6
G= – 5 x 26 x
H = x 1 – x 
H =x ×1 x×– x 
H = x – x2
I =7 x– 5 x3
On ne distribue pas ! Il faudra
faire autre chose...
Calcul mental
1/ – 5×– 7 =35
6/
– 3 x× x= – 3 x 2
2/ 3× – 9=– 27
2
7/ – x× – 5 x=5 x
3/ 8×– 7= – 56
8/ 7×– 6 x=– 42 x
4/ – 1× – 1=1
2
9/ 8 x× – 9 x=– 72 x
5/ 6×7=42
2
10/ – 7 x × – 4 x =28 x
Exercices sur « signe – ou + devant une paire de parenthèses »
A=– 7 x 5 –  – 5 x 8
B=– 5 x – 3– 7 x – 9
C =8 x – 8 –  x – 9
D=– x – 17 – x 
4ème9
Calcul mental
1/ – 83 =
2010-2011
6/
– 2 x5 x =
2/ – 1 – 1 =
7/ – x 5 x =
3/ 2 – 3 =
8/ 7 x – 15 x =
4/ – 5 – 9 =
9/ – 5 x 2 – 8 x 2 =
5/ – 813 =
10/ 22 x – 7 =
Exercice 14 page 115
A=3 x 45 x 2
A=3 x×5 x 3 x ×24×5 x 4×2
A=15 x 26 x20 x 8
A=15 x 226 x 8
C =4 x 5 32 x 
C =4 x×34 x ×2 x 5×35×2 x
C =12 x8 x 21510 x
C =8 x 222 x 15
E=5 x 34 – 2 x
E=5 x 3×43×– 2 x 
E=5 x 12−6 x
E= – 1 x 12
B=52 x3 x 7 
B=5×3 x5×72 x×3 x2 x×7
B=15 x 356 x 214 x
B=6 x 229 x35
D=5 x342 x
D=5 x×45 x×2 x3×43×2 x
D=20 x 10 x 2 126 x
D=10 x 226 x 12
F =7 x27 x2
F =7 x×7 x 7 x ×2 2×7 x2×2
F =49 x 214 x14 x4
F =49 x 228 x4
4ème9
2010-2011
Calcul mental (à l'écrit)
1/ – 8 x×5 x =– 40 x 2
2
6/ – 9 x – 8 x=72 x
2/ – 9 x – 5 x= – 14 x 2
7/ 7 x – x =7 x – 1 x =6 x
3/ 3 x 2 – 9 x 2 =– 6 x 2
2
8/ 8 x×– x=– 8 x
4/ – 3 x  – 8 =– 3 x×– 8=24 x
2
2
9/ – x× – x = – 1 x× – 1 x=1 x = x
5/
10/ – x2 x=1 x= x
– 12 x 16 x =4 x
Développement double plus complexe
A=– 2 x7– 85 x 
A=– 2 x× – 8 – 2 x ×5 x 7×– 87×5 x
A=16 x – 10 x 2 – 5635 x
2
A – 10 x 51 x – 56
A' =– 5 x 6– 98 x 
A' =– 5 x×– 9 – 5 x ×8 x  6× – 96×8 x
A' =45 x – 40 x 2 – 5448 x
A' =– 40 x 293 x – 54
B=– 7 – 3 x– 8 x5
…
B=24 x 241 x – 35
C =– x – 1 x11
…
C =– x 2 – 12 x – 11
4ème9
2010-2011
Correction : n°15 page 115
A=5 x 26 x 4
A=5 x ×6 x 5 x×4 2×6 x 2×4
2
A=30 x 20 x 12 x 8
A=30 x 2 32 x 8
B=– 5 x – 3 – 4 x – 2
B=– 5 x× – 4 x  – 5 x× – 2 – 3× – 4 x  – 3× – 2
B=20 x 2 10 x 12 x 6
B=20 x 2 22 x 6
Calcul mental
1/ – 3 x – 5 x= – 8 x
2
2/ 2 x ×– 4 x = – 8 x
3/ 7 x – 10 x=– 3 x
4/ – 5×3 x =– 15 x
5/ 5 x 2 – 7 x 2 =– 2 x 2
6/
– 6 x× – 3 x =18 x 2
7/ 7 x – x =6 x
2
8/ – x × – x = – 1 x × – 1 x = x
2
2
9/ – 5 x × – 4=20 x
2
10/ 2 x  x – 5=2 x – 10 x
Encore des développements doubles
A=– 5 x9– 83 x 
…
A=– 15 x 267 x – 72
B=– 5 – x 5 x 7
…
B=– 5 x 2 – 32 x – 35
4ème9
Exercices du mardi 15 mars
Factorise :
2
• 16 x – 3 x= x×16 x  x× – 3= x 16 x – 3
• 21 – 3 x =3×73× – x =3 7 – x 
2
2
• 4 y – 6=2×2y²2×−3=2 2 y – 3
2
• 3 x  x = x ×3 x x×1= x 3 x1
De même avec :
2
• A=3 x – 7 x = x× 3 x x×– 7= x 3 x – 7
• B=36 x – 6=6×6 x – 6×1=66 x – 1
2
• C = y – 12 y= y  y −12
2
• D=12 x – 6 x = x 12 – 6 x 
2
ou D=62 x – x 
ou encore D=6 x2− x 
2
• E=3 xy – y = y×3 x y× – y= y 3 x – y
2010-2011