Corrigés – Développement-Factorisation

Exercice 1

A = 11 × (7 + 6) = 11 × 7 + 11 × 6 = 77 + 66 = 143
ou A = 11 × 13 = 143
B = 13 × (100 – 2) = 13 × 100 – 13 × 2 = 1 300 – 26 = 1 274
ou B = 13 × 98 = 1 274
C = 40 × (40 + 3) = 40 × 40 + 40 × 3 = 1 600 + 120 = 1 720
ou C = 40 × 43 = 1720
D = (20 – 3) × 15 = 20 × 15 – 3 × 15 = 300 – 45 = 255
ou D = 17 × 15 = 255

Exercice 2

A = 7 × (13,1 + 14,3) = 7 × 13,1 + 7 × 14,3 = 91,7 + 100,1 = 191,8
ou A = 7 × 27,4 = 191,8

B = (5,4 + 9,8) × 23 = 5,4 × 23 + 9,8 × 23 = 124,2 + 225,4 = 349,6
ou B = 15,2 × 23 = 349,6

C = 2,3 × 5,7 + 2,3 × 4,3 = 13,11 + 9,89 = 23
ou C = 2,3 × (5,7 + 4,3) = 2,3 × 10 = 23

D = 9,73 × 15,3 – 9,73 × 14,3 = 148,869 – 139,139 = 9,73
ou D = 9,73 × (15,3 – 14,3) = 9,73 × 1 = 9,73

Exercice 3

A = (3 + 33 + 333) × 3 = 3 × 3 + 33 × 3 + 333 × 3 = 9 + 99 + 999 = 1 107
ou A = (36 + 333) × 3 = 369 × 3 = 1 107

B = 9,1 × (17,2 – 5,1 – 2,1) = 9,1 × 17,2 – 9,1 × 5,1 – 9,1 × 2,1 = 156,52 – 46,41 – 19,11 = 91
ou B = 9,1 × (11,1 – 2,1) = 9,1 × 10 = 91

C = 3,5 × 2,4 + 3,5 × 7,2 – 3,5 × 4,6 = 8,4 + 25,2 – 16,1 = 17,5
ou C = 3,5 × (2,4 + 7,2 – 4,6) = 3,5 × (9,6 – 4,6) = 3,5 × 5 = 17,5

D = 5,7 × 3,4 – 1,4 × 5,7 = 19,38 – 7,98 = 11,4
ou D = 5,7 × (3,4 – 1,4) = 5,7 × 2 = 11,4

Exercice 4

A = 151 × 47 + 151 × 53
A = 151 × (47 + 53)
A = 151 × 100
A = 15 100

B = 13 × 2,3 + 5,7 × 13
B = 13 × (2,3 + 5,7)
B = 13 × 8
B = 104

C = 21 × 3,4 + 21 × 5,4 – 0,8 × 21
C = 21 × (3,4 + 5,4 – 0,8)
C = 21 × (8,8 – 0,8)
C = 21 × 8
C = 168

D = 32 × 23,5 – 3,5 × 32
D = 32 × (23,5 – 3,5)
D = 32 × 20
D = 640

Exercice 5

A = 43 × 19
A = 43 × (20 – 1)
A = 860 – 43
A = 817

B = 28 × 31
B = 28 × (30 + 1)
B = 840 + 28
B = 868

C = 99 × 417
C = (100 – 1) × 417
C = 41 700 – 417
C = 41 283

D = 101 × 53
D = (100 + 1) × 53
D = 5 300 + 53
D = 5 353

E = 59 × 199
E = 59 × (200 – 1)
E = 11 800 – 59
E = 11 741

F = 299 × 13
F = (300 – 1) × 13
F = 300 × 13 – 1 × 13
F = 3 900 – 13
F = 3 887

Exercice 6

A = 2,5 × 17,3 + 2,5 × 2,7
A = 2,5 × (17,3 + 2,7)
A = 2,5 × 20
A = 50

B = 2,5 × 17,3 – 2,5 × 7,3
B = 2,5 × (17,3 – 7,3)
B = 2,5 × 10
B = 25

C = 22,4 × 41 + 77,6 × 41
C = (22,4 + 77,6) × 41
C = 100 × 41
C = 4 100

D = 2,4 × 41 – 41 × 2,4
D = 2,4 × (41 – 41)
D = 2,4 × 0
D = 0

Exercice 7

A = 37 × 9
A = 37 × (10 – 1)
A = 37 × 10 – 37 × 1
A = 370 – 37
A = 333

B = 375 × 9
B = 375 × (10 – 1)
B = 375 × 10 – 375 × 1
B = 3 750 – 375
B = 3 375

C = 37 × 99
C = 37 × (100 – 1)
C = 37 × 100 – 37 × 1
C = 3 700 – 37
C = 3 663

D = 375 × 99
D = 375 × (100 – 1)
D = 37 500 – 375
D = 37 125

Exercice 8

A = 37 × 11
A = 37 × (10 + 1)
A = 37 × 10 + 37 × 1
A = 370 + 37
A = 407

B = 375 × 11
B = 375 × (10 + 1)
B = 375 × 10 + 375 × 1
B = 3 750 + 375
B = 4 125

C = 37 × 101
C = 37 × (100 + 1)
C = 37 × 100 + 37 × 1
C = 3 700 + 37
C = 3 737

D = 375 × 101
D = 375 × (100 + 1)
D = 375 × 100 + 375 × 1
D = 37 500 + 375
D = 37 875

Exercice 9

Le montant des achats de M. ONDO s’élève à :
3 × 125 + 3 × 75,
c’est-à-dire : 3 × (125 + 75) = 3 × 200 = 600F.
ou encore : 3 × 125 + 3 × 75 = 375 + 225 = 600F
    Conclusion : M. ONDO dépense 600F.

Exercice 10

Procédure : Aire =1,6(6,5+3,5)=1,6

Exercice 11

a) AE =10-x (en cm)
b) L’aire du rectangle AEFD est :5(10-x) ou 5 x 10 – 5x (en cm² )