Bài 2:
a) 135 + 360 + 65 + 24 + 40
= (135 + 65) +(360 + 40) + 24
= 200 + 400 + 24
= 624
b) 17 . 85 + 25 . 17 - 1200
= 17 . (85 + 25) - 1200
= 17 . 100 - 1200
= 1700 - 1200
= 500
c) 129 . 172 - 73 . 129 + 129
= 129 . (172 - 73 + 1)
= 129 . 100
= 12900
d) 34 . 75 + 75 . 66 - 65 . 100
= 75 . (34 + 66) - 6500
= 75 . 100 - 6500
= 7500 - 6500
= 1000
e) 6² : 4 . 3 + 2 . 5²
= 36 : 4 . 3 + 2 . 25
= 9 . 3 + 50
= 27 +50
= 77
f) 3 . 5² - 16 : 2³ + 2015^4 : 2015^3
= 3 . 25 - 16 : 8 + 2015
= 75 - 2 + 2015
= 2088
g) (6^25 . 52 - 6^25 . 16) : 6^27
= [ 6^25 . (52 - 16)] : 6^27
= (6^25 . 36) : 6^27
= (6^25 . 6²) : 6^27
= 6^27 : 6^27
= 1
h) (28 . 37 + 14 . 86) : (7 . 40)
= (14 . 2 . 37 + 14 . 86) : (7 . 40)
= (14 . 74 + 14 . 86) : (7 . 40)
= [14 . (74 + 86)] : (7 . 40)
= (14 . 160) : (7 . 40)
= (14 . 160) : (7 . 2 . 20)
= (14 . 20 . 8) : (14 . 20)
= 8
Bài 3: (chưa học dấu ⇔ phải không, lược bỏ như ở tiểu học nhé!)
a) 427 - (x + 100) = 227
x + 100 = 427 - 227
x + 100 = 200
x = 200 - 100
x = 100
Vậy x=100
b) 440 + 2 . (125 - x) = 546
2 . (125 - x) = 546 - 440
2 . (125 - x) = 106
125 - x = 106 : 2
125 - x = 53
x= 125 - 53
x = 72
Vậy x=72
c) 231 - (2x - 6) = 1339 : 13
231 - (2x - 6) = 103
2x - 6 = 231 - 103
2x - 6 = 128
2x = 128 + 6
2x = 134
x = 67
Vậy x=67
d) (27x + 6) : 3 - 11 = 9
(27x + 6) : 3 = 9 + 11
(27x + 6) : 3 = 20
27x + 6 = 20 . 3
27x + 6 = 60
27x = 60 - 6
27x = 54
x = 54 : 27
x = 2
Vậy x=2
e) 5x + x = 5^11 : 5^9 + 3^1
6x = 5² + 3
6x = 25 + 3
6x = 28
x = $\frac{28}{6}$
x = $\frac{14}{3}$
Vậy x = $\frac{14}{3}$
Bài 5:
a) 90 = 2 . 3² . 5
54 = 2 . 3³
ƯCLN (90; 54) = 2 . 3² = 2 . 9 = 18
ƯC (90; 54) = {±1 ; ±2 ; ±3 ; ±6 ; ±9 ; ±18}
b) 48 = 2^4 . 3
24 = 2³ . 3
72 = 2³ . 3²
ƯCLN (48; 24; 72) = 2³ . 3 = 8 . 3 = 24
ƯC (48; 24; 72) = {±1; ±2; ±3; ±4; ±6; ±8; ±12; ±24}
c) 440 = 2³ . 5 . 11
700 = 2² . 5² . 7
ƯCLN (440; 700) = 2² . 5 = 4 . 5 = 20
ƯC (440; 700) = {±1; ±2; ±4; ±5; ±10; ±20}
d) 147 = 3 . 7²
429 = 3 . 11 . 13
ƯCLN (147; 429) = 3
ƯC (147; 429) = {±1; ±3}
