Bài 1: Thực hiện phép tính:
a) 50 . 79 + 24 : 23 - 15
= 1 . 79 + 24 : 8 - 15
= 79 + 3 - 15
= 82 - 15
= 67.
b) 27 . 34 + 34 . 73
= (27 + 73) . 34
= 100 . 34
= 3400.
c) 43 . 46 + 54 . 43 - 120
= 43. (46 + 54) - 120
= 64 . 100 - 120
= 6400 - 120
= 6280.
d) 2 + 3 + 4 + ... + 69 + 70
= (70 + 2) . [(70 - 2) : 1 + 1] : 2
= 72 . 69 : 2
= 4968 : 2
= 2484.
Bài 2: Tìm số tự nhiên x, biết:
a) 5x = 25
\(\Rightarrow\) 5x = 52
\(\Rightarrow\) x = 2.
b) 3x + 2 = 81
3x . 32 = 81
\(\Rightarrow\) 3x . 32 = 34
\(\Rightarrow\) x + 2 = 4
x = 4 - 2
x = 2.
c) (x + 1)3 = 27
\(\Rightarrow\) (x + 1)3 = 33
\(\Rightarrow\) x + 1 = 3
x = 3 - 1
x = 2.
d) 6 : (2x - 1) + 45 = 490 . 47
6 : (2x - 1) + 45 = 1 . 47
6 : (2x - 1) + 45 = 47
6 : (2x - 1) = 47 - 45
6 : (2x - 1) = 2
2x - 1 = 6 : 2
2x - 1 = 3
2x = 3 + 1
2x = 4
x = 4 : 2
x = 2.
Bài 3: Tính:
a) 27 . 75 + 25 . 27 - 100
= 27 . (75 + 25) - 100
= 27 . 100 - 100
= 2700 - 100
= 2600.
b) 47 : 45 - 35 : 5 + 27 : 32
= 42 - 7 + 27 : 9
= 16 - 7 + 3
= 9 + 3
= 12.
c) 210 : 27 + 40030 . 29 - 135 : 45
= 23 + 1 . 29 - 135 : 45
= 8 + 29 - 3
= 37 - 3
= 34.
d) 12 : {390 : [500 - (125 + 35 . 7)]}
= 12 : {390 : [500 - (125 + 245)]
= 12 : {390 : [500 - 370]}
= 12 : {390 : 130}
= 12 : 3
= 4.
