Câu 1:
a)13/17+[(-4)/5]=65/85+[-68/85]
=(65-68)/85
=3/85
b)-2/9:4/3-1/3=(-2/9) : (4/3) - (1/3)
=(-2/9) x (3/4) - (1/3)
=(-6/36) - (1/3)
=(-1/6) - (1/3)
=-3/6=-1/2
c)(-3)/8.2/5+(-3)/8.9/5-(-3)/8.6/5=[(-3)/8] . (2/5)+[(-3)/8] . (9/5) - [(-3)/8] . (6/5)
= [(-3)/8] . [(2/5)+(9/5)+(6/5)]
= [(-3/8)] . (17/5)
= -51/40
Câu 2:
a)2/x=(-8)/20
Ta có: (-8)/20=2/-5
=>2/x=2/-5
=> x=5∈Z, chọn
Vậy x=5
b)x/2=8/x
=> x.x=2.8
=> x²=16
Ta thấy: 16=4²; 16= (-4)²
=> x²=4²=(-4)²
=> x=4; x=-4 ∈Z, chọn
Vậy x∈{±4}
Câu 3:
S = 1/2.4 + 1/4.6 +...+ 1/2020 . 2022
S = 1/2 - 1/4 + 1/4 - 1/6 + ... + 1/2020 - 1/2022
S = 1/2 - 1/2022
S = 1011/2022 - 1/2022
S = 1010/2022
S = 505/1011
Vậy S = 505/1011