Đáp án + Giải thích các bước giải:
a) `14/21=2/3,60/72=5/6`
Ta có : `2/3=(2*6)/(3*6)=12/18,5/6=(5*3)/(6*3)=15/18`
`=> 12/18 < 15/18 => 2/3 < 5/6 => 14/21 < 60/72`
b) `38/133 = 2/7,129/344=3/8`
Ta có : `2/7=(2*8)/(7*8)=16/56,3/8=(3*7)/(8*7)=21/56`
`=> 16/56 < 21/56 => 2/7<3/8=>38/133<129/344`
c) `11/54=(11*37)/(54*37)=407/1998,22/37=(22*54)/(37*54)=1188/1998` $\\$ `=> 407/1998 < 1188/1998 => 11/54<22/37`
d) `A = (10^1990 + 1)/(10^1991+1)=[10(10^1990+1)]/(10^1991+1)=(10^1991+10)/(10^1991+1)` $\\$ `= (10^1991 + 1 + 9)/(10^1991+1)=1+9/(10^1991+1)`
`B = (10^1991 + 1)/(10^1992 + 1) = [10(10^1991+1)]/(10^1992+1) = (10^1992 + 10)/(10^1992+1)` $\\$ `= (10^1992+1+9)/(10^1992+1)=1+9/(10^1992+1)`
Ta lại có : `9/(10^1991 + 1)>9/(10^1992+1)=>1+9/(10^1991+1)>1+9/(10^1992+1)=>A>B`
