Lời giải:

$a=\frac{20132013}{20142014}=\frac{20132013:10001}{20142014:10001}=\frac{2013}{2014}> \frac{2013}{2015}$

Hay $a> b$

a. Ta có \(\frac{-29}{39}=-1+\frac{10}{39}\)

\(\frac{-39}{49}=-1+\frac{10}{49}\)
có -1 = -1 mà \(\frac{10}{39}>\frac{10}{49}\)do cùng tử mà mẫu càng lớn thì phân số đó bé hơn
vì vậy nên \(\frac{-29}{39}>\frac{-39}{49}\)

b. có \(\frac{20142014:\text{10001}}{20152015:\text{10001}}=\frac{2014}{2015}\)
vậy \(\frac{20142014}{20152015}=\frac{2014}{2015}\)

Chúc bạn học tốt

Ta có:  \(\frac{123}{124}< 1\)

            \(\frac{20142014}{20132013}=\frac{2014}{2013}>1\)

Vậy  \(\frac{123}{124}< \frac{20142014}{20132013}\)

p/s: chúc bạn học tốt

Ta có: \(\frac{20142014}{20132013}=\frac{2014}{2013}\)

Lại có: \(\frac{123}{124}=\frac{124-1}{124}=1-\frac{1}{124}\Rightarrow\frac{123}{124}< 1\) (1)

\(\frac{2014}{2013}=\frac{2013+1}{2013}=1+\frac{1}{2013}\Rightarrow\frac{2014}{2013}>1\)(2)

Từ (1)(2) => \(\frac{123}{123}< \frac{2014}{2013}hay\frac{123}{124}< \frac{20142014}{20132013}\)

\(A=\frac{2013.10001}{2014.10001}=\frac{2013}{2014}=1-\frac{1}{2014}\)A=(2013.10001)/(2014.10001)=2013/2014=1-1/2014

B=(13.10101)/(14.10101)=13/14=1-1/14

Ta thấy 1/14>1/2014 => 1-1/2014>1-1/14 => A>B

Ta có \(A=\frac{20132013}{20142014}=\frac{20132013\div10001}{20142014\div10001}=\frac{2013}{2014}=1-\frac{1}{2014}\)

\(B=\frac{1313}{1414}=\frac{1313\div101}{1414\div101}=\frac{13}{14}=1-\frac{1}{14}\)

Ta thấy \(1=1;\frac{1}{14}>\frac{1}{2014}\Rightarrow1-\frac{1}{14}< 1-\frac{1}{2014}\)

Do đó \(\frac{20132013}{20142014}>\frac{1313}{1414}\)hay \(A>B\)

ta có A=\(\frac{20132013}{20142014}\)=\(\frac{2013.10001}{2014.10001}\)=\(\frac{2013}{2014}\)

B=\(\frac{131313}{141414}\)=\(\frac{13.10101}{14.10101}\)=\(\frac{13}{14}\)

xét 1-\(\frac{2013}{2014}\)=\(\frac{1}{2014}\);1-\(\frac{13}{14}\)=\(\frac{1}{14}\)

vì \(\frac{1}{2014}\)<\(\frac{1}{14}\) suy ra \(\frac{2013}{2014}\)>\(\frac{13}{14}\)suy ra A>B

Vậy ..................................

Ta có: 

\(A=\frac{20132013}{20142014}\)

\(A=\frac{20132013\div10001}{20142014\div10001}\)

\(A=\frac{2013}{2014}\)

và \(B=\frac{131313}{141414}\)

\(B=\frac{131313\div10101}{141414\div10101}\)

\(B=\frac{13}{14}\)

ta có: \(A=\frac{2013}{2014}=1-\frac{1}{2014}\)

và \(B=\frac{13}{14}=1-\frac{1}{14}\)

vì \(\frac{1}{14}>\frac{1}{2014}\)

Nên \(1-\frac{1}{14}< 1-\frac{1}{2014}\)

Hay A > B

a) Ta có: \(\frac{2012}{2013}+\frac{1}{2013}=1\)

\(\frac{2013}{2014}+\frac{1}{2014}=1\)

Vì \(\frac{1}{2013}>\frac{1}{2014}\) nên \(\frac{2012}{2013}< \frac{2013}{2014}\)

Vậy: \(\frac{2012}{2013}< \frac{2013}{2014}\)

b) \(\frac{1006}{1007}+\frac{1}{1007}=1\)

\(\frac{2013}{2015}+\frac{2}{2015}=1\)

Mà \(\frac{1}{1007}=\frac{2}{2014}>\frac{2}{2015}\)

nên: \(\frac{1006}{1007}< \frac{2013}{2015}\)

Vậy:.......