A=20132013/20142014 = B=2014/2015

Lời giải:

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

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

\(\frac{2323}{2424}=\frac{23.101}{24.101}=\frac{23}{24}\)

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

Ta có:

\(1-\frac{23}{24}=\frac{24}{24}-\frac{23}{24}=\frac{1}{24}\)

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

Vì \(\frac{1}{24}>\frac{1}{2014}\) nên \(\frac{23}{24}< \frac{2013}{2014}\)

Vậy \(\frac{2323}{2424}< \frac{20132013}{20142014}\)

Tính phần bù với 1 nhé

mình cũng trình bày giống bạn "Muôn cảm súc"

thank you so much

\(A=\frac{2013.10001}{2014.10001}=\frac{2013}{2014}=1-\frac{1}{2014}\)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 : \(\frac{124124}{125125}=\frac{124124:1001}{125125:1001}=\frac{124}{125}\)

\(\frac{123}{124}=1-\frac{1}{124}\); \(\frac{124}{125}=1-\frac{1}{125}\)

Vì 1/124 < 1/125 => 123/124 > 123/125 => 123/124 > 124124/125125

ta có: \(\frac{124124}{125125}=\frac{124}{125}\)

Lại có: \(1-\frac{123}{124}=\frac{1}{124};1-\frac{124}{125}=\frac{1}{125}\)

\(\Rightarrow\frac{1}{124}>\frac{1}{125}\Rightarrow1-\frac{123}{124}>1-\frac{124}{125}\)

\(\Rightarrow\frac{123}{124}< \frac{124}{125}\Rightarrow\frac{123}{124}< \frac{124124}{125125}\)

So sánh 2 phân số : 123 / 124 và 124124 / 125125

124124 / 125125 = 124 / 125

123 / 124 = 1 - 123 / 124 = 1/124

124 / 125 = 1 - 124 / 125 = 1/125 

Vì 1/ 124 > 1/125 => 123/124 > 124124/125125

Vậy 123/124 > 124124/125125