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:.......

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

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

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 \(A>B\)

- Quy đồng lên thôi bạn

\(\frac{1006}{1007}=1-\frac{1}{1007}\)

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

\(\frac{1}{1007}< \frac{2}{2015}\Rightarrow\frac{1006}{1007}>\frac{2013}{2015}\)

b) Ta có:
\(1-\frac{1006}{1007}=\frac{1}{1007}=\frac{2}{2014}\)

\(1-\frac{2013}{2015}=\frac{2}{2015}\)
Vì \(\frac{2}{2014}>\frac{2}{2015}\) nên \(\frac{1006}{1007}< \frac{2013}{2015}\)

A=20132013/20142014 = B=2014/2015

a)

\(\frac{64}{85}< \frac{64}{81}< \frac{73}{81}\)

=>\(\frac{64}{85}< \frac{73}{81}\)

b)

\(\frac{25}{26}=\frac{25.1010}{26.1010}=\frac{25250}{26260}\)

Ta có: \(1-\frac{25250}{26260}=\frac{1010}{26260}\)

         \(1-\frac{25251}{26261}=\frac{1010}{26261}\)

Vì \(\frac{1010}{26260}>\frac{1010}{26261}\) nên \(\frac{25}{26}< \frac{25251}{26261}\)

a)\(\frac{64}{85}\)<\(\frac{64}{81}\)<\(\frac{73}{81}\)

b)\(\frac{25}{26}\)=\(\frac{25250}{26260}\)=\(1\)- \(\frac{1010}{26260}\)< \(1\)- \(\frac{1010}{26261}\)= \(\frac{25251}{26261}\)

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