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\(A=\frac{2013.10001}{2014.10001}=\frac{2013}{2014}=1-\frac{1}{2014}\)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
Lời giải:
a)
\(\frac{64}{73}=1-\frac{9}{73}=1-\frac{18}{146}\); \(\frac{45}{51}=1-\frac{6}{51}=1-\frac{18}{153}\)
Mà \(\frac{18}{146}> \frac{18}{153}\Rightarrow 1-\frac{18}{146}< 1-\frac{18}{153}\)
\(\Rightarrow \frac{64}{73}<\frac{45}{51}\)
b)
\(\frac{2323}{2424}=\frac{2300+23}{2400+24}=\frac{23(100+1)}{24(100+1)}=\frac{23}{24}=1-\frac{1}{24}\)
\(\frac{20132013}{20142014}=\frac{20130000+2013}{20140000+2014}=\frac{2013(10000+1)}{2014(10000+1)}=\frac{2013}{2014}=1-\frac{1}{2014}\)
Mà \(\frac{1}{24}>\frac{1}{2014}\Rightarrow 1-\frac{1}{24}< 1-\frac{1}{2014}\Rightarrow \frac{2323}{2424}< \frac{20132013}{20142014}\)
\(\frac{2323}{2424}=\frac{23.101}{24.101}=\frac{23}{24}\)
\(\frac{20132013}{20142014}=\frac{2013.10001}{2014.10001}=\frac{2013}{2014}\)
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"
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:.......
\(\left(\frac{1313}{1414}+\frac{10}{160}\right)-\left(\frac{130}{140}-\frac{1515}{1616}\right)\)
\(=\left(\frac{13}{14}+\frac{1}{16}\right)-\left(\frac{13}{14}-\frac{15}{16}\right)\)
\(=\frac{13}{14}+\frac{1}{16}-\frac{13}{14}+\frac{15}{16}\)
\(=\left(\frac{13}{14}-\frac{13}{14}\right)+\left(\frac{1}{16}+\frac{15}{16}\right)\)
\(=0+1\)
\(=1\)
Có (\(\frac{1313}{1414}\)+\(\frac{10}{160}\)) - (\(\frac{130}{140}\)-\(\frac{1515}{1616}\))
=\(\frac{13}{14}\)+\(\frac{1}{16}\)-\(\frac{13}{14}\)+\(\frac{15}{16}\)
=(\(\frac{13}{14}-\frac{13}{14}\)) + (\(\frac{1}{16}+\frac{15}{16}\))
=0+1=1
a)\(\frac{18}{91}\)< \(\frac{23}{114}\) ; b) \(\frac{1313}{9191}\) < \(\frac{1111}{7373}\)
a)\(\frac{18}{91}\)\(< \)\(\frac{23}{114}\)
b)\(\frac{1313}{9191}\)\(< \)\(\frac{1111}{7373}\)
Có : 1717/8585 = 17.101/85.101 = 17/85 = 1/5
1313/5151 = 13.101/51.101 = 13/51
Mà 13/51 > 13/65 = 1/5
=> 1717/8585 < 1313/5151
Tk mk nha
Có : 1717/8585 = 17.101/85.101 = 17/85 = 1/5
1313/5151 = 13.101/51.101 = 13/51
Mà 13/51 > 13/65 = 1/5
=> 1717/8585 < 1313/5151
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 \(A>B\)