Đáp án:

 4040/4038 lớn hơn 4018/4016

13/12 bé hơn 15/14

9/11 bé hơn 13/15

2007/2008 bé hơn 2008/2009

2012/2013 bé hơn 2013/2014

 

$\dfrac{4040}{4038}$ `=` $\dfrac{4038+2}{4038}$ `= 1 +` $\dfrac{2}{4038}$

$\dfrac{4018}{4016}$ `=` $\dfrac{4016+2}{4016}$ `= 1 +` $\dfrac{2}{4016}$

Vì $\dfrac{2}{4038}$ < $\dfrac{2}{4016}$

`=> 1 +` $\dfrac{2}{4038}$ `< 1 +` $\dfrac{2}{4016}$

=> $\dfrac{4040}{4038}$ `<` $\dfrac{4018}{4016}$

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$\dfrac{13}{12}$ `=` $\dfrac{12+1}{12}$ `= 1 +` $\dfrac{1}{12}$

$\dfrac{15}{14}$ `=` $\dfrac{14+1}{14}$ `= 1 +` $\dfrac{1}{14}$

Vì $\dfrac{1}{12}$ > $\dfrac{1}{14}$

`=> 1 +` $\dfrac{1}{12}$ `> 1 +` $\dfrac{1}{14}$

`=>` $\dfrac{13}{12}$ `>` $\dfrac{15}{14}$

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$\dfrac{9}{11}$ `=` $\dfrac{11-2}{11}$ `= 1 -` $\dfrac{2}{11}$

$\dfrac{13}{15}$ `=` $\dfrac{15-2}{15}$ `= 1 -` $\dfrac{2}{15}$

Vì $\dfrac{2}{11}$ `>` $\dfrac{2}{15}$

`=> 1 -` $\dfrac{2}{11}$ `< 1 -` $\dfrac{2}{15}$

`=>` $\dfrac{9}{11}$ `<` $\dfrac{13}{15}$ 

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$\dfrac{2007}{2008}$ `=` $\dfrac{2008-1}{2008}$ `= 1 -` $\dfrac{1}{2008}$

$\dfrac{2008}{2009}$ `=` $\dfrac{2009-1}{2009}$ `= 1 -` $\dfrac{1}{2009}$

Vì $\dfrac{1}{2008}$ `>` $\dfrac{1}{2009}$

`=> 1 -` $\dfrac{1}{2008}$ `< 1 -` $\dfrac{1}{2009}$

`=>` $\dfrac{2007}{2008}$ `<` $\dfrac{2008}{2009}$

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$\dfrac{2012}{2013}$ `=` $\dfrac{2013-1}{2013}$ `= 1 -` $\dfrac{1}{2013}$

$\dfrac{2013}{2014}$ `=` $\dfrac{2014-1}{2014}$ `= 1 -` $\dfrac{1}{2014}$

Vì $\dfrac{1}{2013}$ `>` $\dfrac{1}{2014}$

`=> 1 -` $\dfrac{1}{2013}$ `< 1 -` $\dfrac{1}{2014}$

`=>` $\dfrac{2012}{2013}$ `<` $\dfrac{2013}{2014}$

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