Ta có : \(\frac{1007}{2013}=\frac{2013-6}{2013}=1-\frac{6}{2013}>1-\frac{6}{2012}=\frac{1006}{2012}>\frac{1005}{2012}\)

=> \(\frac{1007}{2013}>\frac{1005}{2012}\)

\(\frac{1007}{2013}\)> \(\frac{1005}{2012}\)

\(\dfrac{4}{17}=\dfrac{16}{68}\\ Vì:\dfrac{16}{68}< \dfrac{16}{63}\Rightarrow\dfrac{4}{17}< \dfrac{16}{63}\\ ---\\ \dfrac{1007}{1009}=1-\dfrac{2}{1009};\dfrac{1005}{1007}=1-\dfrac{2}{1007}\\ Vì:\dfrac{2}{1009}< \dfrac{2}{1007}\Rightarrow1-\dfrac{2}{1009}>1-\dfrac{2}{1007}\\ \Rightarrow\dfrac{1007}{1009}>\dfrac{1005}{1007}\)

a: 4/17=16/68

16/68<16/63

=>4/17<16/63

b: 19/53<20/53

20/53<20/50(Vì 53>50)

=>19/53<20/50=2/5

mà 2/5=30/75<30/73

nên 19/53<30/73

c: 1007/1009=1-2/1009

1005/1007=1-2/1007

1009>1007

=>2/1009<2/1007

=>-2/1009>-2/1007

=>1007/1009>1005/1007

Ta có : \(\frac{2012}{2014}=\frac{1006}{1007}=1-\frac{1}{1007}\)

 \(\frac{2014}{2016}=\frac{1007}{1008}=1-\frac{1}{1008}\)

Vì \(\frac{1}{1007}>\frac{1}{1008}\Rightarrow1-\frac{1}{1007}< 1-\frac{1}{1008}\Rightarrow\frac{2012}{2014}< \frac{2014}{2016}\)

2012/2014=1-2/2014

2014/2016=1-2/2016

vì 2/2014>2/2016

=>2012/2014<2014/2016

   study well

 k nha 

     ai k đúng cho mk mk trả lại gấp đôi

Ta có : 2012/2014 và 2014/2016 <=> 2012 x 2016 và 2014 x2014

        = 4056192 và 4056196

Vì : 4056192 < 4056196

Vậy :2012/2014 < 2014/2016

a) Ta có:

\(\dfrac{2012}{2013}+\dfrac{1}{2013}=1\)

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

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

b) Ta có:

\(\dfrac{1006}{1007}+\dfrac{1}{1007}=1\)

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

Vì \(\dfrac{1}{1007}=\dfrac{2}{2014}>\dfrac{2}{2015}\) 

nên \(\dfrac{1006}{1007}< \dfrac{2013}{2015}\)

c) ta có:

\(1-\dfrac{64}{73}=\dfrac{9}{73}=\dfrac{153}{1241}\)

\(1-\dfrac{45}{51}=\dfrac{2}{17}=\dfrac{146}{1241}\)

Vì \(\dfrac{153}{1241}>\dfrac{146}{1241}\) nên \(\dfrac{63}{73}>\dfrac{45}{51}\)

a) 2012/2013 và 2013/2014

1-2012/2013=1/2013

1-2013/2014=1/2014

Vì 1/2013> 1/2014 nên 2012/2013<2013/2014

b) 1006/1007 và 2013/2015

1-1006/1007=1/1007=2/2014

1-2013/2015=2/2015

Vì 2/2014>2/2015 nên 1006/1007<2013/2015

c) 64/73 và 45/51

1-64/73=9/73=18/146

1-45/51=2/17=18/153

Vì 18/146> 18/153 nên 64/73<45/51

\(1-\frac{1003}{1005}=\frac{2}{1005}>\frac{2}{1007}=1-\frac{1005}{1007}\Rightarrow\frac{1003}{1005}

ta có : 1-1003/1005=2/1005

1-1005/1007=2/1007

vì 2/1005>2/1007 nên 1003/1005<1005/1007

Ta có 1003/1005 + 2/1005 = 1

           1005/1007 + 2/1007 = 1

Vì 2/1005 > 2/1007

Nên 1003/1005 < 1005/1007

CHÚC BẠN THI TỐT

\(\dfrac{1004}{1005}< \dfrac{1005}{1006}< \dfrac{1006}{1007}< \dfrac{1007}{1008}\)

1004/1005<1005/1006<1006/1007<1007/1008

\(\frac{2011}{2010}\times\frac{2012}{2011}\times\frac{2013}{2012}\times\frac{2014}{2013}\times\frac{1005}{1007}\)

\(=\frac{2014}{2010}\times\frac{1005}{1007}\)

\(=\frac{2\times1007\times1005}{2\times1005\times1007}\)

\(=1\)

\(\frac{2011}{2010}\cdot\frac{2012}{2011}\cdot\frac{2013}{2012}\cdot\frac{2014}{2013}\cdot\frac{2010}{2014}\)

\(=\frac{2010\cdot2011\cdot2012\cdot2013\cdot2014}{2010\cdot2011\cdot2012\cdot2013\cdot2014}\)

= 1

\(\frac{2011}{2010}.\frac{2012}{2011}.\frac{2013}{2012}.\frac{2014}{2013}.\frac{1005}{1007}=\frac{2014}{2010}.\frac{1005}{1007}\)

\(\frac{2014}{2010}.\frac{1005}{1007}=\frac{1007}{1005}.\frac{1005}{1007}=1\)