Cách 1:
1.a) $\dfrac65$ và $\dfrac{2014}{2013}$
Quy đồng mẫu hai phân số ta có:
$\dfrac{6}{5}=\dfrac{6.2013}{5.2013}=\dfrac{12078}{10065}$
$\dfrac{2014}{2013}=\dfrac{2014.5}{2013.5}=\dfrac{10070}{10065}$
Do $12078>10070$
$\Rightarrow \dfrac{12078}{10065}>\dfrac{10070}{10065}$
$\Rightarrow\dfrac{6}{5}>\dfrac{2014}{2013}$.
b) $\dfrac{11}{13}$ và $\dfrac{2031}{2033}$
Quy đồng mẫu số hai phân số ta được:
$\dfrac{11}{13}=\dfrac{11.2033}{13.2033}=\dfrac{22363}{26429}$
$\dfrac{2031}{2033}=\dfrac{2031.13}{2033.13}=\dfrac{26403}{26429}$
Do $22363<26403$
$\Rightarrow \dfrac{22363}{26429}<\dfrac{26403}{26429}$
$\Rightarrow\dfrac{11}{13}<\dfrac{2031}{2033}$
Cách 2:
1.a) $\dfrac{6}{5}$ và $\dfrac{2014}{2013}$
Ta có: $\dfrac65=\dfrac{5+1}{5}=1+\dfrac15$
$\dfrac{2014}{2013}=\dfrac{2013+1}{2013}=1+\dfrac1{2013}$
Do $5<2013\Rightarrow\dfrac{1}{5}>\dfrac{1}{2013}$
$\Rightarrow1+\dfrac15>1+\dfrac{1}{2013}$
$\Rightarrow\dfrac56>\dfrac{2014}{2013}$
b) Ta có: $\dfrac{11}{13}=\dfrac{13-2}{13}=1-\dfrac2{13}$
$\dfrac{2031}{2033}=\dfrac{2033-2}{2033}=1-\dfrac{2}{2033}$
Do $13<2033$
nên $\dfrac{2}{13}>\dfrac{2}{2033}$
$\Rightarrow1-\dfrac{2}{13}<1-\dfrac{2}{2033}$
$\Rightarrow\dfrac{11}{13}<\dfrac{2031}{2033}$
