[tex]\dfrac1{\frac25}\cdot\dfrac{\frac52}{\frac52}=\dfrac{\frac52}1=\dfrac52[/tex]
Since [tex]5=2\cdot2+1[/tex], we get
[tex]\dfrac52=\dfrac{2\cdot2+1}2=\dfrac{2\cdot2}2+\dfrac12=2+\dfrac12[/tex]
