There are a few ways.
We can convert both of them to decimals.
[tex]\sf\dfrac{5}{9}\rightarrow0.\overline{5}[/tex]
[tex]\sf\dfrac{11}{20}\rightarrow0.55[/tex]
As you can see, 5/9 has a 5 that goes on forever, and 11/20 has just two 5's, therefore 5/9 is bigger than 11/20.
Another way to do this is to convert both of them to the same denominator.
Just find the least common multiple between 9 and 20, which is 180.
[tex]\sf\dfrac{5}{9}\rightarrow\dfrac{5\times20}{9\times20}\rightarrow\dfrac{100}{180}[/tex]
[tex]\sf\dfrac{11}{20}\rightarrow\dfrac{11\times9}{20\times9}\rightarrow\dfrac{99}{180}[/tex]
Since 100 is greater than 99, 5/9 is greater than 11/20.
