Question

How do you know if 5/9 is bigger then 11/20

Answer 1

There are a few ways.

We can convert both of them to decimals.

$\sf\dfrac{5}{9}\rightarrow0.\overline{5}$

$\sf\dfrac{11}{20}\rightarrow0.55$

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.

$\sf\dfrac{5}{9}\rightarrow\dfrac{5\times20}{9\times20}\rightarrow\dfrac{100}{180}$

$\sf\dfrac{11}{20}\rightarrow\dfrac{11\times9}{20\times9}\rightarrow\dfrac{99}{180}$

Since 100 is greater than 99, 5/9 is greater than 11/20.