Is 9/8 bigger or lesser than 31/32

To make this easy you can make them both have the same denominator.

So as 8 can go into 32 you don't have to change the second fraction. But you do have to change the first one.

So to get from 8 to 32 you times by 4 so therefore you times the 9 by 4 aswell to make:

36/32

So now you have the 2 fractions 36/32 and 31/32 so you can clearly see that 36/32 is bigger, meaning 9/8 is bigger than 31/32