Hello!
To compare fractions, they have to have the same denominator (the number on the bottom.) As you can clearly see, 9/8 has a denominator of 8 and 31/32 had a denominator of 32. Is 8 and 32 the same number? Of course not. We have to make them the same. But how?
Use the LCM. I don't want to go into much detail here on what that is (if you don't already know what that is) if you don't know what it is, please go ahead and look up how to find the LCM of two numbers. In our case we're comparing fractions so it's actually called the LCD, but it's still the LCM.
So, LCM = Largest Common Multiple. The largest common multiple that 8 and 32 shares is 32! So, what do we do? Well, we keep 31/32 the same because it already has the right denominator. 9/8 on the other hand has to change. 8 * 4 = 32. Know that whatever we do to the denominator, we HAVE to do to the numerator. So, 9 * 4 = 36. Our new fraction is 36/32.
So let's compare our fractions
36/32 and 31/32
When comparing fractions, if they have the same denominator, all you have to do is look at the numerators. 36 is larger than 31, yes? So 36/32 is the bigger fraction! Or should I say, 9/8 is bigger.
