We are using reasoning methods like finding the benchmark to come up with which on is greater, but we can't use common denominators. I'm struggling, HELP!
Are you trying to compare the two fractions? If the following isn't what you need, could you please clarify what the requirement is and what exactly you're allowed and not allowed (other than not allowed common deminators). But notice this:
19/20 = 1 - 1/20 and
27/28 = 1 - 1/28
Now 28>20 so 1/28 is smaller than 1/20
Thus 1-(1/28) is BIGGER than 1 - (1/20) since we get a bigger number if we subtracted a smaller amount.
Thus since 1-(1/28) > 1 - (1/20) we conclude that 27/28 > 19/20
If that's not what you're trying to prove or what you're allowed to use, please clarify these two issues and I'll try to respond again.