another cool trick you can use is when you eliminate down to 2 or 3 (preferably 2) you can cross multiply going from denominator to numberator. for instance, if you're comparing 6/7 to 13/15 (this is just an example). you take the 7 and you multiply with 13 giving you 91 (right side). 15 times 6 is 90 (left side). thus, 6/7 (the left side) is smaller than 13/15.
this is probably a lot easier to understand if someone shows you on paper...sorry if i confused you