Here is a quick overview of comparing fractions from Math is Fun. You can cross multiply to see which fraction is greater. However, remember that cross-multiplying is actually finding the common denominator by multiplying the two denominators together. You are just skipping the step of writing the common denominator to compare.
Compare 2/3 to 5/7. When you cross multiply 3*5 and 2*7 you'll see that 2/3 is less than 5/7. What you're really doing is this 2/3 * 7/7 = 14/21 and 5/7* 3/3 = 15/21. You should notice that the numerators are the same as the number you got when you cross multiplied.