We have two positive numbers p and q with p less than q. Which of these expressions is the largest? Our first step will be to give all of them the same denominator. Then we note that because q is greater than p, and the sum of the coefficients of p and q in each expression is the same, the largest expression will be the one that maximizes the coefficient on q, which is 3p plus 9q, which is p plus 3q over 4a.

positive numbers

largest expression

denominator

coefficients

maximize