In the book, Algebraic Inequalities: New Vistas, Andreescu and Saul proved an inequality in one of the exercises: for fractions $\frac{a_1}{b_1} ,\frac{a_2}{b_2},\cdots, \frac{a_n}{b_a}$ , if $m$ and $M$ are the smallest and largest of these fractions, we have $m\leq \frac{a_1+\cdots+a_n}{b_1+\cdots+b_n}\leq M$. Recently, while solving a problem in the journal, MathAMATYC Educator, Vol.15, No.3, Problem Section, we realized that the solution to this problem can be generalized to a proof of the inequality by Andreescu and Saul. In this talk, we will introduce the proof by Andreescu and Saul, and then we will present our new proof.