# Thread: Inequalities and Variables Homework

1. ## Inequalities and Variables Homework

Another summer past, another school year here

I've been having trouble with a certain question for my alg 2/trig class; I just have no idea whatsoever how to approach it. Thanks in advance for helping!

If -4<x<5 and 0.25<y<4, then a<x/y<b. What is a+b?

2. ## Re: Inequalities and Variables Homework

First consider the case with positive numerator and denominator. Increasing the numerator of a fraction increases the value of the fraction. Increasing the denominator of a fraction decreases the value of the fraction. So a fraction is largest when its numerator is largest and its denominator is smallest. A fraction is smallest when it numerator is smallest and its denominator is largest.

Having a numerator or denominator that is negative is the same as starting with numerator and denominator positive and multiplying the entire fraction by -1. What does that do to "largest" and "smallest"?