Math Is Fun Forum

Ah I'm sorry bob, but I don't think you're getting what I'm trying to say. I think I have a better way to explain it, check this out.

What I can't figure out is how the common denominator of 4a is gotten. Let me give an example. Lets say we want to add together 1/4 and 5/8. We would look of course at the multiples of 4 and find one that's equal to other denominator. So we find that 8 is the least common denominator for both fractions. We multiply 1/4 by 2/2 to get 2/8, and now we can solve.

My problem is how do we get the common denominator of 4a from -c/a? Like I said earlier, a variable without a coefficient has an implied coefficient of 1. So now we can look at -c/a as -1c/1a. How can we get the common denominator of 4 from 1, when 1 only has itself as a multiple? If both of the bases were the same we could just say it was equal to 1, divide that in half to get 5/10, get 1/2, and THEN we could have gotten the common denominator of 4. I don't see how this works.

I actually watched a video that explained it that way. I'm still confused on one thing though, I want to know where the 4a that we multiply -c/a comes from. That's what I'm trying to figure out. The 4a we multiply against -c/a can't just come from nowhere right? Nothing in math can just come from "thin air" right? I mean we can't just say "We're going to multiply -c/a by 4a just because", that 4a has to come from some process and that's what I want to know.

Thanks guys. I was learning to do this through a different slightly different method however, and even though this method looks a bit shorter I'd prefer to stick with what I'm already familiar with . If you could explain how -c/a gets the common denominator of 4a in my version of the problem bob that'd be great .