So, I have examples in my math book, and it says study the examples until you understand how the answer was obtained. This one confuses me:

Looking at the answer, I have these questions:

1. Why does 5 end on the bottom of the fraction bar? Why does 5 exist anyway? The answer to -5/25 is -0.2, so why not use that number instead of 5?

** The 5 ends up on the bottom because your original expression has a 25 on the bottom and a 5 on the top. . If you take out a factor of 5 on both sides of the fraction you get . The five on the top will cancel with the five on the bottom, leaving just . The reason we don't write it in decimal form is that fractions are simpler to manipulate than decimals. For example, if I asked you to multiply your equation by a third, if you did it with decimals, you'd end up with an infinite decimal (since a third i 0.333333333333333333333333333.... recurring!). But if you multiplied it by the fraction , there would be no infinite fractions . In general, use fractions instead of demicals, they look nicer!**
2. Why is the negative sign on the outside of the fraction?

**It doesn't really matter if you put it inside or outside. It means the same thing.**
3. Why does

end on top and

on bottom?

** on top, and on the bottom! And the same kind of thing.**
I'm thinking the answer should be:

but that is not the answer. What am I doing wrong? What is the step by step process for dividing polynomials?

**You aren't doing anything wrong. Your answer is correct. The only difference is that they have written 0.2 as a fraction, and you have written it as a decimal.**