Originally Posted by

**bryang** 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:

$\displaystyle \frac{-5a^2bc}{25ab^2c^2}=-\frac{a}{5bc}$

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. $\displaystyle \frac{5}{25}$. If you take out a factor of 5 on both sides of the fraction you get $\displaystyle \frac{5(1)}{5(5)}$. The five on the top will cancel with the five on the bottom, leaving just $\displaystyle \frac{1}{5}$. 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 $\displaystyle \frac{1}{3}$, there would be no infinite fractions :D. 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 $\displaystyle a$ end on top and $\displaystyle bc$ on bottom?

**$\displaystyle a^2$ on top, and $\displaystyle a$ on the bottom! And the same kind of thing.**

I'm thinking the answer should be: $\displaystyle \frac{-0.2a}{bc}$ 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.**