Simple algebraic question mixed up

Question

I know it is very simple but do not know why I am mixed up in it $(.5)(r^2)\cfrac{20-2r}r$ how is this equal to $10r-r^2$

Sorry if it is too easy, thanks for the help.

Answer 1

Note that $$.5=\dfrac{1}{2}$$ Also note that your expression can be rewritten as $$\dfrac{r^2(20-2r)}{r}\cdot \dfrac{1}{2}$$ Use the fact that $$20-2r=2(10-r)$$ and you should be done.

NOTE: $$a(x+y)=ax+ay$$ This is most likely the part you were having trouble with.This property is called the distributive property of multiplication over addition.

Comments: Whenever you want to manipulate some algebraic expression that involve decimals,try to convert them to fractions,and try to factorize since that might help you cancel terms on the numerator and the denominator.Above,I converted $.5$ to a fraction and then tried to factorize what I had in the numerator and that made things easier.