anonymous one year ago Ellie had 44 books in here bookcase. She counted 32 fiction book and the rest were nonfiction. What was the ratio of fiction books to nonfiction book in Ellie's bookcase? A. 8 to 3 B. 8 to 11 C. 11 to 3 D. 3 to 8

1. anonymous

@Lyralei

2. anonymous

First let's find the number of nonfiction books. So if there are 32 fiction and 44 total, to find the nonfiction just do 44-32.

3. anonymous

12

4. anonymous

Right. So now we put together our ratio. Keep in mind that $\large x~to~y~=~\frac{x}{y}$ so $\large fiction~to~nonfiction~=~\frac{fiction}{nonfiction}$

5. anonymous

So if we substitute the values of fiction and nonfiction in, what would it look like?

6. anonymous

I'm not sure

7. anonymous

Well how many fiction books are there and how many nonfiction books are there?

8. anonymous

32 fiction and 12 nonfiction

9. anonymous

Right. So susbtitute the number of fiction and the number of nonfiction into $\large \frac{fiction}{nonfiction}$

10. anonymous

you mean like 12/32

11. anonymous

The opposite $\large \frac{32}{12}$ but anyways now it's time to simplify. Do you know how to do that?

12. anonymous

8/3

13. anonymous

Right! So now, we just have to translate it back to the other ratio form. If $\large \frac{x}{y}~=~x~to~y$ then what will $\large \frac{8}{3}$be?

14. anonymous

8 to 3

15. anonymous

Correct! Good job! :)

16. anonymous

Thank you for the help

17. anonymous

$\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile$