Question

suppose the number of fiction books is 2/7 times the number of nonfiction books. what would be the ratio of the numbers of nonfiction books to the total number of books.

Answer 1

well, the total amount of books is all fiction books and nonfiction books, let's say is "x", total

now, the fiction books are 2:7 or 2/7 to nonfiction

so, if we divide the total "x" by 2+7, or 9, 2 of those quotients go to fiction and 7 of those go to nonfiction

if we divide "x" by 9, a "whole" is 9/9 or (9/9)x or 1x or just "x"

and we know 7 of those 9ths belong to nonfiction, thus


`\bf \begin{array}{clclclll} \cfrac{2}{9}&+&\cfrac{7}{9}&=&\cfrac{9}{9}\\ \uparrow &&\uparrow &&\uparrow \\ fiction&&nonfiction&&whole \end{array}\\\\ -----------------------------\\\\ \cfrac{nonfiction}{whole}\implies \cfrac{7}{9}\implies 7:9\impliedby ratio`