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
[tex]\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[/tex]
