Operations with Asymptotic Notations
Classical resources: CLRS Introduction to Algorithms, 3d edition, pages 47, 1150,  Donald Ervin Knuth TAOCP, 1997, volume 1, page 107.
More formal good resource for such cheatsheet you can find  in Jeremy Avigad and Kevin Donnelly article.
And, at end, for non negative case, let me bring some well known properties:
$$ \begin{array}{l}O(f ) + O(g) = O(f + g) =O(\max(f,g))\\
C=Const. \Rightarrow C\cdot O(f) = O(C \cdot f) = O(f) \\
 O(f )  O(g) = O(f g) \\
O( O( f)) = O(f ) \\
 g \ne 0 \Rightarrow \frac{O(f)}{g} = O\left(\frac{f}{g}\right)
\end{array}
$$
For your case: $f \in \frac{\Theta(n)}{o(n)}$, if an only if $\lim\limits_{n \to \infty}f(n)=\infty$.