Trying to make a simple tree, but when I finished I realized I'd gone about it totally the wrong way... Would appreciate some help trying to make this the "correct" way. Oh, and also to circle the last 5/3
\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[swedish]{babel}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usetikzlibrary{calc,trees,positioning,arrows,fit,shapes,decorations.markings}
\begin{document}
\begin{tikzpicture}
\matrix(m)[matrix of math nodes,column sep=0.5cm,row sep=0.3cm,]{
& & & \dfrac{1}{1} & & & \\
& \dfrac{1}{2} & & & & \dfrac{2}{1} & \\
\dfrac{1}{3} & & \dfrac{3}{2} & & \dfrac{2}{3} & & \dfrac{3}{1} \\
\vdots & & \vdots & & & \dfrac{5}{3} & \vdots \\
};
\draw[->]
(m-1-4)edge(m-2-2)
(m-1-4)edge(m-2-6)
(m-2-2)edge(m-3-1)
(m-2-2)edge(m-3-3)
(m-2-6)edge(m-3-5)
(m-2-6)edge(m-3-7)
(m-3-5)edge(m-4-6);
\end{tikzpicture}
\end{document}


childpath action which is better suited to construct trees than using\matrix+ edges. – Bordaigorl May 19 '15 at 09:26