How to make a long equation small to fit in LaTeX?

Question

I am trying to use one equation in my thesis but that equation is long enough to fit in LaTeX format, I found one image but don't know how to convert that into LaTeX format, it uses some different symbols.

How to write this in LaTeX and make it small.

What I have tried:

\begin{equation}
\frac{\sum_{i j}\left(\begin{array}{l}{n_{i j}} \\ {2}\end{array}\right)-\left[\sum_{i}\left(\begin{array}{l}{a_{i}} \\ {2}\end{array}\right) \sum_{j}\left(\begin{array}{l}{b_{j}} \\ {2}\end{array}\right)\right] /\left(\begin{array}{l}{n} \\ {2}\end{array}\right)}{\frac{1}{2}\left[\sum_{i}\left(\begin{array}{l}{a_{i}} \\ {2}\end{array}\right)+\sum_{j}\left(\begin{array}{l}{b_{j}} \\ {2}\end{array}\right)-\left[\sum_{i}\left(\begin{array}{l}{a_{i}} \\ {2}\end{array}\right) \sum_{j}\left(\begin{array}{l}{a_{j}} \\ {2}\end{array}\right)\right] /\left(\begin{array}{l}{n} \\ {2}\end{array}\right)\right.}
\end{equation}

But it's appearing like this:

Edit:

%File: formatting-instruction.tex
\documentclass[letterpaper]{article}
\usepackage{aaai}
\usepackage{times}
\usepackage{helvet}
\usepackage{amsmath}

\usepackage{courier}
\frenchspacing
\setlength{\pdfpagewidth}{8.5in}
\setlength{\pdfpageheight}{11in}
\pdfinfo{
/Title (Insert Your Title Here)
/Author (Put All Your Authors Here, Separated by Commas)}
\setcounter{secnumdepth}{0}  
 \begin{document}
% The file aaai.sty is the style file for AAAI Press 
% proceedings, working notes, and technical reports.
%
\title{Thesis}
\author{Anonymous Author 
}
\maketitle
\begin{abstract}
\begin{quote}
AAAI creates proceedings, working notes, and technical reports directly from electronic source furnished by the authors. To ensure that all papers in the publication have a uniform appearance, authors must adhere to the following instructions. 
\end{quote}
\end{abstract}

\section{Model}

In this section we describe the architecture of our model.

\begin{equation}
\frac{\sum_{i j}\left(\begin{array}{l}{n_{i j}} \\ {2}\end{array}\right)-\left[\sum_{i}\left(\begin{array}{l}{a_{i}} \\ {2}\end{array}\right) \sum_{j}\left(\begin{array}{l}{b_{j}} \\ {2}\end{array}\right)\right] /\left(\begin{array}{l}{n} \\ {2}\end{array}\right)}{\frac{1}{2}\left[\sum_{i}\left(\begin{array}{l}{a_{i}} \\ {2}\end{array}\right)+\sum_{j}\left(\begin{array}{l}{b_{j}} \\ {2}\end{array}\right)-\left[\sum_{i}\left(\begin{array}{l}{a_{i}} \\ {2}\end{array}\right) \sum_{j}\left(\begin{array}{l}{a_{j}} \\ {2}\end{array}\right)\right] /\left(\begin{array}{l}{n} \\ {2}\end{array}\right)\right.}
\end{equation}



\end{document}

Answer 1

If I change \usepackage{times} into \usepackage{mathptmx} in your code and also the equation into

\begin{equation}
\frac{
  \sum_{ij}\binom{n_{ij}}{2}-\bigl[\sum_{i}\binom{a_{i}}{2} \sum_{j}\binom{b_{j}}{2}\bigr]\big/\binom{n}{2}
}{
  \frac{1}{2}\bigl[\sum_{i}\binom{a_{i}}{2}+\sum_{j}\binom{b_{j}}{2}\bigr]-
  \bigl[\sum_{i}\binom{a_{i}}{2} \sum_{j}\binom{a_{j}}{2}\bigr]
  \big/\binom{n}{2}     
}
\end{equation}

I get (dummy text added for context)

The output is even better if I change \usepackage{mathptmx} into

\usepackage{newtxtext,newtxmath}

If you want the description texts,

\begin{equation}
\overbrace{\mathit{ARI}}^{\hidewidth\substack{\text{Adjusted}\\\text{Index}}\hidewidth}=
\frac{
  \overbrace{\textstyle\sum_{ij}\binom{\vphantom{b}n_{ij}}{2}}^{\text{Index}}
  -
  \overbrace{\textstyle\bigl[\sum_{i}\binom{a_{i}}{2} \sum_{j}\binom{b_{j}}{2}\bigr]\big/\binom{n}{2}}%
    ^{\text{Expected Index}}
}{
  \underbrace{\textstyle\frac{1}{2}\bigl[\sum_{i}\binom{a_{i}}{2}+\sum_{j}\binom{b_{j}}{2}\bigr]}%
    _{\text{Max Index}}
  -
  \underbrace{\textstyle\bigl[\sum_{i}\binom{a_{i}}{2} \sum_{j}\binom{a_{j}}{2}\bigr]\big/\binom{n}{2}}%
    _{\text{Expected Index}}
}
\end{equation}

1. With \hidewidth, the description above “ARI” takes no space; it is also split into two lines not to intrude the right-hand side.

2. \textstyle is necessary, because \overbrace and \underbrace force \displaystyle

3. The \vphantom{b} has been added to set “Index” at the same height as the other description.