How to make an empty box

You can use \framebox(200,300){} where the size is given in multiples of \unitlength, defaulting to 1pt.

Surprised no one has mentioned this. Latex has feature specifically for questions and answers:

% allow for answer boxes:
\documentclass[12pt]{exam}
\printanswers

\usepackage{amsmath}

\begin{document}
\begin{enumerate}

    % questions can be list items
    \item (Problem 7 \S 2.1)\\
    Evaluate the following expression using Euclid's algorithm (2.1.3). (\textbf{Write each step down for credit})

    \[\gcd(98,\ 35)\]

    % make an answer box
    \begin{solutionorbox}[2in] \\
    $98\mod 35 = 28$ \\
    $35\mod 28 = 7$ \\
    $28\mod 7 = 0$ \\
    $\gcd(98,\ 35) = 7$
    \end{solutionorbox}

    \end{enumerate}
\end{document} 

To add, if you need space for students to work on this printed out, you can use vspace.

% answer box with space
\begin{solutionorbox}
\vspace{10cm}
\end{solutionorbox}

To make empty boxes that align nicely with the text, you can combine \fbox with \phantom in this way:

\fbox{\phantom{This is my answer}}

You set the width and height by the width and height of the text in \phantom. The resulting box will align perfectly with a line of text, contrarily to the box created with \framebox .