%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
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\usepackage{sw20jart}

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%TCIDATA{<META NAME="ViewSettings" CONTENT="17">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Apr 10 09:33:19 1997}
%TCIDATA{CSTFile=Exam.cst}
%TCIDATA{PageSetup=72,72,72,72,0}
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%F=36,\PARA{038<p type="texpara" tag="Body Text" >\hfill \thepage}
%}


\input{tcilatex}
\begin{document}


\section{Exam}

\subsection{\protect\vspace{1pt}Text}

\section{Fractions}

Your Name: 
%TCIMACRO{\HTML{<Input TYPE="Text" NAME="STUDENTNAME" VALUE=" " SIZE=0>}}
%BeginExpansion
%%
%EndExpansion

\vspace{1pt}

\subsection{Setup}

Some global delayed definitions to reduce typing:

$\limfunc{num}=\limfunc{rand}(1,10)$ \lbrack $\limfunc{num}$ will generate
numerators for the fraction problems\rbrack 

$\limfunc{den}=\limfunc{rand}(2,10)$ \ [$\limfunc{den}$ will generate
denominators]

Choice Space: 2

Choices: No Break, Radio Buttons, Permute

Title:Test on Fractions

\section{Question}

\subsection{Comment}

Add two fractions or mixed numbers.

\subsection{Setup}

$n_{1}:=\limfunc{rand}(1,4)$

$d_{1}:=\limfunc{rand}(2,10)$

$f_{1}:=n_{1}/d_{1}$

Conditions:\ $(n_{1}<d_{1})$

$n_{2}:=\limfunc{rand}(1,4)$

$d_{2}:=\limfunc{rand}(2,10)$

$f_{2}:=n_{2}/d_{2}$

Conditions:$(n_{2}<d_{2})\wedge (d_{2}\neq d_{1})\wedge \left( \left(
f_{1}+f_{2}\right) \neq \left( \dfrac{n_{1}+n_{2}}{d_{1}d_{2}}\right)
\right) \wedge \left( \left( f_{1}+f_{2}\right) \neq \left( \dfrac{%
n_{1}+n_{2}}{d_{1}+d_{2}}\right) \right) $

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
+%
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}+n_{2})/(d_{1}d_{2})}{\frac{n_{1}+n_{2}}{d_{1}d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}+n_{2}}{d_{1}d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}+n_{2})/(d_{1}+d_{2})}{\frac{n_{1}+n_{2}}{d_{1}+d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}+n_{2}}{d_{1}+d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f_{1}+f_{2}}{f_{1}+f_{2}}{evaluate}}
%BeginExpansion
f_{1}+f_{2}%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
-%
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{f_{1}-f_{2}}{f_{1}-f_{2}}{evaluate}}
%BeginExpansion
f_{1}-f_{2}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}-n_{2})/(d_{1}-d_{2})}{\frac{n_{1}-n_{2}}{d_{1}-d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}-n_{2}}{d_{1}-d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}-n_{2})/(d_{1}d_{2})}{\frac{n_{1}-n_{2}}{d_{1}d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}-n_{2}}{d_{1}d_{2}}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Question}

\subsection{Comment}

Add two fractions or mixed numbers.

\subsection{Setup}

$n_{1}:=\limfunc{rand}(-10,-5)$

$d_{1}:=\limfunc{rand}(2,10)$

$f_{1}:=n_{1}/d_{1}$

Conditions:\ $(\left| n_{1}\right| <d_{1})$

$n_{2}:=\limfunc{rand}(5,10)$

$d_{2}:=\limfunc{rand}(2,10)$

$f_{2}:=n_{2}/d_{2}$

Conditions:$(n_{2}<d_{2})\wedge (d_{2}\neq d_{1})\wedge \left( \left(
f_{1}+f_{2}\right) \neq \left( \dfrac{n_{1}+n_{2}}{d_{1}d_{2}}\right)
\right) \wedge \left( \left( f_{1}+f_{2}\right) \neq \left( \dfrac{
n_{1}+n_{2}}{d_{1}+d_{2}}\right) \right) \wedge \left( \left(
n_{1}+n_{2}\right) \neq 0\right) $

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
+%
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}+n_{2})/(d_{1}+d_{2})}{\frac{n_{1}+n_{2}}{d_{1}+d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}+n_{2}}{d_{1}+d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f_{1}+f_{2}}{f_{1}+f_{2}}{evaluate}}
%BeginExpansion
f_{1}+f_{2}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}+n_{2})/(d_{1}d_{2})}{\frac{n_{1}+n_{2}}{d_{1}d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}+n_{2}}{d_{1}d_{2}}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
-%
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}-n_{2})/(d_{1}d_{2})}{\frac{n_{1}-n_{2}}{d_{1}d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}-n_{2}}{d_{1}d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(n_{1}-n_{2})/(d_{1}-d_{2})}{\frac{n_{1}-n_{2}}{d_{1}-d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}-n_{2}}{d_{1}-d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f_{1}-f_{2}}{f_{1}-f_{2}}{evaluate}}
%BeginExpansion
f_{1}-f_{2}%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Question}

\subsection{Comment}

Multiply two fractions

\subsection{Setup}

$n_{1}:=\limfunc{rand}(1,5)$

$d_{1}:=\limfunc{rand}(2,10)$

$f_{1}:=n_{1}/d_{1}$

Conditions:\ $(n_{1}<d_{1})$

$n_{2}:=\limfunc{rand}(1,5)$

$d_{2}:=\limfunc{rand}(2,10)$

$f_{2}:=n_{2}/d_{2}$

Conditions:$(n_{2}<d_{2})\wedge (d_{2}\neq d_{1})\wedge \left( \gcd \left(
d_{1},d_{2}\right) \neq 1\right) \wedge (f_{2}\neq f_{1})$

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
\times 
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{\left( n_{1}n_{2}\right) /\gcd (d_{1},d_{2})}{n_{1}n_{2}}{evaluate}}
%BeginExpansion
n_{1}n_{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f_{1}f_{2}}{f_{1}f_{2}}{evaluate}}
%BeginExpansion
f_{1}f_{2}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{\left( n_{1}d_{2}\right) /\left( n_{2}d_{1}\right) }{n_{1}\frac{d_{2}}{n_{2}d_{1}}}{evaluate}}
%BeginExpansion
n_{1}\frac{d_{2}}{n_{2}d_{1}}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
\div 
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{f_{1}\div f_{2}}{\frac{f_{1}}{f_{2}}}{evaluate}}
%BeginExpansion
\frac{f_{1}}{f_{2}}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{\left( n_{1}n_{2}\right) /\gcd (d_{1},d_{2})}{n_{1}n_{2}}{evaluate}}
%BeginExpansion
n_{1}n_{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f_{1}f_{2}}{f_{1}f_{2}}{evaluate}}
%BeginExpansion
f_{1}f_{2}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Question}

\subsection{Comment}

Multiply two fractions

\subsection{Setup}

$n_{1}:=\limfunc{rand}(-10,-6)$

$d_{1}:=\limfunc{rand}(2,10)$

$f_{1}:=n_{1}/d_{1}$

Conditions:\ $(\left| n_{1}\right| <d_{1})$

$n_{2}:=\limfunc{rand}(6,10)$

$d_{2}:=\limfunc{rand}(2,10)$

$f_{2}:=n_{2}/d_{2}$

Conditions:$(n_{2}<d_{2})\wedge (d_{2}\neq d_{1})\wedge \left( \gcd \left(
d_{1},d_{2}\right) \neq 1\right) \wedge (f_{2}\neq f_{1})$

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
\times 
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{f_{1}f_{2}}{f_{1}f_{2}}{evaluate}}
%BeginExpansion
f_{1}f_{2}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{\left( n_{1}n_{2}\right) /\gcd (d_{1},d_{2})}{n_{1}n_{2}}{evaluate}}
%BeginExpansion
n_{1}n_{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\left( n_{1}d_{2}\right) /\left( n_{2}d_{1}\right) }{n_{1}\frac{d_{2}}{n_{2}d_{1}}}{evaluate}}
%BeginExpansion
n_{1}\frac{d_{2}}{n_{2}d_{1}}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Variant}

\subsection{Statement}

What is $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
\div 
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{\left( n_{1}n_{2}\right) /\gcd (d_{1},d_{2})}{n_{1}n_{2}}{evaluate}}
%BeginExpansion
n_{1}n_{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f_{1}\div f_{2}}{\frac{f_{1}}{f_{2}}}{evaluate}}
%BeginExpansion
\frac{f_{1}}{f_{2}}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{f_{1}f_{2}}{f_{1}f_{2}}{evaluate}}
%BeginExpansion
f_{1}f_{2}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these.
\end{description}

\section{Question}

\subsection{Comment}

Add a mixed number to a proper fraction. There must be a ``carry''. Example: 
$3\frac{2}{5}+\frac{3}{4}$.

\subsection{Setup}

$a:=\limfunc{rand}(2,5)\qquad $[integer part of the mixed number]

$n_{1}:=\limfunc{rand}(1,10)$\ \ \ [numerator of the mixed number]\ \ 

$d_{1}:=\limfunc{rand}(2,10)$ \ \ \ [denominator of the mixed number]

Conditions: $(n_{1}<d_{1})$

$n_{2}:=\limfunc{rand}(1,10)$ \ \ \ [numerator of second fraction]

$d_{2}:=\limfunc{rand}(2,10)$ \ \ \ [denominator of second fraction]

Conditions: $(n_{2}<d_{2})\wedge \left( d_{1}\neq d_{2}\right) $

$x:=\frac{n_{1}}{d_{1}}+\frac{n_{2}}{d_{2}}$ \ \ \ \ \ \ \ \ \ [sum of the
two fractions, we'll require it to be \TEXTsymbol{>} 1 to get a carry]

Conditions: $(x>1)$

$y:=\frac{n_{1}}{d_{1}}-\frac{n_{2}}{d_{2}}$ \ \ \ \ \ \ \ \ \ [difference
of the two fractions, we'll require it to be \TEXTsymbol{>}0 to get a carry]

Conditions: $(y<0)$

\section{Variant}

\subsection{Statement}

Find $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{n_{1}/d_{1}}{\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{d_{1}}%
%EndExpansion
+%
%TCIMACRO{\FORMULA{n_{2}/d_{2}}{\frac{n_{2}}{d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{2}}{d_{2}}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{a+1}{a+1}{evaluate}}
%BeginExpansion
a+1%
%EndExpansion
%TCIMACRO{
%\FORMULA{(n_{1}+n_{2})/(d_{1}+d_{2})}{\frac{n_{1}+n_{2}}{d_{1}+d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}+n_{2}}{d_{1}+d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{a+1}{a+1}{evaluate}}
%BeginExpansion
a+1%
%EndExpansion
%TCIMACRO{\FORMULA{x-1}{x-1}{evaluate}}
%BeginExpansion
x-1%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{x-1}{x-1}{evaluate}}
%BeginExpansion
x-1%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Variant}

\subsection{Statement}

Find $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{n_{1}/d_{1}}{\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{d_{1}}%
%EndExpansion
-%
%TCIMACRO{\FORMULA{n_{2}/d_{2}}{\frac{n_{2}}{d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{2}}{d_{2}}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{y+1}{y+1}{evaluate}}
%BeginExpansion
y+1%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{a-1}{a-1}{evaluate}}
%BeginExpansion
a-1%
%EndExpansion
%TCIMACRO{
%\FORMULA{(n_{1}-n_{2})/(d_{1}-d_{2})}{\frac{n_{1}-n_{2}}{d_{1}-d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}-n_{2}}{d_{1}-d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{a-1}{a-1}{evaluate}}
%BeginExpansion
a-1%
%EndExpansion
%TCIMACRO{\FORMULA{y+1}{y+1}{evaluate}}
%BeginExpansion
y+1%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Comment}

Add a mixed number to a proper fraction. There must be a ``carry''. Example: 
$3\frac{2}{5}+\frac{3}{4}$.

\subsection{Setup}

$a:=\limfunc{rand}(-8,-5)\qquad $[integer part of the mixed number]

$n_{1}:=\limfunc{rand}(1,10)$\ \ \ [numerator of the mixed number]\ \ 

$d_{1}:=\limfunc{rand}(2,10)$ \ \ \ [denominator of the mixed number]

Conditions: $(n_{1}<d_{1})$

$n_{2}:=\limfunc{rand}(1,10)$ \ \ \ [numerator of second fraction]

$d_{2}:=\limfunc{rand}(2,10)$ \ \ \ [denominator of second fraction]

Conditions: $(n_{2}<d_{2})\wedge \left( d_{1}\neq d_{2}\right) $

$x:=\frac{-n_{1}}{d_{1}}+\frac{n_{2}}{d_{2}}$ \ \ \ \ \ \ \ \ \ [sum of the
two fractions, we'll require it to be \TEXTsymbol{>}0 to get a carry]

Conditions: $(x>0)$

$y:=\frac{-n_{1}}{d_{1}}-\frac{n_{2}}{d_{2}}$ \ \ \ \ \ \ \ \ \ [difference
of the two fractions, we'll require it to be \TEXTsymbol{<}-1 to get a carry]

Conditions: $(y<-1)$

\section{Variant}

\subsection{Statement}

Find $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{n_{1}/d_{1}}{\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{d_{1}}%
%EndExpansion
+%
%TCIMACRO{\FORMULA{n_{2}/d_{2}}{\frac{n_{2}}{d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{2}}{d_{2}}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{a+1}{a+1}{evaluate}}
%BeginExpansion
a+1%
%EndExpansion
%TCIMACRO{\FORMULA{x-1}{x-1}{evaluate}}
%BeginExpansion
x-1%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{a+1}{a+1}{evaluate}}
%BeginExpansion
a+1%
%EndExpansion
%TCIMACRO{
%\FORMULA{(n_{1}+n_{2})/(d_{1}+d_{2})}{\frac{n_{1}+n_{2}}{d_{1}+d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{1}+n_{2}}{d_{1}+d_{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{x-1}{x-1}{evaluate}}
%BeginExpansion
x-1%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Variant}

\subsection{Statement}

Find $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{n_{1}/d_{1}}{\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{d_{1}}%
%EndExpansion
-%
%TCIMACRO{\FORMULA{n_{2}/d_{2}}{\frac{n_{2}}{d_{2}}}{evaluate}}
%BeginExpansion
\frac{n_{2}}{d_{2}}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{a-1}{a-1}{evaluate}}
%BeginExpansion
a-1%
%EndExpansion
%TCIMACRO{\FORMULA{\left| y+1\right| }{\left| y+1\right| }{evaluate}}
%BeginExpansion
\left| y+1\right| %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{\FORMULA{a-1}{a-1}{evaluate}}
%BeginExpansion
a-1%
%EndExpansion
%TCIMACRO{
%\FORMULA{\left| (-n_{1}-n_{2})/(d_{1}+d_{2})\right| }{\left| \frac{-n_{1}-n_{2}}{d_{1}+d_{2}}\right| }{evaluate}}
%BeginExpansion
\left| \frac{-n_{1}-n_{2}}{d_{1}+d_{2}}\right| %
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{\left| y+1\right| }{\left| y+1\right| }{evaluate}}
%BeginExpansion
\left| y+1\right| %
%EndExpansion
$
\end{itemize}

\begin{enumerate}
\item  None of these
\end{enumerate}

\section{Question}

\subsection{Comment}

Reduce a fraction to lowest terms

\subsection{Setup}

$n:=\func{rand}(1,10)$

$d:=\func{rand}(2,10)$

$m_{1}:=\limfunc{rand}(2,9)$

$m_{2}:=\limfunc{rand}(2,9)$

$p:=m_{1}m_{2}$

Conditions:\ $(n<d)\wedge (\gcd (n,d)=1)$

\subsection{Statement}

Reduce this fraction to lowest terms:\ $\frac{%
%TCIMACRO{\FORMULA{pn}{pn}{evaluate} }
%BeginExpansion
pn%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{pd}{pd}{evaluate} }
%BeginExpansion
pd%
%EndExpansion
}$

\subsection{\protect\vspace{1pt}Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{n/d}{\frac{n}{d}}{evaluate}}
%BeginExpansion
\frac{n}{d}%
%EndExpansion
\correctchoice{}$

\item  $\frac{%
%TCIMACRO{\FORMULA{m_{1}n}{m_{1}n}{evaluate}}
%BeginExpansion
m_{1}n%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{m_{1}d}{m_{1}d}{evaluate}}
%BeginExpansion
m_{1}d%
%EndExpansion
}$

\item  $\frac{%
%TCIMACRO{\FORMULA{m_{2}n}{m_{2}n}{evaluate}}
%BeginExpansion
m_{2}n%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{m_{2}d}{m_{2}d}{evaluate}}
%BeginExpansion
m_{2}d%
%EndExpansion
}$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Comment}

Conversions between mixed numbers and rational numbers

\subsection{Setup}

$a:=\limfunc{rand}(2,5)\qquad $[integer part of the mixed number]

$n_{1}:=\func{rand}(1,10)$\ \ \ [numerator of the mixed number]\ \ 

$d_{1}:=\func{rand}(2,10)$ \ \ \ [denominator of the mixed number]

Conditions: $(n_{1}<d_{1})\wedge \left( \gcd \left( n_{1},d_{1}\right)
=1\right) $

\section{Variant}

\subsection{Statement}

Convert $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{n_{1}/d_{1}}{\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{d_{1}}%
%EndExpansion
$ to a fraction

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{an_{1}}{an_{1}}{evaluate}}
%BeginExpansion
an_{1}%
%EndExpansion
/%
%TCIMACRO{\FORMULA{ad_{1}}{ad_{1}}{evaluate}}
%BeginExpansion
ad_{1}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\left( ad_{1}+n_{1}\right) /d_{1}}{\frac{ad_{1}+n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{ad_{1}+n_{1}}{d_{1}}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{\FORMULA{an_{1}/d_{1}}{a\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
a\frac{n_{1}}{d_{1}}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Variant}

\subsection{Statement}

Convert $\frac{%
%TCIMACRO{\FORMULA{ad_{1}+n_{1}}{ad_{1}+n_{1}}{evaluate}}
%BeginExpansion
ad_{1}+n_{1}%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{d_{1}}{d_{1}}{evaluate}}
%BeginExpansion
d_{1}%
%EndExpansion
}$to a mixed number

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{an_{1}/d_{1}}{a\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
a\frac{n_{1}}{d_{1}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
%TCIMACRO{\FORMULA{n_{1}/d_{1}}{\frac{n_{1}}{d_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{d_{1}}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{n_{1}/\left( ad_{1}\right) }{\frac{n_{1}}{ad_{1}}}{evaluate}}
%BeginExpansion
\frac{n_{1}}{ad_{1}}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Comment}

Fractions raised to a power

\subsection{Setup}

$a:=\func{rand}(2,4)$

$b:=\func{rand}(\{-4,-3,-2,2,3,4\})$

$c:=\func{rand}(2,4)$

Conditions:$\left( c\neq \left| b\right| \right) \wedge \left( \gcd \left(
b,c\right) =1\right) $

\subsection{Statement}

What is $\left( 
%TCIMACRO{\FORMULA{b/c}{\frac{b}{c}}{evaluate}}
%BeginExpansion
\frac{b}{c}%
%EndExpansion
\right) ^{%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
}?$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{b/c^{a}}{\frac{b}{c^{a}}}{evaluate}}
%BeginExpansion
\frac{b}{c^{a}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{b^{a}/c}{\frac{b^{a}}{c}}{evaluate}}
%BeginExpansion
\frac{b^{a}}{c}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\left( b/c\right) ^{a}}{\left( \frac{b}{c}\right) ^{a}}{evaluate}}
%BeginExpansion
\left( \frac{b}{c}\right) ^{a}%
%EndExpansion
$\correctchoice{}
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Comment}

Sqare root of a fraction

\subsection{Setup}

$a:=\func{rand}(2,4)$

$b:=\func{rand}(\left\{ 2,3,4\right\} )$

$c:=\func{rand}(2,4)$

Conditions:$\left( c\neq b\right) \wedge \left( \gcd \left( b,c\right)
=1\right) $

\subsection{Statement}

What is $\sqrt{%
%TCIMACRO{\FORMULA{b^{2}/c^{2}}{\frac{b^{2}}{c^{2}}}{evaluate} }
%BeginExpansion
\frac{b^{2}}{c^{2}}%
%EndExpansion
}?$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{b/c}{\frac{b}{c}}{evaluate}}
%BeginExpansion
\frac{b}{c}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{\FORMULA{b/c^{2}}{\frac{b}{c^{2}}}{evaluate}}
%BeginExpansion
\frac{b}{c^{2}}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{b^{2}/c}{\frac{b^{2}}{c}}{evaluate}}
%BeginExpansion
\frac{b^{2}}{c}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\end{document}
