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%TCIDATA{<META NAME="Title" CONTENT="Integers and Fractions">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:07:20 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=MathHelp.cst}
%TCIDATA{<LINK REL="author" HREF="DM0-1.tex">}
%TCIDATA{<LINK REL="first" HREF="DM2-1.tex">}
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%TCIDATA{<LINK REL="copyright" HREF="DM0-2.tex">}
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\input{tcilatex}
\begin{document}


\section{Integers \label{Numbers}and Fractions}

Numbers to be computed with should be entered in mathematics mode and appear
red on your screen. If that is not the case, select the number and click 
\FRAME{itbpF}{0.2992in}{0.2992in}{0.0692in}{}{}{text.wmf}{\special{language
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"0";croptop "1.0179";cropright "1.0179";cropbottom "0";filename
'Text.wmf';file-properties "XNPEU";}} to change the number to mathematics.

\begin{quote}
$\blacktriangleright $ To enter a mathematics expression for a computation
\end{quote}

\begin{itemize}
\item  Begin a new line with the mathematics expression.

- or -

\item  Type the expression immediately to the right of text or a text space.
\end{itemize}

If you enter mathematics immediately to the right of other mathematics, the
expressions will be combined in ways you may not intend. A safe way to begin
is to press \textsc{enter} and start on a new line.

\strut

\subsection{\ Addition\label{Addition} and Subtraction}

\begin{quote}
$\blacktriangleright $ To add $3$, $6$ and $14$
\end{quote}

\begin{enumerate}
\item[1.]  To put the insertion point in mathematics mode, do one of the
following

\begin{itemize}
\item  Choose \textsf{Insert + Math}
\end{itemize}

- or -

\begin{itemize}
\item  Click \FRAME{itbpF}{0.2992in}{0.2992in}{0.0692in}{}{}{text.wmf}{%
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'Text.wmf';file-properties "XNPEU";}}
\end{itemize}

- or\medskip 

\begin{itemize}
\item  Press \textsc{ctrl } \textsc{+} \textsc{m}
\end{itemize}

\item[2.]  Type $3+6+14$ (This sum should appear red on your screen.)

\item[3.]  Leaving the insertion point in the expression $3+6+14$, do one of
the following:

\begin{itemize}
\item  From the \textsf{Maple }menu, choose\textsf{\ Evaluate} 
\index{Evaluate@Evaluate}\medskip 

- or -

\item  Click $%
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"1";cropbottom "0";filename 'Evaluate.wmf';file-properties "XNPEU";}}$

- or -\medskip

\item  Press \textsc{ctrl + e}.
\end{itemize}
\end{enumerate}

\strut

This sequence prompts \textsl{Scientific Notebook} to insert $=23$ to the
right of the $3+6+14$, resulting in the equation $3+6+14=\allowbreak 23$.

By following the \emph{same} procedure, you can carry out the following
operations and perform a vast variety of other mathematical computations.

\strut

\begin{quotation}
\emph{Note}\textbf{\quad }The mathematical contents of gray boxes display
the mathematical expressions you enter, together with the results of the
indicated operation. In general, throughout this document, the mathematical
contents of gray boxes display both the input for an action and the results.
\end{quotation}

\strut

\begin{quote}
$\blacktriangleright $ With the insertion point in the sum (or difference)
choose \textsf{Evaluate}
\end{quote}

\begin{quotation}
$235+813=1048\vspace{6pt}$

$\dfrac{2}{3}+\dfrac{1}{7}=\,\dfrac{17}{21}\vspace{6pt}$

$96-27=\,69\vspace{6pt}$

$\dfrac{2}{3}-\dfrac{8}{7}=\,-\dfrac{10}{21}\vspace{6pt}$

$34+162-\dfrac{25}{4}+\dfrac{13}{7}-29=\allowbreak \dfrac{4553}{28}$
\end{quotation}

\strut

\subsection{\ Multiplication and Division\label{Multiplication}}

Use any standard linear notation for multiplication and division.

\begin{quote}
$\blacktriangleright $ With the insertion point in the product (or quotient)
choose \textsf{Evaluate}
\end{quote}

\begin{quotation}
$82\times 37=\,3034\vspace{4pt}$

$\left( 936\right) \left( -14\right) =\,-13104\vspace{4pt}$

$\dfrac{2}{3}\;\dfrac{8}{7}=\,\dfrac{16}{21}\vspace{4pt}$

$82\div 37=\,\dfrac{82}{37}\vspace{4pt}$

$36/14=\,\dfrac{18}{7}\vspace{4pt}$

$\dfrac{-\frac{2}{3}}{\frac{8}{7}}=\,-\dfrac{7}{12}\vspace{6pt}$

$85\left( 13+5\right) -27\left( 16-3\right) =\allowbreak 1179$
\end{quotation}

\strut

\begin{quotation}
\emph{Important}\textbf{\quad }Except that it be mathematically correct,
there are \emph{no rules} about the form for entering a mathematical
expression.\strut
\end{quotation}

\strut

For example, the expressions 
\[
\frac{\frac{2}{3}}{\frac{8}{7}}\ \qquad \frac{2}{3}\div \frac{8}{7}\ \qquad 
\frac{2}{3}/\frac{8}{7}\qquad \left( 2/3\right) /\left( 8/7\right) 
\]
are equally acceptable ways of entering a quotient of fractions. Also, 
\[
\left( 936\right) \left( 14\right) \ \quad 936\cdot 14\ \quad 936\times 14\
\quad \left( 936\right) \ast 14\ \quad 936\left[ 14\right] 
\]
and many other variations are acceptable. \textsl{Scientific Notebook}
provides a completely natural way for you to enter and perform mathematical
computations.

\strut

\begin{quotation}
\emph{Exception\quad }One of the few exceptions to the claim of ``no rules''
is the following. The ``vertical'' notation such as 
\[
\begin{tabular}{r}
$24$ \\ 
\underline{$+15$}
\end{tabular}
\text{\ and } 
\begin{tabular}{r}
$235$ \\ 
\underline{$-47$}
\end{tabular}
\text{\ and\quad }2\overline{)364} 
\]
used when doing arithmetic by hand is not generally recognized in \textsl{%
Scientific Notebook}. Write sums and differences of numbers in ``linear''
notation, such as $24+15$ and $235-47$ and $364/2$ or $\frac{364}{2}$ or $%
364\div 2$.
\end{quotation}

\strut

\strut

\subsection{\ Mixed Numbers and Long Division\label{Mixed number}}

A number written in the form $14\frac{5}{9}$ is interpreted as the \emph{%
mixed number} 
\index{Mixed number@Mixed number}$14+%
\frac{5}{9}$. Most commands applied to a mixed number return a fraction. For
example, applying \textsf{Evaluate} or \textsf{Simplify} to $14\frac{5}{9}$
gives the result $\frac{131}{9}$. The reverse is accomplished by \textsf{%
Expand}, which 
\index{Expand@Expand!mixed number@mixed number}\label{Expand}converts a
fraction to a mixed number. These commands are also available directly on
the \textsf{Compute} Toolbar. Click 
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\begin{quote}
$\blacktriangleright $ \textsf{Evaluate}
\end{quote}

\begin{quotation}
$1\frac{2}{3}=\allowbreak \frac{5}{3}\medskip $

$193\frac{87}{94}=\frac{18229}{94}\medskip $

$1\frac{2}{3}+2\frac{3}{4}=\allowbreak \frac{53}{12}$
\end{quotation}

\begin{quote}
$\blacktriangleright $ \textsf{Expand}
\end{quote}

\begin{quotation}
$\frac{18229}{94}=193\frac{87}{94}\medskip $

$\frac{53}{12}=\allowbreak 4\frac{5}{12}$
\end{quotation}

\strut

The expansion of a fraction into a mixed number uses the familiar \emph{%
long-division algorithm}. 
\index{Long division@Long division!integers@integers}\label{Long division} 
\index{Divide@Divide!integers@integers}\label{Divide}In the preceding
example, $18229$ divided by $94$ is equal to $193$ with \emph{remainder} $87$%
.\medskip

\subsection{\ Related topics}

\begin{itemize}
\item  
\hyperref{Basic Operations with Real Numbers}{}{}{DM2-3.tex#Basic operations}

\item  \hyperref{Powers and Radicals}{}{}{DM2-3.tex#Powers}

\item  \hyperref{Rationalizing a Denominator}{}{}{DM2-3.tex#Rationalizing a
denominator}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{0.5275in}{0.3399in}{0.0519in}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
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"1";cropbottom "0";filename 'index.wmf';file-properties "XNPEU";}}}{}{}{%
DMIndex.tex#Math Index}\quad {\small Index entries: \hyperref{Addition}{}{}{%
DMIndex.tex#Addition}, \hyperref{Division}{}{}{DMIndex.tex#Division}, 
\hyperref{Expand}{}{}{DMIndex.tex#Expand}, \hyperref{Long division}{}{}{%
DMIndex.tex#Long division}, \hyperref{Mixed numbers}{}{}{DMIndex.tex#Mixed
numbers}, \hyperref{Multiplication}{}{}{DMIndex.tex#Multiplication}, 
\hyperref{Subtraction}{}{}{DMIndex.tex#Subtraction}}

\end{document}
