\documentclass[12pt]{article}

    \oddsidemargin -.25in       % Lt Margin adj for odd pages (0 = 1" margin)
    \evensidemargin -.25in      % Rt Margin adjustment for even pages
    \topmargin -.5in            % adj top margin from 1"
    \footskip .5in
    \textwidth 7in              % width of printed area
    \textheight 9in             % height of printed area

   % \pagestyle{empty}

\usepackage{amsfonts}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{psfig}

\newcommand {\pic}[1]{\hspace*{\fill}\epsfbox{#1}\hspace*{\fill}}
\newcommand{\bfrac}[2]{\displaystyle \frac{#1}{#2}}
\newcommand{\limit}[2]{\displaystyle \lim_{{#1} \rightarrow {#2}} }
\newcommand{\displ}{\displaystyle}
\newcommand{\be}{\begin{enumerate}}
\newcommand{\ee}{\end{enumerate}}
\newcommand{\pict}[3]{\epsfxsize=#1in \epsfysize=#2in
                            \epsffile{#3.eps}}

\newcommand{\ck}{{\checkmark}}
\newcommand{\C}{{\mathbb C}}
\newcommand{\Z}{{\mathbb Z}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\N}{{\mathbb N}}
\newcommand{\D}{{\cal D}}
\newcommand{\Q}{{\cal Q}}
\newcommand{\h}{{\mathfrak h}}
\newcommand{\spc}{\underline {\hspace {1in}} }
\newcommand{\series}[3]{\displaystyle \sum_{{#1}={#2}}^{#3} }
\newcommand{\norm}[1]{\displaystyle \|{#1}\|}
\newcommand{\bb}{{$\bullet$}}
\newcommand{\integral}[2]{\displaystyle \int_{#1}^{#2}}
\newcommand{\set}[1]{\displaystyle \{{#1}\}}
\newcommand{\ol}[1]{\overline {#1}}


\begin{document}

\noindent
{\Large 
Fractions Worksheet II \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~201} 
\vspace{.25in}


\be 
\item Use Cuisenaire Rods to explain why $\frac{2}{5} +
\frac {1}{5} = \frac {3}{5}$.
\item Use Cuisenaire Rods to explain why $\frac{2}{5} +
\frac {3}{4} \neq \frac {2+3}{5+4}$.
\item How should we define addition of fractions?
\item How should we define subtraction of fractions?
\item Do we need to find common denominators before we add fractions?
\item Do we need to find common denominators before we subtract fractions?
\item Use the area model to explain why $\frac{4}{7} \times
\frac {3}{5} = \frac {4\times3}{7\times5}$.
\item How should we define multiplication of fractions?
\item How should we define division of fractions? 
\item Do we need to find common denominators before we multiply fractions?
\item Do we need to find common denominators before we divide fractions?
\item Use the missing factor model to explain the following {\bf theorem}.
\\
\begin{center}
{\em The Invert and Multiply Algorithm for Division of Fractions and
Rational Numbers} (page 378)
\end{center}
$$\frac{a}{b} \div \frac {c}{d} = \frac{a}{b} \cdot \frac{d}{c}, \rm{ \,
where \,} \frac{c}{d} \neq 0$$
\item What is meant by $4 \frac{1}{5}$?
\item Convert $4 \frac{1}{5}$ to an improper fraction.  Use a diagram to
explain your answer.
\item Use the area model to evaluate $2 \frac{1}{3} \times 4 \frac{1}{5}$?
\item Find the reciprocal of $\frac{5}{3}$.
\item Find the reciprocal of $2 \frac{1}{9}$.
\item Find a rational number between $\frac{4}{5}$ and $\frac {5}{6}$
\item Find a rational number between $\frac{3}{5}$ and $\frac {1}{6}$
\item Find a rational number between $\frac{1}{3}$ and $\frac {2}{3}$
\item Do numbers 17 and 19--21 on pages 382--383 of your textbook.
\item Do number 21 on page 398 of your text.
\ee
\end {document}
