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\begin{center}

\Huge{Fractions}\\
\end{center}

\noindent
While working in a group make sure you:
\begin{packed_itemize}
\item Expect to make mistakes but be sure to reflect/learn from them!
\item Are civil and are aware of your impact on others.
\item Assume and engage with the strongest argument while assuming best intent.
\end{packed_itemize}

\normalsize \noindent
Get into groups of two to three and work on the following.  Elect one person to write up your answers neatly and turn the first two pages of these activity with WrittenHW1.  You may need to arrange a meeting outside of class, so consider exchanging contact information. 


\begin{enumerate}
\item Perform the following and simplify:

$\displaystyle{\frac{6x}{3x+1}\cdot\frac{x-3}{x}}$  \hspace{1.3in} $\displaystyle{\frac{x-2}{x}\div\frac{x}{x+1}}$  \hspace{1.3in} 
$\displaystyle{\frac{\frac{4}{(x-5)^2}}{\frac{x}{x-5}}}$  \hspace{1in} 

\vspace{1.8in}

$\displaystyle{\frac{x}{2x-3}+\frac{2}{x+1}}$  \hspace{1.3in} $\displaystyle{\frac{x-2}{x}+\frac{x}{x+1}}$  \hspace{1.3in} 
$\displaystyle{\frac{4}{(x+1)^2}-\frac{x}{x+1}}$  \hspace{1in} 

\vspace{1.8in}

$\displaystyle{\frac{\frac{5x}{3}}{11}+\frac{1}{11}}$  \hspace{1.6in} $\displaystyle{\frac{x-2}{\frac{x}{3}}+\frac{x}{5}}$  \hspace{1.8in} 
$\displaystyle{\frac{\frac{4}{x+1}}{x+1}-\frac{1}{\frac{x+1}{x}}}$  \hspace{1in} 

\vspace{2in}
 
 

\newpage
\item A 100-gallon mixture of citrus extract and water is 3\% citrus extract.  
\begin{enumerate}
\item Write a fraction with $x$ whose values give the percentage (in decimal form) of the mixture that is citrus extract when $x$ gallons of water are added to the mixture.
\item Find the percentage of citrus extract in the mixture if 50 gallons of water are added to it.
\end{enumerate}

\vfill
\item A reservoir holds 600,000 gallons and is half-full.  Scientists do tests to find that the reservoir is .75\% acid.
\begin{enumerate}
\item Find a fraction with $x$ whose value give the percentage (in decimal form) of acid in the reservoir when $x$ gallons of water are added to it.
\item Find the percentage of acid in the reservoir if 150,000 gallons of water are added to it.
\end{enumerate}

\vfill





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\begin{center}

\Huge{Dimensional Analysis}\\
\end{center}

\normalsize


\item Given 1 foot (ft) is about 30.5 centimeters (cm):
\begin{enumerate}
\item convert 5 ft and 4 inches into cm
\vspace{.75in}
\item convert 2 cubic feet into cm$^3$
\vspace{1.0in}
\end{enumerate}
\end{enumerate}

\newpage
\begin{center}

\Huge{Language of Variation}\\
\end{center}

\begin{itemize}
\item ``P varies directly as T" means there exists a constant $k$ so that $P=kT$
\item ``P varies inversely as V" means there exists a constant $k$ so that $P=\frac{k}{V}$
\end{itemize}

\begin{enumerate}
\item Write ``$w$ varies directly as the square root of $x$ and inversly as $y$" in math symbols.
\vspace{1in}

\item Suppose $y$ varies directly as $x$.  If $y=6$ when $x=30$, find $y$ when $x=120$.

\vspace{1.9in}

\item The intensity (I) of light varies inversely as the square of the distance (d) from the light source.  If $I=4$ when $d=3$, what is $d$ when $I=7$?
%\item If a person doubles her/his distance from a lamp, what happens to the intensity of the light at her/his new location? 



 \end{enumerate}








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