\hfill \hfill } %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}{Definition} \newtheorem{example}{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \geometry{left=0.6in,right=0.6in,top=0.6in,bottom=0.6in} \pagestyle{fancy} \lhead{\color{cyan} \Large Sample Quiz} \chead{\LARGE Fractions - Part 1} \rhead{} \cfoot{} \lfoot{\small \copyright \; Hidegkuti, 2013} \rfoot{\small Last revised: July 20, 2013} \textwidth 7.5in \textheight 9.5in \setlength{\headheight}{27pt} \rhead{page \thepage} \setlength{\parindent}{0pt} \begin{document} \begin{center} {\huge Answers\bigskip } \end{center} \begin{enumerate} \item Compute $\dfrac{4}{9}$ of $63$.$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion 16$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item Shade $\dfrac{5}{9}$ of the circle shown below.\FRAME{dtbpF}{1.5056in}{% 1.5056in}{0pt}{}{}{pic3a.bmp}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 1.5056in;height 1.5056in;depth 0pt;original-width 0.045in;original-height 0.0432in;cropleft "0";croptop "1.0484";cropright "1";cropbottom "0";filename '../../../../../../../Desktop/pic3a.bmp';file-properties "XNPEU";}} \item Compute $\dfrac{5}{6}$ of $24$.$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \allowbreak 20$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item The price of a TV is $\$~400$. \ We want to raise the price by $5\%$. \ What is the new price?$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \$420$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item The price of a couch is $\$700$. \ Next week, it will go on a $15\%$ sale. \ What is the new price? (A $15\%$ sale means that the price of the item is lowered by $15\%$.) \ \ $~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \$595$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item Find $\dfrac{3}{4}$ of $56$.$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion 42$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item We placed $\$2000$ into a bank account with $6\%$ yearly interest rate. How much money do we have in the bank after one year?$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \$2120$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item This problem is about a method of comparing fractions. \begin{enumerate} \item Compute $\dfrac{3}{7}$ \ of \ $420$.$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion 180$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item Compute $\dfrac{4}{10}$ of $420$.$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion 168$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item Based on the results of parts a) and b), which fraction is larger, $% \dfrac{3}{7}$ \ or $\dfrac{4}{10}$? $~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \dfrac{3}{7}$ %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion is $\ $larger% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \end{enumerate} \item Bert has made $\$54\,000$ last year. \ If he has to pay $32\%$ of his income in taxes, how much taxes does he owe and how much of his income will he keep?$~~~$% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion He must pay $\ %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \$17\,280$ in taxes and will keep $\$36\,720$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion . \item Sally used to make $\$2400$ per month, but now she got a $3\%$ raise. \ How much is her monthly salary now?$~~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \$2472$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \item Mr. X won \thinspace $\$600\,000$ in the lottery two yers ago. \ By now he has spent some of the money. \ When he was asked what happened, he said the following. \ "\textit{I didn't spend it all. \ I spent }$\dfrac{1}{3% }$\textit{\ of the money by taking a luxury yacht trip around the world. \ Then I put the rest in the bank. \ Later I decided to buy a house I really liked. \ So I took }$\dfrac{3}{4}$\textit{\ of the money out of the bank and baught the house. \ For half of what was left, I purchased stocks that completely lost their value. \ Finally, I gave }$\dfrac{2}{5}$\textit{\ of what's left to my niece for her college education.}" \ How much money is left from the winnings? \ $~~% %TCIMACRO{\TeXButton{red}{\color{red}}}% %BeginExpansion \color{red}% %EndExpansion \$30\,000$% %TCIMACRO{\TeXButton{black}{\color{black}}}% %BeginExpansion \color{black}% %EndExpansion \end{enumerate} \end{document}