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‎M101_Reading_HTML/M101_WeBWorK_QuickSheet.html

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<!DOCTYPE html>
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<!--Pretty this up-->
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<html>
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<head>
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<title>MAT-101: WeBWorK Quick Reference</title>
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<link href="M101webwork.css" rel="stylesheet" type="text/css">
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
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</script>
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<script type="text/javascript"
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src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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</script>
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</head>
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<body>
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<h1>MAT-101: WeBWorK Quick Reference</h1>
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<h2>Real Numbers</h2>
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<ul>
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<li>It is generally a good idea to maintain \(3\) to \(5\) decimals of accuracy when submitting answers in <tt>WeBWorK</tt></li>
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<li>Type <b>3/7</b> for \( \dfrac{3}{7} \)</li>
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<li>Type <b>.375 </b> for \( .375 \)</li>
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<li>Type <b>7.25% </b> for \(7.25\% \)</li>
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<li></li>
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</ul>
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<h2>Arithmetic Operations</h2>
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<ul>
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<li>Type <b>x^2 </b> for \( x^2 \)</li>
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</ul>
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<h2>Set Operations</h2>
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<ul>
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<li>Type <b>{1,4,5,6,7,8} </b> for \(\{1,4,5,6,7,8 \} \) in <tt>WeBWorK.</tt> Elements of sets are contained in curly braces.</li>
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<li>Type capital <b>U</b> for \(\cup \) the union symbol</li>
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<li> Type <b>(-inf,-2]U[1,inf)</b> for \((-\infty, -2]\cup [1,\infty)\)</li>
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<li>Type <b>None</b> for empty sets</li>
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</ul>
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<h2>Intervals</h2>
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<ul>
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<li>Type <b>[4,inf)</b> for the interval \( [4,\infty )\)</li>
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<li>Type <b>(-inf,-4)</b> for the interval \( (-\infty, -4)\)</li>
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<li>Type <b>(-inf,inf)</b> for the interval \( (-\infty, \infty)\)</li>
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</ul>
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<h2>Inequalities</h2>
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<ul>
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<li>Type the two symbols <b>&gt = </b> together for \(\geq\)</li>
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<li>Type the two symbols <b>&lt = </b> together for \(\leq\)</li>
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<li>Type <b>-inf &lt x &lt inf</b> for the inequality \(-\infty \lt x \lt \infty\)</li>
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<li>Type <b>x &lt = -3</b> for the inequality \(x \leq -3\)</li>
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</ul>
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<h2>Equations</h2>
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<ul>
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<li>2 solutions: Type <b>x=7 or x=-7</b></li>
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<li>0 solutions: Type <b>No solution</b></li>
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</ul>
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<H2>Graphs and Lines</H2>
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<ul>
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<li>Points in the plane are entered as <b>(#,#)=(horizontal #, vertical #)=(independent, dependent)=(predictor, response)</b></li>
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<li>For the first quadrant, type <b>Q1</b>, for the second quadrant, type <b>Q2</b>, etc.</li>
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<li>Type <b>undefined</b> for the slope of a vertical line in <tt>WeBWorK</tt></li>
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</ul>
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</body>
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</html>

‎M101_Reading_HTML/M101webwork.css

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@charset "utf-8";
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/* CSS Document */
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body {
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width: 720px;
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margin: auto;
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}
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td {
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padding: 0 15px 0 15px;
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}
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table, td {
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padding-top: 0.5em;
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padding-bottom: 0.5em;
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}
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table.center {
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margin-left: auto;
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margin-right: auto;
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}
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table {
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border-collapse: collapse;
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}
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.boxed {
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border: 2px solid green ;
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width: 75%;
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}
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.WWbox{
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background-color: yellow;
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border: solid 2px green;
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box-shadow: 0px 3px 5px 1px silver;
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}
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h1{
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color: #006600;
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}
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h2{
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color: #006600;
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text-decoration: underline;
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}
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h3{
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font-weight: bold;
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}
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‎M101_Reading_HTML/Thumbs.db

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‎M101_Reading_HTML/WeBWorK_ModuleContentFiles_2015Fall/Old Files/set1A_Fractions_text.html

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<!DOCTYPE html>
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<!-- Cite Beginning and Intermediate Algebra by Tyler Wallace is licensed under a Creative Commons
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Attribution 3.0 Unported License. (http://creativecommons.org/licenses/by/3.0/)
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Based on a work at http://wallace.ccfaculty.org/book/book.html. pages 12-15-->
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<html>
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<head>
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<title>MAT-101: Module 1A Fractions</title>
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<style>
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table, td
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{
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padding-top: 0.5em;
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padding-bottom: 0.5em;
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}
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table.center
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{
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margin-left:auto;
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margin-right:auto;
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}
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</style>
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
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</script>
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<script type="text/javascript"
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src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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</script>
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</head>
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<body>
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<b>Fractions</b><br><br>
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Working with fractions is a very important foundation to algebra. Here we will
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briefly review reducing, multiplying, dividing, adding, and subtracting fractions.
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As this is a review, concepts will not be explained in detail as other lessons are.
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<br><br>
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<b>World View Note:</b> The earliest known use of fraction comes from the Middle
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Kingdom of Egypt around 2000 BC!
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<br><br>
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We always like our final answers when working with fractions to be reduced
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(the numerator and denominator are divided by their greatest common factor (GCF)). This is shown in the following example:
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<br><br>
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<b>Example 1A-1:</b> <br>
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<center>
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<table class = "center">
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<tr>
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<td>$\dfrac{36}{84}$</td>
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<td>Both numerator and denominator are divisible by $4$</td>
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</tr>
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<tr>
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<td>$\dfrac{36 \div 4}{84 \div 4} = \dfrac{9}{21}$</td>
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<td>Both numerator and denominator are still divisible by $3$</td>
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</tr>
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<tr>
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<td>$\dfrac{9 \div 3}{21 \div 3} = \dfrac{3}{7}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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</center>
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<br>
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The previous example could have been done in one step by dividing both numerator
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and denominator by $12.$ We also could have divided by $2$ twice and then
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divided by $3$ once (in any order). It is not important which method we use as
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long as we continue reducing our fraction until it cannot be reduced any further.
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<br><br>
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The easiest operation with fractions is multiplication. We can multiply fractions
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by multiplying straight across, multiplying numerators together and denominators
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together.
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<br><br>
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<b>Example 1A-2:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{6}{7} \cdot \dfrac{3}{5}$</td>
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<td>Multiply numerators across and denominators across</td>
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</tr>
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<tr>
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<td>$\dfrac{18}{35}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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When multiplying we can reduce our fractions before we multiply. We can either
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reduce vertically with a single fraction, or diagonally with several fractions, as
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long as we use one number from the numerator and one number from the denominator.
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<br><br>
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<b>Example 1A-3:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{25}{24} \cdot \dfrac{32}{55}$</td>
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<td>Reduce $25$ and $55$ by dividing by $5$. Reduce $32$ and $24$ by dividing by $8$</td>
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</tr>
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<tr>
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<td>$\dfrac{5}{3} \cdot \dfrac{4}{11}$</td>
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<td>Multiply numerators across and denominators across</td>
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</tr>
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<tr>
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<td>$\dfrac{20}{33}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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Dividing fractions is very similar to multiplying with one extra step. Dividing
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fractions requires us to first take the reciprocal of the second fraction and multiply.
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Once we do this, the multiplication problem solves just as the previous
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problem.
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<br><br>
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<b>Example 1A-4:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{21}{16} \div \dfrac{28}{6}$</td>
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<td>Multiply by the reciprocal</td>
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</tr>
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<tr>
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<td>$\dfrac{21}{6} \cdot \dfrac{6}{28}$</td>
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<td>Reduce $21$ and $28$ by dividing by $7.$ Reduce $6$ and $16$ by dividing by $2$</td>
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</tr>
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<tr>
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<td>$\dfrac{3}{8} \cdot \dfrac{3}{4}$</td>
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<td>Multiply numerators across and denominators across</td>
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</tr>
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<tr>
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<td>$\dfrac{9}{32}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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To add and subtract fractions we will first have to find the least common denominator
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(LCD). There are several ways to find an LCD. One way is to find the
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smallest multiple of the larger denominator that is also divisible by the smaller
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denominator.
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<br><br>
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<b>Example 1A-5:</b> <br>
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<table class = "center">
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<tr>
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<td>Find the LCD of 8 and 12</td>
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<td>Test multiples of 12</td>
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</tr>
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<tr>
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<td>$12?\dfrac{12}{8}$</td>
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<td>No! Can't divide 12 by 8</td>
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</tr>
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<tr>
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<td>$24?\dfrac{24}{8}=3$</td>
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<td>Yes! We can divide 24 by 8</td>
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</tr>
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<tr>
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<td>24</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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Adding and subtracting fractions is identical in process. If both fractions already
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have a common denominator we just add or subtract the numerators and keep the
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denominator.
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<br><br>
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<b>Example 1A-6:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{7}{8}+\dfrac{3}{8}$</td>
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<td>Same denominator, add numerators $7+3$</td>
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</tr>
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<tr>
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<td>$\dfrac{10}{8}$</td>
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<td>Reduce answer, dividing by 2</td>
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</tr>
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<tr>
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<td>$\dfrac{5}{4}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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While $\dfrac{5}{4}$ can be written as the mixed number $1\dfrac{1}{4} , in algebra we will almost never
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use mixed numbers. For this reason we will always use the improper fraction, not
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the mixed number.
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<br><br>
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<b>Example 1A-7:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{13}{6}-\dfrac{9}{6}$</td>
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<td>Same denominator, subtract numerators $13-9$</td>
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</tr>
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<tr>
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<td>$\dfrac{4}{6}$</td>
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<td>Reduce answer, dividing by $2$</td>
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</tr>
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<tr>
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<td>$\dfrac{2}{3}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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If the denominators do not match we will first have to identify the LCD and build
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up each fraction by multiplying the numerators and denominators by the same
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number so the denominator is built up to the LCD.
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<br><br>
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<b>Example 1A-8:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{5}{6}+\dfrac{4}{9}$</td>
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<td> LCD is $18$</td>
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</tr>
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<tr>
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<td>$\dfrac{3\cdot 5}{3\cdot 6}+\dfrac{4\cdot 2}{9\cdot 2}$</td>
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<td>Multiply first fraction by $\dfrac{3}{3}$ and the second by $\dfrac{2}{2}$</td>
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</tr>
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<tr>
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<td>$\dfrac{15}{18}+\dfrac{8}{18}$</td>
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<td>Same denominator, add numerators, $15+8$</td>
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</tr>
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<tr>
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<td>$\dfrac{23}{18}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br
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<br><br>
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<b>Example 1A-9:</b> <br>
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<table class = "center">
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<tr>
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<td>$\dfrac{2}{3}-\dfrac{1}{6}$</td>
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<td> LCD is $6$</td>
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</tr>
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<tr>
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<td>$\dfrac{2\cdot 2}{2\cdot 3}-\dfrac{1}{6}$</td>
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<td>Multiply first fraction by $\dfrac{2}{2}$, the second already has a denominator of $6$</td>
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</tr>
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<tr>
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<td>$\dfrac{4}{6}-\dfrac{1}{6}$</td>
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<td>Same denominator, subtract numerators, $4-1$</td>
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</tr>
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<tr>
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<td>$\dfrac{3}{6}$</td>
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<td>Reduce answer, dividing numerator and denominator by $3$</td>
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</tr>
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<tr>
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<td>$\dfrac{1}{2}$</td>
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<td>Our solution</td>
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</tr>
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</table>
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<br>
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</body>
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</html>

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