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<title>Equations and Formulas</title>
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<h1 align="center">Equations and Formulas </h1>
<h2>What is an Equation?</h2>
<p>An equation says that two things are equal. It will have an equals sign &quot;=&quot; like this:</p>
<table border="0" align="center">
<tr valign="middle">
<td align="center" width="50" class="huge"><b><i>x</i></b></td>
<td align="center" width="50" class="huge"><b>+</b></td>
<td align="center" width="50" class="huge"><b>2</b></td>
<td align="center" width="50" class="huge"><b>=</b></td>
<td align="center" width="50" class="huge"><b>6</b></td>
</tr>
</table>
<p>That equations says: <b>what is on the left (x + 2) is equal to what is on the right (6)</b></p>
<p>So an equation is like a <b>statement</b> &quot;<i>this</i> equals <i>that</i>&quot;</p>
<p><i>(Note: this equation has the solution <b>x=4</b>, read <a href="equations-solving.html">how to solve equations</a>.</i></p>
<h2>What is a Formula?</h2>
<p>A formula is a fact or rule that uses mathematical symbols.<br>
<br>
It will usually have:</p>
<ul>
<li>an equals sign (=)</li>
<li>two or more <b>variables</b> (x, y, etc) that stand in for values we don't know yet</li>
</ul>
<p>It shows us how things are related to each other.</p>
<div class="example">
<h3>Example:
The formula for finding the <a href="../geometry/cuboids-rectangular-prisms.html">volume of a box</a> is: </h3>
<p align="center" class="large">V = lwh</p>
<p align="center"><b>V</b> stands for volume, <b>l</b> for length, <b>w</b> for width, and <b>h</b> for height. </p><br />
<p style="float:right; margin: 0 0 5px 10px;">
<img src="../geometry/images/cuboid-example.svg" alt="cuboid" /></p>
<p>When l=10, w=4, and h=5, then:</p>
<p class="center"> <b>V = 10 &times; 4 &times; 5 = 200</b></p><div style="clear:both"></div>
</div>
<p>These are all equations, but only some are formulas:</p>
<div class="beach">
<table border="0" align="center">
<tr>
<td width="150" align="center"><b>x</b> = 2<b>y</b> - 7</td>
<td>Formula (relating <b>x</b> and <b>y</b>)</td>
</tr>
<tr>
<td width="150" align="center"><b>a<sup>2</sup></b> + <b>b<sup>2</sup></b> = <b>c<sup>2</sup></b></td>
<td>Formula (relating <b>a</b>, <b>b</b> and <b>c</b>)</td>
</tr>
<tr>
<td width="150" align="center"><b>x</b>/2 + 7 = 0</td>
<td>Not a Formula (just an equation)</td>
</tr>
</table>
</div>
<h2>Without the Equals</h2>
<p>Sometimes a formula is written without the &quot;=&quot;:</p>
<div class="example">
<h3>Example: The formula for the volume of a box is:</h3>
<p align="center"><b>lwh</b></p>
</div>
<p>But in a way the &quot;=&quot; is still there, because we can write <b>V = lwh</b> if we want to.</p>
<h2>Subject of a Formula</h2>
<p>The &quot;subject&quot; of a formula is the single variable (usually on the left of the &quot;=&quot;) that everything else is equal to.</p>
<div class="example">
<h3>Example: in the formula </h3>
<p align="center"><span class="large">s = ut + &frac12; at<sup>2</sup></span> </p>
<p><span class="large">&quot;s&quot;</span> is the subject of the formula</p>
</div>
<h2>Changing the Subject </h2>
<p>A very powerful thing that Algebra can do is to &quot;rearrange&quot; a formula so that another variable is the subject. </p>
<div class="example">
<h3>Example: Rearrange the volume of a box formula (<b>V = lwh</b>) so that the width is the subject</h3>
<div class="tbl">
<div class="row"><span class="left">Start with:</span><span class="right"><b>V = lwh</b></span></div>
<div class="row"><span class="left">divide both sides by h:</span><span class="right"><b>V/h = lw</b></span></div>
<div class="row"><span class="left">divide both sides by l:</span><span class="right"><b>V/(hl) = w</b></span></div>
<div class="row"><span class="left">swap sides:</span><span class="right"><b>w = V/(hl)</b></span></div>
</div>
<p>So if we want a box with a volume of 12, a length of 2, and a height of 2, we can calculate its width:</p>
<div class="tbl">
<div class="row"><span class="left"> w =</span><span class="right"> V/(hl)</span></div>
<div class="row"><span class="left">=</span><span class="right"> 12 / (2 × 2) </span></div>
<div class="row"><span class="left">=</span><span class="right"> 12 / 4 </span></div>
<div class="row"><span class="left">=</span><span class="right"> 3</span></div>
</div>
</div><p>&nbsp;</p>
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<div class="related"> <a href="introduction.html">Introduction to Algebra</a> <a href="index.html">Algebra Index</a> </div>
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