<p>By the end of this lesson and the next few, you should be able to:</p>
<ul>
<li>Use multiplication notation</li>
<li>Model multiplication of whole numbers</li>
<li>Multiply whole numbers</li>
<li>Translate word phrases to math notation</li>
<li>Multiply whole numbers in applications</li>
</ul>
<p><a href="https://data.ulearngo.com/assets/c16fa7b7-a63c-4e6b-bf54-7917644ae627"><img alt="multiplication" class="size-full wp-image-101862 alignnone" height="569" src="https://data.ulearngo.com/assets/c16fa7b7-a63c-4e6b-bf54-7917644ae627" width="800"/></a></p>
<h2>Use Multiplication Notation</h2>
<p>Suppose you were asked to count all these pennies shown the figure below.</p>
<p><img alt="An image of 3 horizontal rows of pennies, each row containing 8 pennies." class="alignnone" src="https://data.ulearngo.com/assets/8c59cb32-b996-4f86-934c-2c0b98be5f32"/></p>
<p>Would you count the pennies individually? Or would you count the number of pennies in each row and add that number \(3\) times.</p>
<div data-label="">\(8+8+8\)</div>
<p>Multiplication is a way to represent repeated addition. So instead of adding \(8\) three times, we could write a multiplication expression.</p>
<div data-label="">
<div>\(3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}8\)</div>
</div>
<p>We call each number being multiplied a factor and the result the <strong>product</strong>. We read \(3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}8\) as <em>three times eight</em>, and the result as <em>the product of three and eight</em>.</p>
<p>There are several symbols that represent multiplication. These include the symbol \(×\) as well as the dot, \(·\), and parentheses \(\left( \right ).\)</p>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Operation Symbols for Multiplication:</h3>
<p>To describe multiplication, we can use symbols and words.</p>
<table data-label="" summary="A table with 5 columns and 1 row. The first column is labeled “operation” and has the value “multiplication”. The second column is labeled “notation” and has three values - the x multiplication symbol, the dot multiplication symbol, and the parenthesis multiplication symbol. The third column is labeled “expression” and has three values - 3 times 8 with the different multiplication symbols from the second column. The fourth column is labeled “read as” and has the value “three times eight”. The fifth column has the label “result” and has the value “the product of 3 and 8”.">
<thead>
<tr>
<th>Operation</th>
<th>Notation</th>
<th>Expression</th>
<th>Read as</th>
<th>Result</th>
</tr>
</thead>
<tbody>
<tr>
<td data-valign="top">\(\text{Multiplication}\)</td>
<td data-valign="top">\(×\)

<div> </div>

\(·\)

<div> </div>

\(\left( \right)\)</td>
<td data-valign="top">\(3×8\)

<div> </div>

\(3·8\)

<div> </div>

\(3\left(8\right)\)</td>
<td data-valign="top">\(\text{three times eight}\)</td>
<td data-valign="top">\(\text{the product of 3 and 8}\)</td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<div data-type="example">
<section></section>
<section>
<div>
<p>Translate from math notation to words:</p>
<ol type="1">
<li>\(7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}6\)</li>
<li>\(12·14\)</li>
<li>\(6\left(13\right)\)</li>
</ol>
</div>
<div>
<section>
<h4>Solution</h4>
<ol data-labeled-item="true">
<li>We read this as <em>seven times six</em> and the result is <em>the product of seven and six</em>.</li>
<li>We read this as <em>twelve times fourteen</em> and the result is <em>the product of twelve and fourteen</em>.</li>
<li>We read this as <em>six times thirteen</em> and the result is <em>the product of six and thirteen</em>.</li>
</ol>
</section>
</div>
</section>
</div>
</div>
</div>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Extra:</h3>
<div data-type="note">
<section></section>
<section>
<div>
<p>Translate from math notation to words:</p>
<ol type="1">
<li>\(8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}7\)</li>
<li>\(18·11\)</li>
</ol>
</div>
<div>
<h4>Solution</h4>
<section>
<ol type="1">
<li>eight times seven; the product of eight and seven</li>
<li>eighteen times eleven; the product of eighteen and eleven</li>
</ol>
</section>
</div>
</section>
</div>
</div>
</div>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Extra:</h3>
<div data-type="note">
<section></section>
<section>
<div>
<p>Translate from math notation to words:</p>
<ol type="1">
<li>\(\left(13\right)\left(7\right)\)</li>
<li>\(5\left(16\right)\)</li>
</ol>
</div>
<div>
<h4>Solution</h4>
<section>
<ol type="1">
<li>thirteen times seven; the product of thirteen and seven</li>
<li>five times sixteen; the product of five and sixteen</li>
</ol>
</section>
</div>
</section>
</div>
</div>
</div>
<section></section>

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Multiplication Notation

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Explore the world of numbers and learn about their history, properties, and applications, including place value, addition, subtraction, multiplication, and division.


Multiplication Notation

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