<h2>Key Concepts</h2>
<h3>Multiply Whole Numbers</h3>
<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>
<ul>
<li><strong>Multiplication Property of Zero</strong>
<ol>
<li>The product of any number and 0 is 0.

<div> </div>

\(a\cdot 0=0\)

<div> </div>

\(0\cdot a=0\)</li>
</ol>
</li>
<li><strong>Identity Property of Multiplication</strong>
<ol>
<li>The product of any number and 1 is the number.

<div> </div>

\(1\cdot a=a\)

<div> </div>

\(a\cdot 1=a\)</li>
</ol>
</li>
<li><strong>Commutative Property of Multiplication</strong>
<ol>
<li>Changing the order of the factors does not change their product.

<div> </div>

\(a\cdot b=b\cdot a\)</li>
</ol>
</li>
<li><strong>Multiply two whole numbers to find the product.</strong>
<ol type="1">
<li>Write the numbers so each place value lines up vertically.</li>
<li>Multiply the digits in each place value.</li>
<li>Work from right to left, starting with the ones place in the bottom number.</li>
<li>Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.</li>
<li>If a product in a place value is more than 9, carry to the next place value.</li>
<li>Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.</li>
<li>Insert a zero as a placeholder with each additional partial product.</li>
<li>Add the partial products.</li>
</ol>
</li>
</ul>
<h3>Divide Whole Numbers</h3>
<table data-label="" summary="A table with 5 columns and 1 row. The first column is labeled “operation” and has the value “division”. 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">\(\text{Division}\)</td>
<td data-valign="top">\(÷\)

<div> </div>

\(\frac{a}{b}\)

<div> </div>

\(b\overline{)a}\)

<div> </div>

\(a/b\)</td>
<td data-valign="top">\(12÷4\)

<div> </div>

\(\frac{12}{4}\)

<div> </div>

\(4\overline{)12}\)

<div> </div>

\(12/4\)</td>
<td data-valign="top">\(\text{Twelve divided by four}\)</td>
<td data-valign="top">\(\text{the quotient of 12 and 4}\)</td>
</tr>
</tbody>
</table>
<ul>
<li><strong>Division Properties of One</strong>
<ol>
<li>Any number (except 0) divided by itself is one. \(a÷a=1\)</li>
<li>Any number divided by one is the same number. \(a÷1=a\)</li>
</ol>
</li>
<li><strong>Division Properties of Zero</strong>
<ol>
<li>Zero divided by any number is 0. \(0÷a=0\)</li>
<li>Dividing a number by zero is undefined. \(a÷0\) undefined</li>
</ol>
</li>
<li><strong>Divide whole numbers.</strong>
<ol type="1">
<li>Divide the first digit of the dividend by the divisor.

<div> </div>

If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.</li>
<li>Write the quotient above the dividend.</li>
<li>Multiply the quotient by the divisor and write the product under the dividend.</li>
<li>Subtract that product from the dividend.</li>
<li>Bring down the next digit of the dividend.</li>
<li>Repeat from Step 1 until there are no more digits in the dividend to bring down.</li>
<li>Check by multiplying the quotient times the divisor.</li>
</ol>
</li>
</ul>
<h2>Glossary</h2>
<h3>dividend</h3>
<p>When dividing two numbers, the dividend is the number being divided.</p>
<h3>divisor</h3>
<p>When dividing two numbers, the divisor is the number dividing the dividend.</p>
<h3>product</h3>
<p>The product is the result of multiplying two or more numbers.</p>
<h3>quotient</h3>
<p>The quotient is the result of dividing two numbers.</p>

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Key Concepts and Glossary

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

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


Key Concepts and Glossary

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