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abe84fc0-8397-4e87-9c9a-84dad7a6fe87.html
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<h4>Warm Up Activity</h4>
<p>Finding a product mentally can be done by changing the way you look at a multiplication problem.</p>
<p>For example, \(9 \cdot 39\) can be thought of as \(9 \cdot (40 − 1)\). For some people, this might be easier to calculate mentally since you can imagine the solution as \(360 − 9\), or 351. This method leverages the distributive property of multiplication over addition.</p>
<p>For the following questions, find each product mentally. Then, explain how you changed the way you looked at each multiplication problem to use the distributive property.</p>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a52ef1ab-f382-42d6-9e47-be9379e27fab" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>(\(9 \cdot 11\))</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter the product and your explanation.</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>99</p>
<p>For example, \(9 \cdot 11\) can be thought of as \(9 \cdot (10 + 1)\). This simplifies to \(90 + 9\), or 99.</p>
</div>
</div>
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<br>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="fb18c558-8d3b-45eb-afb5-91a906aa5b36" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>(\(19 \cdot 21\))</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter the product and your explanation.</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>399</p>
<p>For example, \(19 \cdot 21\) can be thought of as \(19 \cdot (20 + 1)\). This simplifies to \(380 + 19\), or 399.</p>
</div>
</div>
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<br>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b580c4ac-4a60-4e76-82b1-ed6f8682b792" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>(\(99 \cdot 101\))</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter the product and your explanation.</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>9999</p>
<p>For example, \(99 \cdot 101\) can be thought of as \(99 \cdot (100 + 1)\). This simplifies to \(9900 + 99\), or 9999.</p>
</div>
</div>
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<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d4537fb8-ae14-4009-823f-f0b248a9e49b" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>(\(109 \cdot 101\))</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter the product and your explanation.</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>11,009</p>
<p>For example, \(109 \cdot 101\) can be thought of as \(109 \cdot (100 + 1)\). This simplifies to \(10,900 + 109\), or 11,009.</p>
</div>
</div>
<!--Interaction End -->