be3cb8b6-1154-48ab-964b-eb8609c9aee0.html

<h4>Translate an English Phrase to an Algebraic Expression</h4>
<p>You can use the following operation symbols to translate English phrases into algebraic expressions. <br>
</p>
<p>Look closely at these phrases using the four operations:</p>
<p>the <strong>sum</strong> of \( a \) and \( b \)<br>
  the <strong>difference</strong> of \( a \) and \( b \)<br>
  the <strong>product</strong> of \( a \) and \( b \)<br>
  the <strong>quotient</strong> of \( a \) and \( b \) </p>
<p>Then, identify other phrases that represent the same algebraic concepts.</p>
<div class="os-raise-usermessage-link">
  <p>Log into <a href="https://student.desmos.com" target="_blank">student.desmos.com</a> using the information provided by your teacher to complete the activity.</p>
</div>
<p>Each phrase tells us to operate on two numbers. Look for the words "of" and "and" to find the numbers.</p>
<p>Later in this course, we&rsquo;ll apply our skills in algebra to solving applications. The first step will be to translate an English phrase to an algebraic expression.</p>
<p><strong>Example</strong><br>
  The length of a rectangle is 14 less than the width. Let \( w \) represent the width of the rectangle. Write an expression for the length of the rectangle.</p>
<p><strong>Step 1 - </strong> Write a phrase about the length of the rectangle.</p>
<p>14 less than the width</p>
<p><strong>Step 2 - </strong> Substitute  \(w\) for "the width."</p>
<p>14 less than \( w \)</p>
<p><strong>Step 3 - </strong> Rewrite <em>less than </em> as <em>subtracted from</em>.</p>
<p>14 subtracted from <em>w </em></p>
<p><strong>Step 4 - </strong> Translate the phrase into algebra.</p>
<p>\( w &minus; 14 \)</p>
<br>
<h4>Try It: Translate an English Phrase to an Algebraic Expression</h4>
<p>Translate the following into an algebraic expression: </p>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="eventShow1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <p>June has dimes and quarters in her purse. The number of dimes is seven less than four times the number of quarters. Let \( q \) represent the number of quarters. Write an expression for the number of dimes.</p>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="eventShow1">
  <p>Compare your answer:</p>
  <p>Here is how to translate this into an algebraic expression: <br>
  </p>
  <p><strong>Step 1 - </strong> Write a phrase about the number of dimes.</p>
  <p>seven less than four times the number of quarters</p>
  <p><strong>Step 2 - </strong> Substitute \( q \)  for the number of quarters.</p>
  <p>7 less than 4 times \( q \)</p>
  <p><strong>Step 3 - </strong> Translate \(4\) times \( q \).</p>
  <p>7 less than \( 4q \)</p>
  <p><strong>Step 4 - </strong> Translate the phrase into algebra. </p>
  <p>\( 4q &minus; 7 \)</p>
</div>