<h2 data-type="title">Identifying Expressions and Equations</h2>
<p>What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. “Running very fast” is a phrase, but “The football player was running very fast” is a sentence. A sentence has a subject and a verb.</p>
<p>In algebra, we have <em>expressions</em> and <em>equations</em>. An <strong>expression</strong> is like a phrase. Here are some examples of expressions and how they relate to word phrases:</p>
<table data-label="" summary="This table has five rows and three columns. The first row is a header row and it labels each column. The first column is labeled “Expression”, the second “Words” and the third “Phrase”. In the second row, under the “Expression” column is three plus five. Under the “Words” column is the phrase “three plus five”. Under the “Phrase” column is the phrase “the sum of three and five”. In the third row, under the “Expression” column is n minus one. Under the “Words” column is the phrase “n minus one.” Under the “Phrase” column is the phrase “the difference of n and one.” In the fourth row, under the “Expression” column is  six times seven. Under the “Words” column is the phrase “six times seven.” Under the “Phrase” column is the phrase “the product of six and seven.” In the fifth row, under the “Expression” column is x divided by y. Under the “Words” column is the phrase “x divided by y.” Under the “Phrase” column is the phrase “the quotient of x and y.”">
<thead>
<tr>
<th>Expression</th>
<th>Words</th>
<th>Phrase</th>
</tr>
</thead>
<tbody>
<tr>
<td><span tabindex="0">\(3+5\)</span></td>
<td><span tabindex="0">\(3\phantom{\rule{0.2em}{0ex}}\text{plus}\phantom{\rule{0.2em}{0ex}}5\)</span></td>
<td>the sum of three and five</td>
</tr>
<tr>
<td><span tabindex="0">\(n-1\)</span></td>
<td><span tabindex="0">\(n\) minus one</span></td>
<td>the difference of <span tabindex="0">\(n\) and one</span></td>
</tr>
<tr>
<td><span tabindex="0">\(6·7\)</span></td>
<td><span tabindex="0">\(6\phantom{\rule{0.2em}{0ex}}\text{times}\phantom{\rule{0.2em}{0ex}}7\)</span></td>
<td>the product of six and seven</td>
</tr>
<tr>
<td><span tabindex="0">\(\frac{x}{y}\)</span></td>
<td><span tabindex="0">\(x\) divided by \(y\)</span></td>
<td>the quotient of <span tabindex="0">\(x\) and \(y\)</span></td>
</tr>
</tbody>
</table>
<p>Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:</p>
<table data-label="" summary="This table has six rows and two columns. The first row is a header row  labeling each column. The first column is labeled “Equation” and the second “Sentence”. In the second row, under the “Equation” column is three plus five equals eight. Under the “Sentence” column is the sentence “The sum of three and five is equal to eight”. In the third row, under the “Equation” column is  n minus one equals fourteen. Under the “Sentence” column is the Sentence “The difference of n and one equals fourteen.” In the fourth row, under the “Equation” column is six times seven equals forty-two. Under the “Sentence” column is the sentence “The product of six and seven is equal to forty-two.” In the fifth row, under the “Equation” column is  x equals fifty-three. Under the “Sentence” column is the sentence “x is equal to fifty-three.” In the sixth row, under the “Equation” column is y plus  nine equals two times y minus 3. Under the “Sentence” column is the sentence “y plus nine is equal to two y minus three.”">
<thead>
<tr>
<th>Equation</th>
<th>Sentence</th>
</tr>
</thead>
<tbody>
<tr>
<td><span tabindex="0">\(3+5=8\)</span></td>
<td>The sum of three and five is equal to eight.</td>
</tr>
<tr>
<td><span tabindex="0">\(n-1=14\)</span></td>
<td><span tabindex="0">\(n\) minus one equals fourteen.</span></td>
</tr>
<tr>
<td><span tabindex="0">\(6·7=42\)</span></td>
<td>The product of six and seven is equal to forty-two.</td>
</tr>
<tr>
<td><span tabindex="0">\(x=53\)</span></td>
<td><span tabindex="0">\(x\) is equal to fifty-three.</span></td>
</tr>
<tr>
<td><span tabindex="0">\(y+9=2y-3\)</span></td>
<td><span tabindex="0">\(y\) plus nine is equal to two \(y\) minus three.</span></td>
</tr>
</tbody>
</table>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3 data-type="title">Expressions and Equations</h3>
<p>An <strong>expression</strong> is a number, a variable, or a combination of numbers and variables and operation symbols.</p>
<p>An <strong>equation</strong> is made up of two expressions connected by an equal sign.</p>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<p>Determine if each is an expression or an equation:</p>
<ol type="1">
<li><span tabindex="0">\(\phantom{\rule{0.2em}{0ex}}16-6=10\)</span></li>
<li><span tabindex="0">\(\phantom{\rule{0.2em}{0ex}}4·2+1\)</span></li>
<li><span tabindex="0">\(\phantom{\rule{0.2em}{0ex}}x÷25\)</span></li>
<li><span tabindex="0">\(\phantom{\rule{0.2em}{0ex}}y+8=40\)</span></li>
</ol>
</div>
<div>
<h3 data-type="title">Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td>\(\phantom{\rule{0.2em}{0ex}}16-6=10\)</td>
<td>This is an equation—two expressions are connected with an equal sign.</td>
</tr>
<tr>
<td>\(\phantom{\rule{0.2em}{0ex}}4·2+1\)</td>
<td>This is an expression—no equal sign.</td>
</tr>
<tr>
<td>\(\phantom{\rule{0.2em}{0ex}}x÷25\)</td>
<td>This is an expression—no equal sign.</td>
</tr>
<tr>
<td>\(\phantom{\rule{0.2em}{0ex}}y+8=40\)</td>
<td>This is an equation—two expressions are connected with an equal sign.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>

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Identifying Expressions and Equations

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

Learn to identify and simplify algebraic expressions, evaluate expressions, and translate word problems into algebraic equations in this comprehensive tutorial on the language of algebra.


Identifying Expressions and Equations

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