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Algebraic property wording tweaks
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@sophiebits
sophiebits committed May 2, 2013
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39 changes: 19 additions & 20 deletions exercises/number_properties_terminology_1.html
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<p>Notice that on the left side of the equation the parentheses indicate to add the <code>b</code> and the <code>c</code> before you add the <code>a</code>.</p>
<p>On the right side of the equation, we first add <code>a</code> and <code>b</code> before adding <code>c</code>.</p>
<p>The order of the variables has not changed but the groupings (what's inside the parentheses) have.</p>
<p>The groups have changed, and another word for a group is <em>association</em>.The above equation demonstrates the Associative Property of addition.</p>
<p>The groups have changed, and another word for a group is <em>association</em>.The above equation demonstrates the associative property of addition.</p>
</div>
</div>

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<p>Evaluating the right side, the result is the same:</p>
<p><code>(<var>A</var>+<var>B</var>)+<var>C</var>=<var>ASSOCIATIVE_RESULT</var></code></p>
</div>
<p>The groups have changed, and another word for a group is <em>association</em>. The equation demonstrates the Associative Property.</p>
<p>The groups have changed, and another word for a group is <em>association</em>. The equation demonstrates the associative property.</p>
</div>
</div>

<div id="associative-variable">
<p class="question">Which one of the equations on the right represents the Associative Property of addition?</p>
<p class="question">Which one of the equations on the right represents the associative property of addition?</p>
<p class="solution"><code>a+(b+c)=(a+b)+c</code></p>
<ul class="choices" data-category="true">
<li data-each="EQUATIONS as value"><code><var>value</var></code></li>
</ul>
<div class="hints">
<p>The Associative Property should not be confused with the Commutative Property, in which the sequence or order of numbers is changed.</p>
<p>In contrast to the Commutative Property, the Associative Property justifies rearranging our parentheses. For example, adding <code>(4+2)+3</code> is equivalent to adding <code>4+(2+3)</code> and represents the Associative Property.</p>
<p><code>a+(b+c)=(a+b)+c</code> demonstrates the Associative Property.</p>
<p>The associative property should not be confused with the commutative property, in which the sequence or order of numbers is changed.</p>
<p>In contrast to the commutative property, the associative property justifies rearranging our parentheses. For example, adding <code>(4+2)+3</code> is equivalent to adding <code>4+(2+3)</code> and represents the associative property.</p>
<p><code>a+(b+c)=(a+b)+c</code> demonstrates the associative property.</p>
</div>
</div>

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</ul>
<div class="hints">
<p>As this equation implies, changing the order of <code>a</code> and <code>b</code> will not change the end result.</p>
<p>This property should not be confused with the Associative Property, in which groupings (what's inside the parentheses) are changed.</p>
<p>This equation demonstrates the Commutative Property. The following sentence may help you to remember this property: The <em>commuting</em> distance is the same in either direction, from school to home or home to school.</p>
<p>This property should not be confused with the associative property, in which groupings (what's inside the parentheses) are changed.</p>
<p>This equation demonstrates the commutative property.</p>
</div>
</div>

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<li data-each="PROPERTIES as value"><var>value</var></li>
</ul>
<div class="hints">
<p>This property should not be confused with the Associative Property, in which the order of operations is changed.</p>
<p>This property should not be confused with the associative property, in which the order of operations is changed.</p>
<p>As this equation implies, changing the order of <var>A</var> and <var>B</var> doesn't change the end result.</p>
<div>
<p>Evaluating the left side:</p>
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<p>Evaluating the right side, the result is the same:</p>
<p><code><var>B</var>+<var>A</var>=<var>COMMUTATIVE_RESULT</var></code></p>
</div>
<p>This equation demonstrates the Commutative Property. The following sentence may help you to remember this property: The <em>commuting</em> distance is the same in either direction, from school to home or home to school.</p>
<p>This equation demonstrates the commutative property.</p>
</div>
</div>

<div id="commutative-variable">
<p class="question">Which one of the equations on the right represents the Commutative Property of addition?</p>
<p class="question">Which one of the equations on the right represents the commutative property of addition?</p>
<p class="solution"><code>a+b=b+a</code></p>
<ul class="choices" data-category="true">
<li data-each="EQUATIONS as value"><code><var>value</var></code></li>
</ul>
<div class="hints">
<p>According to the Commutative Property, the order of the numbers doesn't matter.</p>
<p>The Commutative Property should not be confused with the Associative Property, in which you change the groupings (what is contained inside the parentheses).</p>
<p>The following sentence may help you to remember the Commutative Property: "The <em>commuting</em> distance is the same in either direction, from school to home or home to school."</p>
<p><code>a+b=b+a</code> demonstrates the Commutative Property.</p>
<p>According to the commutative property, the order of the numbers doesn't matter.</p>
<p>The commutative property should not be confused with the associative property, in which you change the groupings (what is contained inside the parentheses).</p>
<p><code>a+b=b+a</code> demonstrates the commutative property.</p>
</div>
</div>

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<div class="hints">
<p>On the left side of the equation, <code>b</code> is multiplied by the sum of <code>c</code> and <code>d</code>.</p>
<p>On the right side of the equation, we first multiply <code>b</code> by <code>c</code> and <code>d</code> individually and then add their products.</p>
<p>We say that multiplication <em>distributes</em> <code>b</code> over addition of <code>c</code> and <code>d</code>, and this equation demonstrates the Distributive Property.</p>
<p>We say that multiplication <em>distributes</em> <code>b</code> over addition of <code>c</code> and <code>d</code>, and this equation demonstrates the distributive property.</p>
</div>
</div>

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<p>Evaluating the right side, the result is the same:</p>
<p><code><var>A</var>+(<var>B</var>)(<var>C</var>)+(<var>B</var>)(<var>D</var>)=<var>DISTRIBUTIVE_RESULT</var></code></p>
</div>
<p>We say that multiplication <em>distributes</em> <code><var>B</var></code> over addition of <code><var>C</var></code> and <code><var>D</var></code> and so this is called the Distributive Property.</p>
<p>We say that multiplication <em>distributes</em> <code><var>B</var></code> over addition of <code><var>C</var></code> and <code><var>D</var></code> and so this is called the distributive property.</p>
</div>
</div>

<div id="distributive-variable">
<p class="question">Which one of the equations on the right represents the Distributive Property of addition?</p>
<p class="question">Which one of the equations on the right represents the distributive property of addition over multiplication?</p>
<p class="solution"><code>a+b(c+d)=a+bc+bd</code></p>
<ul class="choices" data-category="true">
<li data-each="EQUATIONS as value"><code><var>value</var></code></li>
</ul>
<div class="hints">
<p>In the correct answer, on the left side the equation <code>b</code> is multiplied by the sum of <code>c</code> and <code>d</code>.</p>
<p>On the right side of this equation, we first multiply <code>b</code> by <code>c</code> and <code>d</code> individually and then add their products.</p>
<p>In this equation, <code>b</code> gets <em>distributed</em> to <code>c</code> and <code>d</code>, and so we call this the Distributive Property.</p>
<p><code>a+b(c+d)=a+bc+bd</code> represents the Distributive Property.</p>
<p>In this equation, <code>b</code> gets <em>distributed</em> to <code>c</code> and <code>d</code>, and so we call this the distributive property.</p>
<p><code>a+b(c+d)=a+bc+bd</code> represents the distributive property.</p>
</div>
</div>
</div>
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