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Include domain in rational expression question #43415

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Include domain in rational expression question #43415

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4ce451b
Merge branch 'graph-legend'
petercollingridge Mar 16, 2013
9ceff02
Create new solution box for domain
petercollingridge Mar 16, 2013
fc2f508
Ensure domain box only shows when needed and accepts the correct answer
petercollingridge Mar 16, 2013
e5d8212
Rearrange solution boxes
petercollingridge Mar 16, 2013
8fffb16
Add hints to explain the domain
petercollingridge Mar 16, 2013
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2 changes: 1 addition & 1 deletion exercises/converting_decimals_to_fractions_1.html
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Original file line number Original file line Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@
<div class="vars"> <div class="vars">
<var id="D">randRangeExclude(1, 99, [10,20,30,40,50,60,70,80,90]) / 100</var> <var id="D">randRangeExclude(1, 99, [10,20,30,40,50,60,70,80,90]) / 100</var>
<var id="T">floor( D * 10 )</var> <var id="T">floor( D * 10 )</var>
<var id="H">floor( ( D * 100 ) % 10 )</var> <var id="H">round( ( D * 100 ) % 10 )</var>
</div> </div>
<p class="question">Express <code><var>D.toFixed( 2 )</var></code> as a fraction.</p> <p class="question">Express <code><var>D.toFixed( 2 )</var></code> as a fraction.</p>
<p class="solution" data-type="rational" data-simplify="optional"><var>D</var></p> <p class="solution" data-type="rational" data-simplify="optional"><var>D</var></p>
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185 changes: 144 additions & 41 deletions exercises/simplifying_rational_expressions_3.html
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Original file line number Original file line Diff line number Diff line change
Expand Up @@ -18,6 +18,9 @@
padding-top: 1px; padding-top: 1px;
border-top: 1px solid black; border-top: 1px solid black;
} }
#solutionarea .soln-dom {
padding-left: 3px;
}
</style> </style>
</head> </head>
<body> <body>
Expand Down Expand Up @@ -45,6 +48,54 @@
<var id="POSITIVEDENOMINATOR">getExpressionRegex(1, X, C)</var> <var id="POSITIVEDENOMINATOR">getExpressionRegex(1, X, C)</var>
<var id="NEGATIVENUMERATOR">getExpressionRegex(-1, X, -B)</var> <var id="NEGATIVENUMERATOR">getExpressionRegex(-1, X, -B)</var>
<var id="NEGATIVEDENOMINATOR">getExpressionRegex(-1, X, -C)</var> <var id="NEGATIVEDENOMINATOR">getExpressionRegex(-1, X, -C)</var>
<var id="DOMAIN">-C</var>
</div>

<div class="solution" data-type="set">
<div class="set-sol" data-type="multiple">
<span class="sol" data-type="regex"><var>POSITIVENUMERATOR</var></span>
<span class="sol" data-type="number"><var>-A</var></span>
<span class="sol" data-type="regex"><var>POSITIVEDENOMINATOR</var></span>
</div>
<div class="set-sol" data-type="multiple">
<span class="sol" data-type="regex"><var>NEGATIVENUMERATOR</var></span>
<span class="sol" data-type="number"><var>-A</var></span>
<span class="sol" data-type="regex"><var>NEGATIVEDENOMINATOR</var></span>
</div>

<div class="input-format">
<div class="entry" data-type="multiple">
<table>
<tr>
<td rowspan="2">
<code><var>Y</var> = </code>
</td>
<td class="soln-top">
<span class="sol short40">a</span>
</td>
<td rowspan="2">;
<code> \space <var>X</var> \neq </code><span class="sol soln-dom short32">a</span>
</td>
</tr>
<tr>
<td class="soln-bot">
<span class="sol short40" data-fallback="1">a</span>
</td>
</tr>
</table>
</div>
</div>
<div class="example">a simplifed expression, like <code>x + 2</code></div>
</div>

<div class="hints" data-apply="appendContents">
<div>
<p>The original expression has <code>(<var>X</var> + <var>A</var>)</code> in the denominator,
so is not defined when <code><var>X</var> = <var>-A</var></code>.</p>
We must therefore include this condition with the simplified expression:</p>
<code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}; \space
<var>X</var> \neq <var>-A</var></code>
</div>
</div> </div>
</div> </div>


Expand All @@ -59,6 +110,53 @@
<var id="NEGATIVENUMERATOR">getExpressionRegex(0, X, -B)</var> <var id="NEGATIVENUMERATOR">getExpressionRegex(0, X, -B)</var>
<var id="NEGATIVEDENOMINATOR">getExpressionRegex(-1, X, -C)</var> <var id="NEGATIVEDENOMINATOR">getExpressionRegex(-1, X, -C)</var>
</div> </div>

<div class="solution" data-type="set">
<div class="set-sol" data-type="multiple">
<span class="sol" data-type="regex"><var>POSITIVENUMERATOR</var></span>
<span class="sol" data-type="number"><var>-A</var></span>
<span class="sol" data-type="regex"><var>POSITIVEDENOMINATOR</var></span>
</div>
<div class="set-sol" data-type="multiple">
<span class="sol" data-type="regex"><var>NEGATIVENUMERATOR</var></span>
<span class="sol" data-type="number"><var>-A</var></span>
<span class="sol" data-type="regex"><var>NEGATIVEDENOMINATOR</var></span>
</div>

<div class="input-format">
<div class="entry" data-type="multiple">
<table>
<tr>
<td rowspan="2">
<code><var>Y</var> = </code>
</td>
<td class="soln-top">
<span class="sol short40">a</span>
</td>
<td rowspan="2">;
<code> \space <var>X</var> \neq </code><span class="sol soln-dom short32">a</span>
</td>
</tr>
<tr>
<td class="soln-bot">
<span class="sol short40" data-fallback="1">a</span>
</td>
</tr>
</table>
</div>
</div>
<div class="example">a simplifed expression, like <code>x + 2</code></div>
</div>

<div class="hints" data-apply="appendContents">
<div>
<p>The original expression has <code>(<var>X</var> + <var>A</var>)</code> in the denominator,
so is not defined when <code><var>X</var> = <var>-A</var></code>.</p>
We must therefore include this condition with the simplified expression:</p>
<code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}; \space
<var>X</var> \neq <var>-A</var></code>
</div>
</div>
</div> </div>


<div id="bottom-constant"> <div id="bottom-constant">
Expand All @@ -72,44 +170,58 @@
<var id="NEGATIVENUMERATOR">getExpressionRegex(-1, X, -B)</var> <var id="NEGATIVENUMERATOR">getExpressionRegex(-1, X, -B)</var>
<var id="NEGATIVEDENOMINATOR">getExpressionRegex(0, X, -C)</var> <var id="NEGATIVEDENOMINATOR">getExpressionRegex(0, X, -C)</var>
</div> </div>
</div>
</div>


<p class="problem">Simplify the following expression:</p> <p class="problem">Simplify the following expression:</p>
<p class="question"><code><var>Y</var> = \dfrac{<var>NUMERATOR</var>}{<var>DENOMINATOR</var>}</code></p>
<div class="solution" data-type="set">
<div class="set-sol" data-type="multiple">
<span class="sol" data-type="regex"><var>POSITIVENUMERATOR</var></span>
<span class="sol" data-type="regex"><var>POSITIVEDENOMINATOR</var></span>
</div>
<div class="set-sol" data-type="multiple">
<span class="sol" data-type="regex"><var>NEGATIVENUMERATOR</var></span>
<span class="sol" data-type="regex"><var>NEGATIVEDENOMINATOR</var></span>
</div>


<div class="solution" data-type="set"> <div class="input-format">
<div class="set-sol" data-type="multiple"> <div class="entry" data-type="multiple">
<span class="sol" data-type="regex"><var>POSITIVENUMERATOR</var></span> <table>
<span class="sol" data-type="regex"><var>POSITIVEDENOMINATOR</var></span> <tr>
</div> <td rowspan="2">
<div class="set-sol" data-type="multiple"> <code><var>Y</var> = </code>
<span class="sol" data-type="regex"><var>NEGATIVENUMERATOR</var></span> </td>
<span class="sol" data-type="regex"><var>NEGATIVEDENOMINATOR</var></span> <td class="soln-top">
</div> <span class="sol short32">a</span>
<div class="input-format"> </td>
<div class="entry" data-type="multiple"> </tr>
<table> <tr>
<tr> <td class="soln-bot">
<td rowspan="2" class="soln-name"> <span class="sol short32" data-fallback="1">a</span>
<code><var>Y</var> = </code> </td>
</td> </tr>
<td class="soln-top"> </table>
<span class="sol short50">a</span> </div>
</td> </div>
</tr> <div class="example">a simplifed expression, like <code>x + 2</code></div>
<tr> </div>
<td class="soln-bot">
<span class="sol short50" data-fallback="1">a</span> <div class="hints" data-apply="appendContents">
</td> <div data-if="FACTOR2 < -1">
</tr> <p>To remove the negative denominator, multiply the numerator and denominator by -1:</p>
</table> <div><code><var>Y</var> = \dfrac{-<var>X</var> + <var>-B</var>}{<var>-C</var>}</code></div>
</div>
<div data-if="FACTOR2 === -1">
<p>Dividing by -1 is the same thing as multiplying by -1, so the answer is:</p>
<div><code><var>Y</var> = -<var>X</var> + <var>-B</var></code></div>
</div> </div>
</div> </div>


<p class="example">a simplifed expression, like <code>x + 2</code></p> </div>
</div> </div>


<p class="problem">Simplify the following expression and state the domain:</p>
<p class="question"><code><var>Y</var> = \dfrac{<var>NUMERATOR</var>}{<var>DENOMINATOR</var>}</code></p>

<div class="hints"> <div class="hints">
<p>First factor the expressions in the numerator and denominator.</p> <p>First factor the expressions in the numerator and denominator.</p>


Expand All @@ -122,23 +234,14 @@


<div> <div>
<p>Dividing both the numerator and denominator by <code>(<var>X</var> + <var>A</var>)</code> gives:</p> <p>Dividing both the numerator and denominator by <code>(<var>X</var> + <var>A</var>)</code> gives:</p>
<div data-if="C === 1"> <div data-if="FACTOR2 === 1">
<code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}</code> or more simply, <code><var>Y</var> = <var>FACTOR1</var></code> <code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}</code> or more simply, <code><var>Y</var> = <var>FACTOR1</var></code>
</div> </div>
<div data-else> <div data-else>
<code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}</code> <code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}</code>
</div> </div>
</div> </div>


<div data-if="FACTOR2 < -1">
<p>To remove the negative denominator, multiply the numerator and denominator by -1:</p>
<div><code><var>Y</var> = \dfrac{-<var>X</var> + <var>-B</var>}{<var>-C</var>}</code></div>
</div>
<div data-if="FACTOR2 === -1">
<p>Dividing by -1 is the same thing as multiplying by -1, so the answer is:</p>
<div><code><var>Y</var> = -<var>X</var> + <var>-B</var></code></div>
</div>

</div> </div>
</div> </div>
</body> </body>
Expand Down