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<!DOCTYPE html>
<html data-require="math math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
<title>Proportions 2</title>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="numerator">
<div class="vars">
<var id="X">randVar()</var>
<var id="ORDER">rand(2)</var>
<var id="DENOMINATOR2">randRange(2, 6)</var>
<var id="NUMERATOR2" data-ensure="getGCD(NUMERATOR2, DENOMINATOR2) === 1">randRange(2, 12)</var>
<var id="DENOMINATOR1">DENOMINATOR2 * randRange(2, 6)</var>
<var id="CONSTANT">randRangeNonZero(-12, 12)</var>
<var id="EXPR">plus(X, CONSTANT)</var>
<var id="SOLUTION">DENOMINATOR1 * NUMERATOR2 / DENOMINATOR2 - CONSTANT</var>
</div>
<div class="question">
<p>Solve for <code><var>X</var></code>.</p>
<p data-if="ORDER === 0"><code>
\dfrac{<var>EXPR</var>}{<var>DENOMINATOR1</var>} = \dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>}
</code></p>
<p data-else=""><code>
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} = \dfrac{<var>EXPR</var>}{<var>DENOMINATOR1</var>}
</code></p>
</div>
<div class="solution" data-type="multiple">
<p>
<code><var>X</var> =</code>
<span class="sol" data-simplify="optional"><var>SOLUTION</var></span>
</p>
</div>
<div class="hints">
<div>
<p>Multiply both sides by <code>\blue{<var>DENOMINATOR1</var>}</code>.</p>
<p data-if="ORDER === 0"><code>
\blue{<var>DENOMINATOR1</var>} \times \dfrac{<var>EXPR</var>}{<var>DENOMINATOR1</var>} =
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} \times \blue{<var>DENOMINATOR1</var>}
</code></p>
<p data-else=""><code>
\blue{<var>DENOMINATOR1</var>} \times \dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} =
\dfrac{<var>EXPR</var>}{<var>DENOMINATOR1</var>} \times \blue{<var>DENOMINATOR1</var>}
</code></p>
</div>
<p data-if="ORDER === 0"><code>
<var>EXPR</var> = \dfrac{\blue{<var>DENOMINATOR1</var>} \times <var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>}
</code></p>
<p data-else=""><code>
\dfrac{\blue{<var>DENOMINATOR1</var>} \times <var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} = <var>EXPR</var>
</code></p>
<p><code><var>EXPR</var> = \dfrac{<var>DENOMINATOR1 * NUMERATOR2</var>}{<var>DENOMINATOR2</var>}</code></p>
<p><code><var>EXPR</var> = <var>fractionReduce(DENOMINATOR1 * NUMERATOR2, DENOMINATOR2)</var></code></p>
<p><code><var>X</var> = <var>SOLUTION</var></code></p>
</div>
</div>
<div id="denominator">
<div class="vars">
<var id="X">randVar()</var>
<var id="ORDER">rand(2)</var>
<var id="NUMERATOR2">randRange(2, 6)</var>
<var id="DENOMINATOR2" data-ensure="getGCD(NUMERATOR2, DENOMINATOR2) === 1">randRange(2, 12)</var>
<var id="NUMERATOR1">NUMERATOR2 * randRange(2, 6)</var>
<var id="CONSTANT">randRangeNonZero(-12, 12)</var>
<var id="EXPR">plus(X, CONSTANT)</var>
<var id="SOLUTION">DENOMINATOR2 * NUMERATOR1 / NUMERATOR2 - CONSTANT</var>
</div>
<div class="question">
<p>Solve for <code><var>X</var></code>.</p>
<p data-if="ORDER === 0"><code>
\dfrac{<var>NUMERATOR1</var>}{<var>EXPR</var>} = \dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>}
</code></p>
<p data-else=""><code>
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} = \dfrac{<var>NUMERATOR1</var>}{<var>EXPR</var>}
</code></p>
</div>
<div class="solution" data-type="multiple">
<p>
<code><var>X</var> =</code>
<span class="sol" data-simplify="optional"><var>SOLUTION</var></span>
</p>
</div>
<div class="hints">
<div data-if="ORDER === 0" data-unwrap="">
<div>
<p>Multiply both sides by <code>\blue{(<var>EXPR</var>)}</code>.</p>
<p><code>
\dfrac{<var>NUMERATOR1</var>}{<var>EXPR</var>} \times \blue{(<var>EXPR</var>)} =
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} \times \blue{(<var>EXPR</var>)}
</code></p>
</div>
<p><code>
<var>NUMERATOR1</var> = \dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>}\blue{(<var>EXPR</var>)}
</code></p>
<div>
<p>Multiply both sides by <code>\green{\dfrac{<var>DENOMINATOR2</var>}{<var>NUMERATOR2</var>}}</code>.</p>
<p><code>
<var>NUMERATOR1</var> \times \green{\dfrac{<var>DENOMINATOR2</var>}{<var>NUMERATOR2</var>}} =
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} \blue{(<var>EXPR</var>)} \times
\green{\dfrac{<var>DENOMINATOR2</var>}{<var>NUMERATOR2</var>}}
</code></p>
</div>
<p><code>
\dfrac{<var>NUMERATOR1</var> \times \green{<var>DENOMINATOR2</var>}}{\green{<var>NUMERATOR2</var>}} =
\blue{<var>EXPR</var>}
</code></p>
</div>
<div data-else="" data-unwrap="">
<div>
<p>Multiply both sides by <code>\blue{(<var>EXPR</var>)}</code>.</p>
<p><code>
\blue{(<var>EXPR</var>)} \times \dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} =
\dfrac{<var>NUMERATOR1</var>}{<var>EXPR</var>} \times \blue{(<var>EXPR</var>)}
</code></p>
</div>
<p><code>
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>}\blue{(<var>EXPR</var>)} = <var>NUMERATOR1</var>
</code></p>
<div>
<p>Multiply both sides by <code>\green{\dfrac{<var>DENOMINATOR2</var>}{<var>NUMERATOR2</var>}}</code>.</p>
<p><code>
\dfrac{<var>NUMERATOR2</var>}{<var>DENOMINATOR2</var>} \blue{(<var>EXPR</var>)} \times
\green{\dfrac{<var>DENOMINATOR2</var>}{<var>NUMERATOR2</var>}} =
<var>NUMERATOR1</var> \times \green{\dfrac{<var>DENOMINATOR2</var>}{<var>NUMERATOR2</var>}}
</code></p>
</div>
<p><code>
\blue{<var>EXPR</var>} =
\dfrac{<var>NUMERATOR1</var> \times \green{<var>DENOMINATOR2</var>}}{\green{<var>NUMERATOR2</var>}}
</code></p>
</div>
<p><code><var>EXPR</var> = \dfrac{<var>DENOMINATOR2 * NUMERATOR1</var>}{<var>NUMERATOR2</var>}</code></p>
<p><code><var>EXPR</var> = <var>fractionReduce(DENOMINATOR2 * NUMERATOR1, NUMERATOR2)</var></code></p>
<p><code><var>X</var> = <var>SOLUTION</var></code></p>
</div>
</div>
</div>
</div>
</body>
</html>