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<!DOCTYPE html>
<html data-require="math math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Adding and subtracting fractions</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars" data-ensure="D1 !== D2">
<var id="N1">randRangeNonZero( -9, 9 )</var>
<var id="N2">randRangeNonZero( -9, 9 )</var>
<var id="D1">randRangeExclude( 2, 9, [ N1, -N1 ] )</var>
<var id="D2">randRangeExclude( 2, 9, [ N2, -N2 ] )</var>
<var id="LCM">getLCM( D1, D2 )</var>
<var id="F1">LCM / D1</var>
<var id="F2">LCM / D2</var>
</div>
<div class="problems">
<div>
<div class="question">
<p><code><var>fraction( N1, D1 )</var> + <var>fraction( N2, D2 )</var> = {?}</code></p>
</div>
<div class="solution" data-type="rational"><var>N1 / D1 + N2 / D2</var></div>
</div>
</div>
<div class="hints">
<p>First, we need to find a common denominator. The least common multiple of <code><var>D1</var></code> and <code><var>D2</var></code> is the smallest possible common denominator.</p>
<p><code>\lcm(<var>D1</var>, <var>D2</var>) = <var>LCM</var></code></p>
<p>Now, we need to change both fractions to have a denominator of <code><var>LCM</var></code>.</p>
<p><code>\begin{align*}<var>fraction( N1, D1 )</var>\cdot <var>fraction( F1, F1 )</var> &= <var>fraction( N1 * F1, LCM )</var>\\
<var>fraction( N2, D2 )</var>\cdot <var>fraction( F2, F2 )</var> &= <var>fraction( N2 * F2, LCM )</var>\end{align*}</code></p>
<div>
<p>So, the problem becomes:</p>
<p><code><var>fraction( N1 * F1, LCM )</var> + <var>fraction( N2 * F2, LCM )</var> = {?}</code></p>
</div>
<div>
<p><var>N2 &gt; 0 ? "Add" : "Subtract"</var> the numerators.</p>
<p><code><var>fraction( F1 * N1 + F2 * N2, LCM)</var></code></p>
</div>
<div data-if="getGCD( F1 * N1 + F2 * N2, LCM ) !== 1">
<p>Simplify.</p>
<p><code><var>fractionReduce( F1 * N1 + F2 * N2, LCM )</var></code></p>
</div>
</div>
</div>
</body>
</html>
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