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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 fractions</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars" data-ensure="SIMP_D1 !== SIMP_D2">
<var id="N1">randRange( 1, 9 )</var>
<var id="D1">randRange( N1 + 1, 13 )</var>
<var id="GCD1">getGCD( N1, D1 )</var>
<var id="SIMP_N1">N1 / GCD1</var>
<var id="SIMP_D1">D1 / GCD1</var>
<var id="N2">randRange( 1, 9 )</var>
<var id="D2">randRange( N2 + 1, 13 )</var>
<var id="GCD2">getGCD( N2, D2 )</var>
<var id="SIMP_N2">N2 / GCD2</var>
<var id="SIMP_D2">D2 / GCD2</var>
<var id="LCM">getLCM( SIMP_D1, SIMP_D2 )</var>
</div>
<div class="problems">
<div>
<p class="question"><code><var>fraction( N1, D1 )</var> + <var>fraction( N2, D2 )</var> = {?}</code></p>
<p class="solution" data-type="rational"><var>N1 / D1 + N2 / D2</var></p>
</div>
</div>
<div class="hints">
<div data-if="GCD1 !== 1 || GCD2 !== 1">
<p>Simplify each fraction.</p>
<p><code><var>fraction( SIMP_N1, SIMP_D1 )</var> + <var>fraction( SIMP_N2, SIMP_D2 )</var></code></p>
</div>
<p>Find a common denominator by finding the least common multiple of <code><var>SIMP_D1</var></code> and <code><var>SIMP_D2</var></code>.</p>
<p><code>\lcm(<var>SIMP_D1</var>, <var>SIMP_D2</var>) = <var>LCM</var></code></p>
<div>
<p>Change each fraction to an equivalent fraction with a denominator of <code><var>LCM</var></code>.</p>
<p><code><var>fraction( SIMP_N1, SIMP_D1 )</var> + <var>fraction( SIMP_N2, SIMP_D2 )</var></code></p>
<p><code>=<var>fraction( SIMP_N1, SIMP_D1 )</var> <span data-if="LCM !== SIMP_D1">\cdot <var>fraction( LCM / SIMP_D1, LCM / SIMP_D1 )</var></span> + <var>fraction( SIMP_N2, SIMP_D2 )</var> <span data-if="LCM !== SIMP_D2">\cdot <var>fraction( LCM / SIMP_D2, LCM / SIMP_D2 )</var></span></code></p>
</div>
<p><code>=<var>fraction( SIMP_N1 * LCM / SIMP_D1, LCM )</var> + <var>fraction( SIMP_N2 * LCM / SIMP_D2, LCM )</var></code></p>
<p><code>=<var>fraction( SIMP_N1 * LCM / SIMP_D1 + SIMP_N2 * LCM / SIMP_D2, LCM )</var></code></p>
<div data-if="getGCD( SIMP_N1 * LCM / SIMP_D1 + SIMP_N2 * LCM / SIMP_D2, LCM ) !== 1">
<p>Simplify.</p>
<p><code>=<var>fractionReduce( SIMP_N1 * LCM / SIMP_D1 + SIMP_N2 * LCM / SIMP_D2, LCM )</var></code></p>
</div>
</div>
</div>
</body>
</html>
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