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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>Converting multi-digit repeating decimals to fractions</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars" data-ensure="( N3 % 10 ) !== floor( N3 / 10 ) &amp;&amp; N2 !== ( N3 % 10 )">
<var id="N1">randRangeWeighted( 0, 3, 0, 0.5 )</var>
<var id="N2">randRange( 1, 8 )</var>
<var id="N3">randRange( 10, 99 )</var>
<var id="N4">N1 + N2 / 9</var>
<var id="D1">0</var>
<var id="D2">1</var>
<var id="MULT1">pow( 10, D2 )</var>
<var id="MULT2">pow( 10, D1 )</var>
<var id="RES1">floorTo( 4,( MULT1 * N4 ) )</var>
<var id="RES2">floorTo( 4,( MULT2 * N4 ) )</var>
<var id="DIFF">round( RES1 - RES2 )</var>
</div>
<div class="problems">
<div id="onedigit">
<p class="question">Rewrite as a simplified fraction.</p>
<p><code>\large{<var>N1</var>.\overline{<var>N2</var>} = {?}}</code></p>
<p class="solution" data-type="rational"><var>N4</var></p>
</div>
<div id="twodigit">
<div class="vars">
<var id="N4">N1 + N3 / 99</var>
<var id="D2">2</var>
</div>
<p class="question">Rewrite as a simplified fraction.</p>
<p><code>\large{<var>N1</var>.\overline{<var>N3</var>} = {?}}</code></p>
<p class="solution" data-type="rational"><var>N4</var></p>
</div>
<div id="oneandone">
<div class="vars">
<var id="N3" data-ensure="N2 !== N3">randRange( 1, 8 )</var>
<var id="N4">N1 + N2 / 10 + N3 / 90</var>
<var id="D1">1</var>
<var id="D2">2</var>
</div>
<p class="question">Rewrite as a simplified fraction.</p>
<p><code>\large{<var>N1</var>.<var>N2</var>\overline{<var>N3</var>} = {?}}</code></p>
<p class="solution" data-type="rational"><var>N4</var></p>
</div>
<div id="hardone">
<div class="vars">
<var id="N2">randRange( 1, 9 )</var>
<var id="N4">N1 + N2 / 10 + N3 / 990</var>
<var id="D1">1</var>
<var id="D2">3</var>
</div>
<p class="question">Rewrite as a simplified fraction.</p>
<p><code>\large{<var>N1</var>.<var>N2</var>\overline{<var>N3</var>} = {?}}</code></p>
<p class="solution" data-type="rational"><var>N4</var></p>
</div>
<div id="hardtwo">
<div class="vars">
<var id="N2">randRange( 1, 8 )</var>
<var id="N4">N1 + N3 / 100 + N2 / 900</var>
<var id="D1">2</var>
<var id="D2">3</var>
</div>
<p class="question">Rewrite as a simplified fraction.</p>
<p><code>\large{<var>N1</var>.<var>N3</var>\overline{<var>N2</var>} = {?}}</code></p>
<p class="solution" data-type="rational"><var>N4</var></p>
</div>
</div>
<div class="hints">
<p>Let <code>x</code> equal the decimal. Set up two equations such that the digits after the decimal point are identical.</p>
<p><code>\large{\begin{align*}<var>MULT1</var>x &amp;= <var>RES1</var>...\\
<var>MULT2</var>x &amp;= <var>RES2</var>...\end{align*}}</code></p>
<div>
<p>Subtracting the two equations, we have:</p>
<p><code>\large{<var>(MULT1 - MULT2)</var>x = <var>DIFF</var>}</code></p>
</div>
<p><code>\large{x = <var>fraction( DIFF, MULT1 - MULT2 )</var>}\quad<span data-if="getGCD( DIFF, MULT1 - MULT2 ) === 1 && DIFF > ( MULT1 - MULT2 )"> \text{or} \quad\large{<var>mixedFractionFromImproper( DIFF, MULT1 - MULT2 )</var>}</span></code></p>
<p data-if="getGCD( DIFF, MULT1 - MULT2 ) !== 1"><code>\large{x = <var>fraction( toFraction( N4 )[ 0 ], toFraction( N4 )[ 1 ])</var>}\quad<span data-if="DIFF > ( MULT1 - MULT2 )"> \text{or} \quad\large{<var>mixedFractionFromImproper( toFraction( N4 )[ 0 ], toFraction( N4 )[ 1 ] )</var>}</span></code></p>
</div>
</div>
</body>
</html>
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