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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 1-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="problems">
<div id="thirds-and-ninths" data-weight="4">
<div class="vars">
<var id="N1">randRange(0, 3)</var>
<var id="N2">randFromArray([1, 2, 3, 3, 3, 4, 5, 6, 6, 6, 7, 8])</var>
<var id="N4">N1 + N2 / 9</var>
<var id="MULT1">10</var>
<var id="MULT2">1</var>
<var id="DIFF_MULTI">MULT1 - MULT2</var>
<var id="RES1">floorTo(4, (MULT1 * N4))</var>
<var id="RES2">floorTo(4, (MULT2 * N4))</var>
<var id="DIFF">round(RES1 - RES2)</var>
<var id="GCD">getGCD(DIFF, DIFF_MULTI)</var>
</div>
<p class="question">Rewrite as a simplified fraction.</p>
<p class="problem"><code>\large{<var>N1</var>.\overline{<var>N2</var>} = {?}}</code></p>
<p class="solution" data-type="rational"><var>N4</var></p>
</div>
<div id="sixths" data-weight="1">
<div class="vars">
<var id="N1">randRange(0, 3)</var>
<var id="N2">randFromArray([1, 5])</var>
<var id="N4">N1 + N2 / 6</var>
<var id="MULT1">100</var>
<var id="MULT2">10</var>
<var id="DIFF_MULTI">MULT1 - MULT2</var>
<var id="RES1">floorTo(4, (MULT1 * N4))</var>
<var id="RES2">floorTo(4, (MULT2 * N4))</var>
<var id="DIFF">round(RES1 - RES2)</var>
<var id="GCD">getGCD(DIFF, DIFF_MULTI)</var>
</div>
<p class="question">Rewrite as a simplified fraction.</p>
<p data-if="N2 === 1">
<code>\large{<var>N1</var>.1\overline{6} = ?}</code>
</p><p data-else="">
<code>\large{<var>N1</var>.8\overline{3} = ?}</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>coefficient(MULT2)</var>x &amp;= <var>RES2</var>...
\end{align*}}
</code></p>
<div>
<p>Subtracting the two equations, we have:</p>
<p><code>\large{<var>DIFF_MULTI</var>x = <var>DIFF</var>}</code></p>
</div>
<p><code>\large{
x = <var>fraction(DIFF, MULT1 - MULT2)</var>}
<span data-if="GCD === 1 && DIFF > DIFF_MULTI">
\quad \text{or} \quad\large{<var>mixedFractionFromImproper(DIFF, DIFF_MULTI)</var>}
</span>
</code></p>
<p data-if="GCD !== 1"><code>
\large{x = <var>fractionReduce(DIFF, DIFF_MULTI)</var>}
<span data-if="DIFF > DIFF_MULTI">
\quad \text{or} \quad\large{<var>mixedFractionFromImproper(DIFF / GCD, DIFF_MULTI / GCD)</var>}
</span>
</code></p>
</div>
</div>
</body>
</html>
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