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<!DOCTYPE html>
<html data-require="math math-format word-problems graphie graphie-helpers">
<head>
<title>Converting mixed numbers and improper 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="M_NUM &lt; M_DENOM">
<var id="WHOLE">randRange(1, 10)</var>
<var id="M_NUM">randRange(1, 9)</var>
<var id="M_DENOM">randRange(M_NUM + 1, 10)</var>
<var id="GCD">getGCD(M_NUM, M_DENOM)</var>
<var id="M_REDUCED_NUM">M_NUM / GCD</var>
<var id="M_REDUCED_DENOM">M_DENOM / GCD</var>
<var id="I_NUM">WHOLE * M_REDUCED_DENOM + M_REDUCED_NUM</var>
<var id="I_DENOM">M_REDUCED_DENOM</var>
<var id="FRACTION">"\\dfrac{1}{" + I_DENOM + "}"</var>
<var id="WHOLE_FRAC">"\\dfrac{" + I_DENOM + "}{" + I_DENOM + "}"</var>
<var id="WHOLE_TEXT">$._("whole")</var>
</div>
<div class="problems">
<div id="improper-to-mixed">
<p class="question">Rewrite <code><var>fraction(I_NUM, I_DENOM, false, true)</var></code> as a mixed number.</p>
<p class="solution" data-type="mixed"><var>I_NUM / I_DENOM</var></p>
<div class="hints">
<div>
<p>
<code>\blue{<var>fraction(I_NUM, I_DENOM, false, true)</var>}</code>
is the same as the fraction <code><var>FRACTION</var></code>
added <code><var>I_NUM</var></code> times.
</p>
<p>
We can add <code><var>I_DENOM</var></code> of the <code><var>FRACTION</var></code>
fractions together to get <code>1</code> whole.
</p>
<p>
<code>\qquad<var>_(I_DENOM).times(function() { return FRACTION; }).join("+")</var>
= \green{<var>WHOLE_FRAC</var>}</code>
</p>
<div class="graphie">
init({ range: [[-3, 8], [-2, 2]], scale: 25 });
piechart([I_DENOM], [GREEN], 1.5);
label([2, 0], WHOLE_FRAC + " = 1 \\text{ " + WHOLE_TEXT + "}", "right", { color: GREEN });
</div>
</div>
<div>
<p>So we can write <code>\blue{<var>fraction(I_NUM, I_DENOM, false, true)</var>}</code> like this:</p>
<p>
<code>\blue{<var>fraction(I_NUM, I_DENOM, false, true)</var>} =
<var>_(WHOLE).times(function() { return "\\green{" + WHOLE_FRAC + "}"; }).join("+")</var>
+ \pink{\dfrac{<var>M_REDUCED_NUM</var>}{<var>I_DENOM</var>}}</code>
</p>
<div class="graphie">
init({ range: [[-0.5, 10.5], [-0.5, 0.5]], scale: 40 });
for (var i = 0; i &lt; WHOLE; i++) {
piechart([I_DENOM], [GREEN], 0.48, "#fff", i);
}
piechart([M_REDUCED_NUM, I_DENOM - M_REDUCED_NUM], [PINK, '#bbb'], 0.48, "#fff", WHOLE);
</div>
</div>
<div>
<p>
<code>\green{<var>WHOLE_FRAC</var>} = \green{1\text{ <var>WHOLE_TEXT</var>}}</code>,
so we can rewrite our equation like this:
</p>
<p>
<code>\blue{<var>fraction(I_NUM, I_DENOM, false, true)</var>} =
<var>_(WHOLE).times(function() { return "\\green{1}"; }).join("+")</var>
+ \pink{\dfrac{<var>M_REDUCED_NUM</var>}{<var>I_DENOM</var>}}</code>
</p>
<p>
<code>\blue{<var>fraction(I_NUM, I_DENOM, false, true)</var>} =
\green{<var>WHOLE</var>} + \pink{\dfrac{<var>M_REDUCED_NUM</var>}{<var>I_DENOM</var>}}</code>
</p>
</div>
<p>The mixed number is <code><var>WHOLE</var>\dfrac{<var>M_REDUCED_NUM</var>}{<var>I_DENOM</var>}</code></p>
</div>
</div>
<div id="mixed-to-improper">
<p class="question">
Rewrite <code><var>WHOLE</var><var>fraction(M_NUM, M_DENOM, false, true)</var></code> as a fraction,
<code>\dfrac{a}{b}</code>, where <code>a &gt; b</code>.
</p>
<p class="solution" data-type="improper"><var>I_NUM / I_DENOM</var></p>
<div class="hints">
<div>
<p>
<code>\blue{<var>WHOLE</var><var>fraction(M_NUM, M_DENOM, false, true)</var>} =
\green{<var>WHOLE</var>} + \pink{<var>fraction(M_NUM, M_DENOM, false, true)</var>}</code>
</p>
<p>
<code>\blue{<var>WHOLE</var><var>fraction(M_NUM, M_DENOM, false, true)</var>} =
<var>_(WHOLE).times(function() { return "\\green{1}"; }).join("+")</var>
+ \pink{<var>fraction(M_NUM, M_DENOM, false, true)</var>}</code>
</p>
<div class="graphie">
init({ range: [[-0.5, 10.5], [-0.5, 0.5]], scale: 40 });
for (var x = 0; x &lt; WHOLE; x++) {
circle([x, 0], 0.48, { fill: GREEN, stroke: null });
}
piechart([M_REDUCED_NUM, I_DENOM - M_REDUCED_NUM], [PINK, '#bbb'], 0.48, "#fff", WHOLE);
</div>
</div>
<div>
<p>
<code>\green{1\text{ <var>WHOLE_TEXT</var>}} = \green{<var>WHOLE_FRAC</var>}</code>,
so we can rewrite our equation like this:
</p>
<p>
<code>\blue{<var>WHOLE</var><var>fraction(M_NUM, M_DENOM, false, true)</var>} =
<var>_(WHOLE).times(function() { return "\\green{" + WHOLE_FRAC + "}"; }).join("+")</var>
+ \pink{<var>fraction(M_NUM, M_DENOM, false, true)</var>}</code>
</p>
<div class="graphie">
init({ range: [[-0.5, 10.5], [-0.5, 0.5]], scale: 40 });
for (var i = 0; i &lt; WHOLE; i++) {
piechart([I_DENOM], [GREEN], 0.48, "#fff", i);
}
piechart([M_REDUCED_NUM, I_DENOM - M_REDUCED_NUM], [PINK, '#bbb'], 0.48, "#fff", WHOLE);
</div>
</div>
<div>
<p>Now we can add the fractions:</p>
<p>
<code>\blue{<var>WHOLE</var><var>fraction(M_NUM, M_DENOM, false, true)</var>} =
\green{\dfrac{<var>I_DENOM * WHOLE</var>}{<var>I_DENOM</var>}} +
\pink{\dfrac{<var>M_REDUCED_NUM</var>}{<var>I_DENOM</var>}}</code>
</p>
<p>
<code>\blue{<var>WHOLE</var><var>fraction(M_NUM, M_DENOM, false, true)</var>} =
<var>fraction(I_NUM, I_DENOM, true, true)</var></code>
</p>
</div>
<p>The fraction is <code><var>fraction(I_NUM, I_DENOM, true, true)</var></code>.</p>
</div>
</div>
</div>
</div>
</body>
</html>
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