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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers word-problems">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Recognizing fractions word problems 1</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="A">randRange( 1, 5 )</var>
<var id="B">randRange( 1, 5 )</var>
<var id="LEFT">randRange( 1, 5 )</var>
<var id="TOTAL">A + B + LEFT</var>
</div>
<div class="problems">
<div id="show-total-want-eaten">
<p class="problem">
<var>person( 1 )</var> ate <var>plural( A, "slice" )</var> of <var>pizza( 1 )</var>, and <var>person( 2 )</var>
ate <var>plural( B, "slice" )</var>.
</p>
<p class="question">If there were initially <var>TOTAL</var> slices, what fraction of the <var>pizza( 1 )</var> was eaten?</p>
<p class="solution" data-type="rational" data-simplify="optional"><var>(A + B) / TOTAL</var></p>
<div class="hints">
<p><code>\text{fraction of <var>pizza( 1 )</var> eaten} = \dfrac{\text{number of slices eaten}}{\text{number slices total}}</code></p>
<div>
<p>They ate <code>\color{#6495ED}{<var>A + B</var>}</code> out of <code><var>TOTAL</var></code> slices.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var eaten = A + B;
piechart( [ eaten, TOTAL - eaten ], [ "#6495ED", "#FFA500" ], 2 );
</div>
</div>
<p>They ate <code>\dfrac{<var>A + B</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>.</p>
</div>
</div>
<div id="show-left-want-eaten">
<p class="problem">
<var>person( 1 )</var> ate <var>plural( A, "slice" )</var> of <var>pizza( 1 )</var>, and <var>person( 2 )</var>
ate <var>plural( B, "slice" )</var>.
</p>
<p class="question">If there were <var>plural(LEFT, "slice")</var> remaining, what fraction of the <var>pizza( 1 )</var> was eaten?</p>
<p class="solution" data-type="rational" data-simplify="optional"><var>(A + B) / TOTAL</var></p>
<div class="hints">
<p><code>\text{fraction of <var>pizza( 1 )</var> eaten} = \dfrac{\text{number of slices eaten}}{\text{number slices total}}</code></p>
<p>
Since they ate <var>A + B</var> slices of <var>pizza( 1 )</var> with <var>plural( LEFT, "slice" )</var> remaining,
they must have begun with <var>TOTAL</var> slices.
</p>
<div>
<p>They ate <code>\color{#6495ED}{<var>A + B</var>}</code> out of <code><var>TOTAL</var></code> slices.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var eaten = A + B;
piechart( [ eaten, TOTAL - eaten ], [ "#6495ED", "#FFA500" ], 2 );
</div>
</div>
<p>They ate <code>\dfrac{<var>A + B</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>.</p>
</div>
</div>
<div id="show-first-want-eaten">
<p class="problem">
<var>person( 1 )</var> ate <var>plural( A, "slice" )</var> of <var>pizza( 1 )</var>, and <var>person( 2 )</var>
ate <var>plural( B, "slice" )</var>.
</p>
<p class="question">
If <var>person( 1 )</var> ate <code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>,
what fraction of the <var>pizza( 1 )</var> was eaten?
</p>
<p class="solution" data-type="rational" data-simplify="optional"><var>(A + B) / TOTAL</var></p>
<div class="hints">
<p>
If <var>plural( A, "slice")</var> represent<var>A &gt; 1 ? "" : "s"</var>
<code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>, there must have been a total of
<var>TOTAL</var> slices.
</p>
<p><code>\text{fraction of <var>pizza( 1 )</var> eaten} = \dfrac{\text{number of slices eaten}}{\text{number slices total}}</code></p>
<div>
<p>They ate <code>\color{#6495ED}{<var>A + B</var>}</code> out of <code><var>TOTAL</var></code> slices.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var eaten = A + B;
piechart( [ eaten, TOTAL - eaten ], [ "#6495ED", "#FFA500" ], 2 );
</div>
</div>
<p>They ate <code>\dfrac{<var>A + B</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>.</p>
</div>
</div>
<div id="show-total-want-left">
<p class="problem">
<var>person( 1 )</var> ate <var>plural( A, "slice" )</var> of <var>pizza( 1 )</var>, and
<var>person( 2 )</var> ate <var>plural( B, "slice" )</var>.
</p>
<p class="question">If there were initially <var>TOTAL</var> slices, what fraction of the <var>pizza( 1 )</var> is remaining?</p>
<p class="solution" data-type="rational" data-simplify="optional"><var>LEFT / TOTAL</var></p>
<div class="hints">
<p><code>\text{fraction of <var>pizza( 1 )</var> remaining} = \dfrac{\text{number of slices remaining}}{\text{number slices total}}</code></p>
<div>
<p>Together they ate <var>A + B</var> slices, which leaves <var>LEFT</var> out of <var>TOTAL</var> slices remaining.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var remaining = TOTAL - A - B;
piechart( [ remaining, TOTAL - remaining ], [ "#FFA500", "#6495ED" ], 2 );
</div>
</div>
<p>There is <code>\dfrac{<var>LEFT</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var> remaining.</p>
</div>
</div>
<div id="show-first-want-left">
<p class="problem">
<var>person( 1 )</var> ate <var>plural( A, "slice" )</var> of <var>pizza( 1 )</var>, and
<var>person( 2 )</var> ate <var>plural( B, "slice" )</var>.
</p>
<p class="question">
If <var>person( 1 )</var> ate <code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>,
what fraction of the <var>pizza( 1 )</var> is remaining?
</p>
<p class="solution" data-type="rational" data-simplify="optional"><var>LEFT / TOTAL</var></p>
<div class="hints">
<p>
If <var>plural( A, "slice" )</var> represent<var>A &gt; 1 ? "" : "s"</var>
<code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>,
there must have been a total of <var>TOTAL</var> slices.
</p>
<p><code>\text{fraction of <var>pizza( 1 )</var> remaining} = \dfrac{\text{number of slices remaining}}{\text{number slices total}}</code></p>
<div>
<p>Together they ate <var>A + B</var> slices, which leaves <var>LEFT</var> out of <var>TOTAL</var> slices remaining.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var remaining = TOTAL - A - B;
piechart( [ remaining, TOTAL - remaining ], [ "#FFA500", "#6495ED" ], 2 );
</div>
</div>
<p>There is <code>\dfrac{<var>LEFT</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var> remaining.</p>
</div>
</div>
</div>
</div>
</body>
</html>
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