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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>Fraction word problems 1</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="TOTAL" data-ensure="TOTAL > 2">randFromArray(smallDenominators)</var>
<var id="A">randRange(1, TOTAL - 2)</var>
<var id="B">randRange(1, TOTAL - A - 1)</var>
<var id="EATEN">A + B</var>
<var id="LEFT">TOTAL - EATEN</var>
<var id="FRACTION_OF_PIZZAS_EATEN">i18n._("fraction of %(pizza__1__)s eaten", {pizza__1__: pizza( 1 )})</var>
<var id="NUMBER_OF_SLICES_EATEN">i18n._("number of slices eaten")</var>
<var id="NUMBER_OF_SLICES_TOTAL">i18n._("number of slices total")</var>
<var id="NUMBER_OF_SLICES_REMAINING">i18n._("number of slices remaining")</var>
<var id="FRACTION_OF_PIZZAS_REMAINING">i18n._("fraction of %(pizza__1__)s remaining", {pizza__1__: pizza( 1 )})</var>
</div>
<div class="problems">
<div id="show-total-want-eaten">
<p class="problem">
<span data-if="isSingular(A)">
<var>person(1)</var> ate <code><var>A</var></code> slice of <var>pizza(1)</var>.
</span><span data-else="">
<var>person(1)</var> ate <code><var>A</var></code> slices of <var>pizza(1)</var>.
</span>
<span data-if="isSingular(B)">
<var>person(2)</var> ate <code><var>B</var></code> slice.
</span><span data-else="">
<var>person(2)</var> ate <code><var>B</var></code> slices.
</span>
</p>
<p class="question">
If there were initially <code><var>TOTAL</var></code> slices of equal size,
what fraction of the <var>pizza(1)</var> was eaten?
</p>
<p class="solution" data-simplify="optional" data-type="rational"><var>EATEN / TOTAL</var></p>
<div class="hints">
<p><code>
\text{<var>FRACTION_OF_PIZZAS_EATEN</var>} =
\dfrac{\text{<var>NUMBER_OF_SLICES_EATEN</var>}}{\text{<var>NUMBER_OF_SLICES_TOTAL</var>}}
</code></p>
<p><code>\text{<var>NUMBER_OF_SLICES_EATEN</var>} = <var>A</var> + <var>B</var> = <var>EATEN</var></code></p>
<div>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
piechart([EATEN, TOTAL - EATEN], [BLUE, GRAY], 2);
</div>
<p>They ate <code>\blue{<var>EATEN</var>}</code> out of <code><var>TOTAL</var></code> slices.</p>
</div>
<p>They ate <code>\dfrac{<var>EATEN</var>}{<var>TOTAL</var>}</code> of the <var>pizza( 1 )</var>.</p>
</div>
</div>
<div id="show-left-want-eaten" data-type="show-total-want-eaten">
<p class="question">
<span data-if="isSingular(LEFT)">
If there were <code><var>LEFT</var></code> slice remaining and all the slices were the same size,
what fraction of the <var>pizza(1)</var> was eaten?
</span><span data-else="">
If there were <code><var>LEFT</var></code> slices remaining and all the slices were the same size,
what fraction of the <var>pizza(1)</var> was eaten?
</span>
</p>
<div class="hints">
<p><code>
\text{<var>FRACTION_OF_PIZZAS_EATEN</var>} =
\dfrac{\text{<var>NUMBER_OF_SLICES_EATEN</var>}}{\text{<var>NUMBER_OF_SLICES_TOTAL</var>}}
</code></p>
<p data-if="isSingular(LEFT)">
Since they ate <code><var>EATEN</var></code> slices of <var>pizza(1)</var>
with <code><var>LEFT</var></code> slice remaining,
they must have begun with <code><var>TOTAL</var></code> slices.
</p><p data-else="">
Since they ate <code><var>EATEN</var></code> slices of <var>pizza(1)</var>
with <code><var>LEFT</var></code> slices remaining,
they must have begun with <code><var>TOTAL</var></code> slices.
</p>
<div>
<p>They ate <code>\blue{<var>EATEN</var>}</code> out of <code><var>TOTAL</var></code> slices.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
piechart([EATEN, TOTAL - EATEN], [BLUE, GRAY], 2);
</div>
</div>
<p>They ate <code>\dfrac{<var>EATEN</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>.</p>
</div>
</div>
<div id="show-first-want-eaten" data-type="show-total-want-eaten">
<p class="question">
If <var>person(1)</var> ate <code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>
and all the slices are the same size, what fraction of the <var>pizza(1)</var> was eaten in total?
</p>
<div class="hints">
<p><code>
\text{<var>FRACTION_OF_PIZZAS_EATEN</var>} =
\dfrac{\text{<var>NUMBER_OF_SLICES_EATEN</var>}}{\text{<var>NUMBER_OF_SLICES_TOTAL</var>}}
</code></p>
<p data-if="isSingular(A)">
If <code><var>A</var></code> slice represents
<code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>,
there must have been a total of <code><var>TOTAL</var></code> slices.
</p><p data-else="">
If <code><var>A</var></code> slices represents
<code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>,
there must have been a total of <code><var>TOTAL</var></code> slices.
</p>
<p><code>\text{<var>NUMBER_OF_SLICES_EATEN</var>} = <var>A</var> + <var>B</var> = <var>EATEN</var></code></p>
<div>
<p>They ate <code>\blue{<var>EATEN</var>}</code> out of <code><var>TOTAL</var></code> slices.</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
piechart([EATEN, TOTAL - EATEN], [BLUE, GRAY], 2);
</div>
</div>
<p>They ate <code>\dfrac{<var>EATEN</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>.</p>
</div>
</div>
<div id="show-total-want-left" data-type="show-total-want-eaten">
<p class="question">
If there were initially <code><var>TOTAL</var></code> slices and all the slices are the same size,
what fraction of the <var>pizza(1)</var> is remaining?
</p>
<p class="solution" data-simplify="optional" data-type="rational"><var>LEFT / TOTAL</var></p>
<div class="hints">
<p><code>
\text{<var>FRACTION_OF_PIZZAS_EATEN</var>} =
\dfrac{\text{<var>NUMBER_OF_SLICES_REMAINING</var>}}{\text{<var>NUMBER_OF_SLICES_TOTAL</var>}}
</code></p>
<div>
<p>
Together they ate <code><var>EATEN</var></code> slices,
which leaves <code><var>LEFT</var></code> out of <code><var>TOTAL</var></code> slices remaining.
</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var remaining = TOTAL - EATEN;
piechart([remaining, TOTAL - remaining], [GRAY, BLUE], 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" data-type="show-total-want-eaten">
<p class="question">
If <var>person(1)</var> ate <code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>
and all the slices were the same size, what fraction of the <var>pizza(1)</var> remained after
<var>person(1)</var> and <var>person(2)</var> had eaten?
</p>
<p class="solution" data-simplify="optional" data-type="rational"><var>LEFT / TOTAL</var></p>
<div class="hints">
<p><code>
\text{<var>FRACTION_OF_PIZZAS_REMAINING</var>} =
\dfrac{\text{<var>NUMBER_OF_SLICES_REMAINING</var>}}{\text{<var>NUMBER_OF_SLICES_TOTAL</var>}}
</code></p>
<p data-if="isSingular(A)">
If <code><var>A</var></code> slice represents
<code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>,
there must have been a total of <code><var>TOTAL</var></code> slices.
<p data-else="">
If <code><var>A</var></code> slices represents
<code>\dfrac{<var>A</var>}{<var>TOTAL</var>}</code> of the <var>pizza(1)</var>,
there must have been a total of <code><var>TOTAL</var></code> slices.
</p>
<div>
<p>
Together they ate <code><var>EATEN</var></code> slices,
which leaves <code><var>LEFT</var></code> out of <code><var>TOTAL</var></code> slices remaining.
</p>
<div class="graphie">
init({
range: [ [-2, 2], [-2, 2] ],
scale: 25
});
var remaining = TOTAL - EATEN;
piechart([remaining, TOTAL - remaining], [GRAY, BLUE], 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>