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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers word-problems math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Equivalent fractions 2</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="A">randRange(1, 10)</var>
<var id="Bf">randRange(2, 9)</var>
<var id="B">Bf + (Bf &gt;= A ? 1 : 0)</var>
<var id="M">randRange(3, 9)</var>
<var id="C">A * M</var>
<var id="D">B * M</var>
<var id="N">ceil(A / B)</var>
<var id="SYMBOL">randVar()</var>
<var id="FILLED">1</var>
</div>
<div class="problems">
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>C</var>}{<var>SYMBOL</var>}</code></p>
<div class="solution" data-forms="integer"><var>D</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>B</var> slices,
then taking <var>A</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = A % B;
if (FILLED === 0) {
FILLED = B;
}
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
How many slices would we need to cut each <var>pizza(1)</var> into so that <var>C</var>
slices would give us the same amount of <var>pizza(1)</var>?
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED *= M;
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
Each of the original <var>A</var> slices must be divided into <var>M</var>
slices to get <var>C</var> slices in total.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
rectchart([M, M * B - M], [RED, _BACKGROUND]);
</div>
</div>
<div>
<p>
If we divide all the original slices into <var>M</var> slices, then one
<var>pizza(1)</var> will have a total of <var>D</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
rectchart([M, M * B - M], [RED, GRAY]);
</div>
</div>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>C</var>}{<var>D</var>}</code> and so the answer is <code><var>D</var></code>.</p>
<div>
<p>Another way to get the answer is to multiply by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are multiplying by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>A</var>}{<var>B</var>} \times \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>C</var>}{<var>D</var>} </code> so our answer is <code><var>D</var></code>.
</p>
</div>
</div>
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>SYMBOL</var>}{<var>D</var>}</code></p>
<div class="solution" data-forms="integer"><var>C</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>B</var> slices,
then taking <var>A</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = A % B;
if (FILLED === 0) {
FILLED = B;
}
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>What if we cut each <var>pizza(1)</var> into <var>D</var> slices instead?</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED *= M;
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
In order to take the same amount of <var>pizza(1)</var> as before,
we now need to take <var>C</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<p><code>\dfrac{<var>A</var>}{<var>B</var>} = \dfrac{<var>C</var>}{<var>D</var>}</code> and so the answer is <code><var>C</var></code>.</p>
<div>
<p>Another way to get the answer is to multiply by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are multiplying by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>A</var>}{<var>B</var>} \times \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>C</var>}{<var>D</var>} </code> so our answer is <code><var>C</var></code>.
</p>
</div>
</div>
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>A</var>}{<var>SYMBOL</var>}</code></p>
<div class="solution" data-forms="integer"><var>B</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>D</var> slices,
then taking <var>C</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = C % D;
if (FILLED === 0) {
FILLED = D;
}
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p data-if="isSingular(A)">
If we share those <var>C</var> slices equally between <var>A</var> person,
how many slices does each person get?
</p><p data-else="">
If we share those <var>C</var> slices equally between <var>A</var> people,
how many slices does each person get?
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED /= M;
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p data-if="isSingular(A)">
Sharing <var>C</var> slices equally between <var>A</var> person means each person gets <var>M</var> slices.
</p><p data-else="">
Sharing <var>C</var> slices equally between <var>A</var> people means each person gets <var>M</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
rectchart([M, D - M], [RED, _BACKGROUND]);
</div>
<p>If we give each person <var>M</var> slices, how many people can we feed with one <var>pizza(1)</var>?</p>
</div>
<div>
<div class="graphie">
init({ range: [[0, 1], [0, 1]], scale: [475, 25] });
var filled = A % B;
rectchart([FILLED, B - FILLED], [RED, GRAY]);
</div>
<p>
One <var>pizza(1)</var> has <var>D</var> slices, so if we give each person
<var>M</var> slices, we could feed <var>B</var> people.
</p>
</div>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>A</var>}{<var>B</var>}</code> and so the answer is <code><var>B</var></code>.</p>
<div>
<p>Another way to get the answer is to divide by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are dividing by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>C</var>}{<var>D</var>} \div \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>A</var>}{<var>B</var>}</code> so our answer is <code><var>B</var></code>.
</p>
</div>
</div>
<div>
<p class="question">What number could replace <code><var>SYMBOL</var></code> below?</p>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>SYMBOL</var>}{<var>B</var>}</code></p>
<div class="solution" data-forms="integer"><var>A</var></div>
<div class="hints">
<div>
<p>
The fraction on the left represents dividing some rectangular <var>pizza(1).plural(2)</var> into <var>D</var> slices,
then taking <var>C</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED = C % D;
if (FILLED === 0) {
FILLED = D;
}
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([D], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>What if we cut each <var>pizza(1)</var> into <var>B</var> slices instead?</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
FILLED /= M;
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<div>
<p>
In order to take the same amount of <var>pizza(1)</var> as before,
we now need to take only <var>A</var> slices.
</p>
<div class="graphie">
init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] });
for (var i = 0; i &lt; N; i++) {
if (i === 0) {
rectchart([FILLED, B - FILLED], [RED, _BACKGROUND], i * 1.25);
} else {
rectchart([B], [RED], i * 1.25);
}
}
</div>
</div>
<p><code>\dfrac{<var>C</var>}{<var>D</var>} = \dfrac{<var>A</var>}{<var>B</var>}</code> and so the answer is <code><var>A</var></code>.</p>
<div>
<p>Another way to get the answer is to divide by <code>\dfrac{<var>M</var>}{<var>M</var>}</code>.</p>
<p><code>\dfrac{<var>M</var>}{<var>M</var>} = \dfrac{1}{1} = 1</code> so really we are dividing by 1.</p>
</div>
<p>
The final equation is: <code>\dfrac{<var>C</var>}{<var>D</var>} \div \dfrac{<var>M</var>}{<var>M</var>} =
\dfrac{<var>A</var>}{<var>B</var>}</code> so our answer is <code><var>A</var></code>.
</p>
</div>
</div>
</div>
</div>
</body>
</html>