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adding hints about M/M=1 for equivalent fractions

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1 parent ac9d3cf commit f6091260c13db2397e15f259260d864bcda7f1f7 @koriroys koriroys committed Oct 14, 2011
Showing with 39 additions and 2 deletions.
  1. +15 −2 exercises/equivalent_fractions.html
  2. +24 −0 exercises/equivalent_fractions_2.html
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17 exercises/equivalent_fractions.html
@@ -45,6 +45,12 @@
</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>
@@ -76,11 +82,18 @@
rectchart( [C, D - C], ["#e00", "#999"] );
</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>
- <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>
</div>
</div>
</div>
</body>
-</html>
+</html>
View
24 exercises/equivalent_fractions_2.html
@@ -26,6 +26,12 @@
<p>To get the right numerator <code><var>C</var></code>, the left numerator <code><var>A</var></code> is multiplied by <code><var>M</var></code>.</p>
<p>To find the right denominator, multiply the left denominator by <code><var>M</var></code> as well.</p>
<p><code><var>B</var> \times <var>M</var> = <var>D</var></code></p>
+ <div>
+ <p>Notice both the numerator and denominator are being multiplied by <code>{<var>M</var>}</code>.</p>
+ <p>We can write that as <code>\dfrac{<var>M</var>}{<var>M</var>}</code>, which is equal to <code>1</code> when reduced.
+ <p>So we can solve this problem by multiplying the fraction on the left by <code>1</code>.</p>
+ </div>
+ <p>The equation becomes: <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>
@@ -37,6 +43,12 @@
<p>To get the right denominator <code><var>D</var></code>, the left denominator <code><var>B</var></code> is multiplied by <code><var>M</var></code>.</p>
<p>To find the right numerator, multiply the left numerator by <code><var>M</var></code> as well.</p>
<p><code><var>A</var> \times <var>M</var> = <var>C</var></code></p>
+ <div>
+ <p>Notice both the numerator and denominator are being multiplied by <code>{<var>M</var>}</code>.</p>
+ <p>We can write that as <code>\dfrac{<var>M</var>}{<var>M</var>}</code>, which is equal to <code>1</code> when reduced.
+ <p>So we can solve this problem by multiplying the fraction on the left by <code>1</code>.</p>
+ </div>
+ <p>The equation becomes: <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>
@@ -48,6 +60,12 @@
<p>To get the right numerator <code><var>A</var></code>, the left numerator <code><var>C</var></code> is divided by <code><var>M</var></code>.</p>
<p>To find the right denominator, divide the left denominator by <code><var>M</var></code> as well.</p>
<p><code><var>D</var> \div <var>M</var> = <var>B</var></code></p>
+ <div>
+ <p>Notice both the numerator and denominator are being divided by <code>{<var>M</var>}</code>.</p>
+ <p>We can write that as <code>\dfrac{<var>M</var>}{<var>M</var>}</code>, which is equal to <code>1</code> when reduced.
+ <p>So we can solve this problem by dividing the fraction on the left by <code>1</code>.</p>
+ </div>
+ <p>The equation becomes: <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>
@@ -59,6 +77,12 @@
<p>To get the right denominator <code><var>B</var></code>, the left denominator <code><var>D</var></code> is divided by <code><var>M</var></code>.</p>
<p>To find the right numerator, divide the left numerator by <code><var>M</var></code> as well.</p>
<p><code><var>C</var> \div <var>M</var> = <var>A</var></code></p>
+ <div>
+ <p>Notice both the numerator and denominator are being divided by <code>{<var>M</var>}</code>.</p>
+ <p>We can write that as <code>\dfrac{<var>M</var>}{<var>M</var>}</code>, which is equal to <code>1</code> when reduced.
+ <p>So we can solve this problem by dividing the fraction on the left by <code>1</code>.</p>
+ </div>
+ <p>The equation becomes: <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>

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