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Hints for fractions_cut_and_copy_1

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1 parent b8ff2a6 commit 2773cd90a0093e761352504c30ace580451de664 @jpulgarin jpulgarin committed
Showing with 26 additions and 2 deletions.
  1. +26 −2 exercises/fractions_cut_and_copy_1.html
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28 exercises/fractions_cut_and_copy_1.html
@@ -1,5 +1,4 @@
-<!DOCTYPE html>
-<html data-require="math math-format graphie graphie-helpers word-problems slice-clone">
+<!DOCTYPE html> <html data-require="math math-format graphie graphie-helpers word-problems slice-clone">
<head>
<meta charset="UTF-8" />
<title>Fractions cut and copy 1</title>
@@ -20,6 +19,9 @@
<var id="PARENT">N_PARENT / D_PARENT</var>
<var id="OFFSPRING">N_OFFSPRING / D_OFFSPRING</var>
<var id="ANSWER">OFFSPRING / PARENT</var>
+ <var id="D">D_PARENT === 1 ? D_OFFSPRING : D_PARENT</var>
+ <var id="N_PARENT_EXPANDED">N_PARENT * ( D_PARENT === 1 ? D : 1 )</var>
+ <var id="N_OFFSPRING_EXPANDED">N_OFFSPRING * ( D_OFFSPRING === 1 ? D : 1 )</var>
</div>
<div class="problems">
@@ -65,6 +67,28 @@
<span class="sol" id="current_block_answer" style="display: none;"><var>roundTo( 3, ANSWER )</var></span>
</div>
+
+ <div class="hints">
+ <p data-if="CODE_PARENT !== fraction( N_PARENT, D)">The starting block of length <code><var>CODE_PARENT</var></code> units
+ can be rewritten as <code><var>fraction( N_PARENT_EXPANDED, D )</var></code>.</p>
+ <p data-if="CODE_OFFSPRING !== fraction( N_OFFSPRING, D)">The goal block of length <code><var>CODE_OFFSPRING</var></code> units
+ can be rewritten as <code><var>fraction( N_OFFSPRING_EXPANDED, D )</var></code>.</p>
+ <p>Cutting the starting block by <code>x</code> pieces is the same as dividing it by <code>x</code>.</p>
+ <div>
+ <p>Therefore cutting the starting block into <code><var>N_PARENT_EXPANDED</var></code> pieces is the same as:</p>
+ <p><code>\dfrac{<var>N_PARENT_EXPANDED</var>}{<var>D</var>} ÷ <var>N_PARENT_EXPANDED</var> =
+ \dfrac{<var>N_PARENT_EXPANDED</var>}{<var>D</var>} \cdot \dfrac{1}{<var>N_PARENT_EXPANDED</var>} = \dfrac{1}{<var>D</var>}</code></p>
+ </div>
+ <p>Copying the resulting block <code>y</code> times is the same as multiplying it by <code>y</code>.</p>
+ <div>
+ <p>Therefore copying the resulting block <code><var>N_OFFSPRING_EXPANDED</var></code> times is the same as:</p>
+ <p><code>\dfrac{1}{<var>D</var>} \cdot <var>N_OFFSPRING_EXPANDED</var> = \dfrac{<var>N_OFFSPRING_EXPANDED</var>}{<var>D</var>}</code></p>
+ </div>
+ <div>
+ <p>Notice that we end up with a block the same size as the goal block.</p>
+ <p><strong>Therefore the solution is to cut the starting block into <code><var>N_PARENT_EXPANDED</var></code> pieces and copy the resulting block <code><var>N_OFFSPRING_EXPANDED</var></code> times.</strong></p>
+ </div>
+ </div>
</div>
</div>
</div>

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