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319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
1 <!DOCTYPE html>
2 <html data-require="math word-problems">
3 <head>
4 <title>Simplifying Fractions</title>
5 <script src="../khan-exercise.js"></script>
6 </head>
7 <body>
8 <div class="exercise">
9 <div class="vars" data-ensure="! (getGCD ( NUM, DENOM ) === NUM || getGCD ( NUM, DENOM) === DENOM)">
10 <var id="FACTOR">randRange( 3, 15 )</var>
11 <var id="NUM">randRange(2, 10) * FACTOR</var>
12 <var id="DENOM">randRange(2, 10) * FACTOR</var>
13 <var id="GCD">getGCD( NUM, DENOM )</var>
14 <var id="GCD_FACTORS">getPrimeFactorization( GCD )</var>
15 <var id="GCD_FACTORS_SENTENCE">toSentence( GCD_FACTORS )</var>
16 </div>
17
18 <div class="problems">
19 <div>
20 <p class="problem">Simplify to lowest terms.</p>
21 <p class="question"><code>\dfrac{<var>NUM</var>}{<var>DENOM</var>}</code></p>
22 <p class="solution" data-type="rational"><var>NUM / DENOM</var></p>
23 </div>
24 </div>
25
26 <div class="hints">
27 <p data-if="GCD_FACTORS.length !== 1">There are several ways to tackle this problem.</p>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
28
319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
29 <p>What is the GCD of <var>NUM</var> and <var>DENOM</var>?</p>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
30
319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
31 <p>GCD(<var>NUM</var>, <var>DENOM</var>) = <var>GCD</var></p>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
32
319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
33 <p>
34 <code>\dfrac{<var>NUM</var>}{<var>DENOM</var>}</code>
35 </p>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
36
319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
37 <p>
38 <code>= \dfrac{<var>NUM / GCD</var> \cdot <var>GCD</var>}{ <var>DENOM / GCD</var>\cdot <var>GCD</var>}</code>
39 </p>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
40
319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
41 <p>
42 <code>= \dfrac{<var>NUM / GCD</var>}{<var>DENOM / GCD</var>} \cdot \dfrac{<var>GCD</var>}{<var>GCD</var>}</code>
43 </p>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
44
319325c0 » marcia
2011-05-31 Add exercise -- simplifying fractions
45 <p>
46 <code>= \dfrac{<var>NUM / GCD</var>}{<var>DENOM / GCD</var>}</code>
47 </p>
48 <div data-if="GCD_FACTORS.length !== 1">
49 <p>You can also solve this problem by repeatedly dividing the numerator and denominator by smaller factors.</p>
50 <p>For example:</p>
51 <!-- TODO: iterate prettily to walk student through
52 48 / 64 to 24 / 32 to 3 / 4
53 -->
54 <p><var>GCD_FACTORS_SENTENCE</var></p>
55 </div>
56 </div>
57 </div>
58 </body>
cf021797 » spicyj
2011-06-01 Strip trailing whitespace
59 </html>
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