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9e59905 @marcia Add exercise -- multiplying decimals
marcia authored
1 <!DOCTYPE html>
2 <html data-require="math math-format">
3 <head>
4 <title>Adding and Subtracting Fractions</title>
5 <script src="../khan-exercise.js"></script>
6 </head>
7 <body>
8 <div class="exercise">
9 <div class="vars" data-ensure="D1 !== D2">
10 <var id="N1">randRangeNonZero( -9, 9 )</var>
11 <var id="N2">randRangeNonZero( -9, 9 )</var>
12 <var id="D1">randRangeExclude( 2, 9, [ N1, -N1 ] )</var>
13 <var id="D2">randRangeExclude( 2, 9, [ N2, -N2 ] )</var>
14 <var id="LCM">getLCM( D1, D2 )</var>
15 <var id="F1">LCM / D1</var>
16 <var id="F2">LCM / D2</var>
17 </div>
18
19 <div class="problems">
20 <div>
21 <p class="question"><code><var>fraction( N1, D1 )</var> + <var>fraction( N2, D2 )</var> = ?</code></p>
22 <div class="solution" data-type="rational">N1 / D1 + N2 / D2</div>
23 </div>
24 </div>
25
26 <div class="hints">
27 <p>First, we need to find a common denominator. The least common multiple of <code><var>D1</var></code> and <code><var>D2</var></code> is the smallest possible common denominator.</p>
28 <p>LCM( <code><var>D1</var></code>, <code><var>D2</var></code> ) <code>= <var>LCM</var></code></p>
29 <p>Now, we need to change both fractions to have a denominator of <code><var>LCM</var></code>.</p>
30 <p><code>\begin{align*}<var>fraction( N1, D1 )</var>\cdot <var>fraction( F1, F1 )</var> &= <var>fraction( N1 * F1, LCM )</var>\end{align*}</code></p>
31 <p><code>\begin{align*}<var>fraction( N2, D2 )</var>\cdot <var>fraction( F2, F2 )</var> &= <var>fraction( N2 * F2, LCM )</var>\end{align*}</code></p>
32 <div>
33 <p>So, the problem becomes:</p>
34 <p><code><var>fraction( N1 * F1, LCM )</var> + <var>fraction( N2 * F2, LCM )</var> = ?</code></p>
35 </div>
36 <div>
37 <p>Add the numerators.</p>
38 <p><code><var>fraction( F1 * N1 + F2 * N2, LCM)</var></code></p>
39 </div>
40 <div data-if="getGCD( F1 * N1 + F2 * N2, LCM ) !== 1">
41 <p>Simplify.</p>
42 <p><code><var>fractionReduce( F1 * N1 + F2 * N2, LCM )</var></code></p>
43 </div>
44 </div>
45 </div>
46 </body>
47 </html>
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