# Khan/khan-exercises

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 9e59905 Add exercise -- multiplying decimals marcia authored Jul 13, 2011 1 2 3 65eec09 Content-Type meta tag for libxml2 compatibility spicyj authored Jan 4, 2012 4 07d95d3 Rename EVERYTHING; closes #323. spicyj authored Jul 22, 2011 5 Adding and subtracting fractions 9e59905 Add exercise -- multiplying decimals marcia authored Jul 14, 2011 6 7 8 9
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11 randRangeNonZero( -9, 9 ) 12 randRangeNonZero( -9, 9 ) 13 randRangeExclude( 2, 9, [ N1, -N1 ] ) 14 randRangeExclude( 2, 9, [ N2, -N2 ] ) 15 getLCM( D1, D2 ) 16 LCM / D1 17 LCM / D2 18
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5e22d90 Add note to simplify fraction (re #311) marcia authored Jul 22, 2011 22
3f60401 = ? formatting spicyj authored Jul 27, 2011 23

fraction( N1, D1 ) + fraction( N2, D2 ) = {?}

5e22d90 Add note to simplify fraction (re #311) marcia authored Jul 22, 2011 24
b5754b6 datatype 'improper' -> 'rational'. fixes #1075. jruberg authored Aug 17, 2011 25
N1 / D1 + N2 / D2
9e59905 Add exercise -- multiplying decimals marcia authored Jul 14, 2011 26
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First, we need to find a common denominator. The least common multiple of D1 and D2 is the smallest possible common denominator.

f1c3306 Make MathJax pretty! (fix #212) spicyj authored Jul 26, 2011 31

\lcm(D1, D2) = LCM

9e59905 Add exercise -- multiplying decimals marcia authored Jul 14, 2011 32

Now, we need to change both fractions to have a denominator of LCM.

81e0c90 Align and say add or subtract appropriately marcia authored Jul 15, 2011 33

\begin{align*}fraction( N1, D1 )\cdot fraction( F1, F1 ) &= fraction( N1 * F1, LCM )\\ 34 fraction( N2, D2 )\cdot fraction( F2, F2 ) &= fraction( N2 * F2, LCM )\end{align*}

9e59905 Add exercise -- multiplying decimals marcia authored Jul 14, 2011 35
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So, the problem becomes:

3f60401 = ? formatting spicyj authored Jul 27, 2011 37

fraction( N1 * F1, LCM ) + fraction( N2 * F2, LCM ) = {?}

9e59905 Add exercise -- multiplying decimals marcia authored Jul 14, 2011 38
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81e0c90 Align and say add or subtract appropriately marcia authored Jul 16, 2011 40

N2 > 0 ? "Add" : "Subtract" the numerators.

9e59905 Add exercise -- multiplying decimals marcia authored Jul 14, 2011 41

fraction( F1 * N1 + F2 * N2, LCM)

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Simplify.

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fractionReduce( F1 * N1 + F2 * N2, LCM )

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