# Khan/khan-exercises

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 8171ee1 Add exercise: Proportions 2 mwahl authored Feb 8, 2012 1 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 2 cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 3 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 4 ac1415e Use requirejs for module loading spicyj authored Mar 5, 2014 5 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 6 Proportions 2 8171ee1 Add exercise: Proportions 2 mwahl authored Feb 8, 2012 7 8 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 9
b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 10
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13 randVar() 14 rand(2) 15 randRange(2, 6) 16 randRange(2, 12) 17 DENOMINATOR2 * randRange(2, 6) 18 randRangeNonZero(-12, 12) 19 plus(X, CONSTANT) 20 DENOMINATOR1 * NUMERATOR2 / DENOMINATOR2 - CONSTANT 21
4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 22 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 23 24 Solve for X. 25 26 \dfrac{EXPR}{DENOMINATOR1} = \dfrac{NUMERATOR2}{DENOMINATOR2} 27 28 29 \dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{EXPR}{DENOMINATOR1} 30 31 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 32 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 33
4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 34 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 35 X = 36 SOLUTION 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 37

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39 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 40
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Multiply both sides by \blue{DENOMINATOR1}.

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44 \blue{DENOMINATOR1} \times \dfrac{EXPR}{DENOMINATOR1} = 45 \dfrac{NUMERATOR2}{DENOMINATOR2} \times \blue{DENOMINATOR1} 46

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48 \blue{DENOMINATOR1} \times \dfrac{NUMERATOR2}{DENOMINATOR2} = 49 \dfrac{EXPR}{DENOMINATOR1} \times \blue{DENOMINATOR1} 50

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53 EXPR = \dfrac{\blue{DENOMINATOR1} \times NUMERATOR2}{DENOMINATOR2} 54

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56 \dfrac{\blue{DENOMINATOR1} \times NUMERATOR2}{DENOMINATOR2} = EXPR 57

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EXPR = \dfrac{DENOMINATOR1 * NUMERATOR2}{DENOMINATOR2}

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EXPR = fractionReduce(DENOMINATOR1 * NUMERATOR2, DENOMINATOR2)

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X = SOLUTION

4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 61 62 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 63 64 65 randVar() 66 rand(2) 67 randRange(2, 6) 68 randRange(2, 12) 69 NUMERATOR2 * randRange(2, 6) 70 randRangeNonZero(-12, 12) 71 plus(X, CONSTANT) 72 DENOMINATOR2 * NUMERATOR1 / NUMERATOR2 - CONSTANT 73 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 74 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 75
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Solve for X.

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78 \dfrac{NUMERATOR1}{EXPR} = \dfrac{NUMERATOR2}{DENOMINATOR2} 79

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81 \dfrac{NUMERATOR2}{DENOMINATOR2} = \dfrac{NUMERATOR1}{EXPR} 82

4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 83 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 84 85 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 86

b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 87 X = 88 SOLUTION 89

4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 90 91 b21af93 Remove special styling and make exercise more consistent with others petercollingridge authored Apr 3, 2014 92 93 94 95 Multiply both sides by \blue{(EXPR)}. 96 97 \dfrac{NUMERATOR1}{EXPR} \times \blue{(EXPR)} = 98 \dfrac{NUMERATOR2}{DENOMINATOR2} \times \blue{(EXPR)} 99 100 101 102 NUMERATOR1 = \dfrac{NUMERATOR2}{DENOMINATOR2}\blue{(EXPR)} 103 104 105 Multiply both sides by \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}. 106 107 NUMERATOR1 \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} = 108 \dfrac{NUMERATOR2}{DENOMINATOR2} \blue{(EXPR)} \times 109 \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} 110 111 112 113 \dfrac{NUMERATOR1 \times \green{DENOMINATOR2}}{\green{NUMERATOR2}} = 114 \blue{EXPR} 115 116 117 118 119 Multiply both sides by \blue{(EXPR)}. 120 121 \blue{(EXPR)} \times \dfrac{NUMERATOR2}{DENOMINATOR2} = 122 \dfrac{NUMERATOR1}{EXPR} \times \blue{(EXPR)} 123 124 125 126 \dfrac{NUMERATOR2}{DENOMINATOR2}\blue{(EXPR)} = NUMERATOR1 127 128 129 Multiply both sides by \green{\dfrac{DENOMINATOR2}{NUMERATOR2}}. 130 131 \dfrac{NUMERATOR2}{DENOMINATOR2} \blue{(EXPR)} \times 132 \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} = 133 NUMERATOR1 \times \green{\dfrac{DENOMINATOR2}{NUMERATOR2}} 134 135 136 137 \blue{EXPR} = 138 \dfrac{NUMERATOR1 \times \green{DENOMINATOR2}}{\green{NUMERATOR2}} 139 140 141 EXPR = \dfrac{DENOMINATOR2 * NUMERATOR1}{NUMERATOR2} 142 EXPR = fractionReduce(DENOMINATOR2 * NUMERATOR1, NUMERATOR2) 143 X = SOLUTION 144 145 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 146
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cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 148 149
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