# Khan/khan-exercises

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 319325c Add exercise -- simplifying fractions marcia authored May 31, 2011 1 cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 2 3 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 4 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 5 Simplifying fractions ac1415e Use requirejs for module loading spicyj authored Mar 5, 2014 6 319325c Add exercise -- simplifying fractions marcia authored May 31, 2011 7 8 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 9
0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 10
4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 11 randRange( 3, 15 ) 12 randRange(2, 10) * FACTOR 13 randRange(2, 10) * FACTOR 14 getGCD( NUM, DENOM ) e6378d8 More explanation of GCF petercollingridge authored Apr 2, 2014 15 getPrimeFactorization(GCD) 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 16 17 (function(){ 18 var factorValue = 1; 19 var factorDisplay = ""; 20 var hint = "\\dfrac{" + NUM + "}{" + DENOM + "}"; 21 $.each( GCD_FACTORS, function( index, value) { 22 factorValue *= value; 23 var dot = index === 0 ? "" : "\\cdot "; 24 factorDisplay += dot + value; 25 hint += "= \\dfrac{" + factorDisplay + "\\cdot" + NUM / factorValue + "}{" + factorDisplay + "\\cdot" + DENOM / factorValue + "}"; 26 }); 27 hint += "= \\dfrac{" + NUM / GCD + "}{" + DENOM / GCD + "}"; 41941b3 White space clean up marcia authored Jul 8, 2011 28 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 29 return hint; 30 })() 31 32
319325c Add exercise -- simplifying fractions marcia authored May 31, 2011 33 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 34 35 36 Simplify to lowest terms. 37 \dfrac{NUM}{DENOM} aa85809 Don't penalize non-simplification unless specifically configured to do s... beneater authored Sep 20, 2013 38 NUM / DENOM 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 39
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319325c Add exercise -- simplifying fractions marcia authored May 31, 2011 41 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 42 43 There are several ways to tackle this problem. 075f731 Space/tab cleanup spicyj authored Jun 2, 2011 44 e6378d8 More explanation of GCF petercollingridge authored Apr 2, 2014 45 What is the greatest common factor (GCF) of NUM and DENOM? 075f731 Space/tab cleanup spicyj authored Jun 2, 2011 46 e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 47 NUM = getPrimeFactorization( NUM ).join( "\\cdot" ) 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 48 DENOM = getPrimeFactorization( DENOM ).join( "\\cdot" )

d8a4f39 Issue #5950: Improve hints for simplifying fractions kd5bjo authored Nov 10, 2011 49 e6378d8 More explanation of GCF petercollingridge authored Apr 2, 2014 50

51 The only common factor of NUM and DENOM is GCD. 52

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The common factors of NUM and DENOM are toSentenceTex(GCD_FACTORS).

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So the greatest common factor is GCD_FACTORS.join("\\cdot") = GCD

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075f731 Space/tab cleanup spicyj authored Jun 2, 2011 57 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 58 59 \dfrac{NUM}{DENOM} 60 = \dfrac{NUM / GCD \cdot GCD}{ DENOM / GCD\cdot GCD} 61 075f731 Space/tab cleanup spicyj authored Jun 2, 2011 62 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 63

64 \hphantom{\dfrac{NUM}{DENOM}} 65 = \dfrac{NUM / GCD}{DENOM / GCD} \cdot \dfrac{GCD}{GCD} 66

075f731 Space/tab cleanup spicyj authored Jun 2, 2011 67 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 68 69 \hphantom{\dfrac{NUM}{DENOM}} 70 = \dfrac{NUM / GCD}{DENOM / GCD} \cdot 1 71 72 73 \hphantom{\dfrac{NUM}{DENOM}} 74 = \dfrac{NUM / GCD}{DENOM / GCD} 75 e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 76 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 77

You can also solve this problem by repeatedly breaking the numerator and denominator into common factors.

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For example:

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HINT

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cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 85 86
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