31:T8d5,{ // Display result with prime factors (part 1); // Numerator var power = 1; var use_power = false; var times = ''; var size_A = fraction[0].length; var result_A = ''; for(let i= size_A-1; i>=0; i--){ if(fraction[0][i]==fraction[0][i-1]){ power += 1; use_power = true; } else { if(power==1) {power="";} // We don't display "^1" if(result_A != '') { times = ' × ';} // Condition is fulfilled to add the times (×) symbol. result_A = fraction[0][i].toString().concat('^',power,'',times,result_A); power = 1; // Reinitialize power to 1 } } // Denominator power = 1; use_power = false; times = ''; var size_B = fraction[1].length; var result_B = ''; for(let i= size_B-1; i>=0; i--){ if(fraction[1][i]==fraction[1][i-1]){ power += 1; use_power = true; } else { if(power==1) {power="";} // We don't display "^1" if(result_B != '') { times = ' × ';} // Condition is fulfilled to add the times (×) symbol. result_B = fraction[1][i].toString().concat('^',power,'',times,result_B); power = 1; // Reinitialize power to 1 } } result_A == ''? result_A = 1: ''; result_B == ''? result_B = 1: ''; var numerator_reduced = 1, denominator_reduced = 1; for(var i=0; i < fraction[0].length;i++) { numerator_reduced *= fraction[0][i]; } for(var j=0; j < fraction[1].length;j++) { denominator_reduced *= fraction[1][j]; } if(size_A>1 || size_B>1){ return html`
The prime factorizations of the numerator (${numerator_reduced==numerator?`A`:`A'`}) and denominator (${denominator_reduced==denominator?`B`:`B'`}) can be written as follows:
${numerator_reduced==numerator?`A`:`A'`} = ${numerator_reduced} = ${result_A},
${denominator_reduced==denominator?`B`:`B'`} = ${denominator_reduced} = ${result_B}.
`; } else{ return html ``; } }32:T931,{ // Display result with prime factors (part 2); // Numerator var power = 1; var use_power = false; var times = ''; var size_A = fraction[0].length; var result_A = ''; for(let i= size_A-1; i>=0; i--){ if(fraction[0][i]==fraction[0][i-1]){ power += 1; use_power = true; } else { if(power==1) {power="";} // We don't display "^1" if(result_A != '') { times = ' × ';} // Condition is fulfilled to add the times (×) symbol. result_A = fraction[0][i].toString().concat('^{',power,'}',times,result_A); power = 1; // Reinitialize power to 1 } } // Highlight color var highlight = highlight_color; if(B_primeFactors==fraction[1] && (numerator!=1 || denominator!=1)){ highlight = "#000"; }; // Denominator power = 1; use_power = false; times = ''; var size_B = fraction[1].length; var result_B = ''; for(let i= size_B-1; i>=0; i--){ if(fraction[1][i]==fraction[1][i-1]){ power += 1; use_power = true; } else { if(power==1) {power="";} // We don't display "^1" if(result_B != '') { times = '×';} // Condition is fulfilled to add the times (×) symbol. result_B = fraction[1][i].toString().concat('^{',power,'}',times,result_B); power = 1; // Reinitialize power to 1 } } result_A == ''? result_A = 1: ''; result_B == ''? result_B = 1: ''; var numerator_reduced = 1, denominator_reduced = 1; for(var i=0; i < fraction[0].length;i++) { numerator_reduced *= fraction[0][i]; } for(var j=0; j < fraction[1].length;j++) { denominator_reduced *= fraction[1][j]; } if(size_A>1 || size_B>1){ if(result_B == 1 || denominator == 1) { return tex.block` \frac{A}{B} = \frac{ ${numerator} }{ ${denominator} } = \textcolor{${highlight}}{ ${highlight==highlight_color? ` \\frac{A'}{B'} =` : ``} ${result_A} }`; } else { return tex.block` \frac{A}{B} = \frac{ ${numerator} }{ ${denominator} } = \textcolor{${highlight}}{ ${highlight==highlight_color? ` \\frac{A'}{B'} = \\frac{${numerator_reduced}}{${denominator_reduced}} =` : ``} \frac{ ${result_A} }{ ${result_B} }}`; } } else{ return html ``; } }33:[] 2f:{"title":"Fraction simplifier","cells":[{"id":0,"value":"# Fraction simplifier","pinned":false,"hidden":false,"mode":"md"},{"id":623,"value":"

We compute the prime factors of a numerator (A) and a denominator (B) to simplify the fraction A/B.","pinned":false,"hidden":false,"mode":"html"},{"id":1046,"value":"Click on the sliders or enter new values below. ","pinned":false,"hidden":false,"mode":"html"},{"id":215,"value":"viewof numerator = Inputs.range([1, max_number], {value: initial_value_A, step: 1, label: \"Numerator (A):\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":797,"value":"viewof denominator = Inputs.range([1, max_number], {value: initial_value_B, step: 1, label: \"Denominator (B):\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1063,"value":"{\n if(B_primeFactors==fraction[1] && numerator!=1 && denominator!=1){\n return html`
The fraction can not be simplified because there is no common factor between A and B.

`;\n } else if(denominator==1) {\n return html`
The denominator is B = 1. Nothing needs to be simplified …
`;\n } else if(numerator==1) {\n return html`
The numerators is A = 1. The fraction can not be simplified.
`;\n } else {\n return html`
The simplified fraction is highlighted hereafter:

`; \n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":984,"value":"{\n var numerator_reduced = 1, denominator_reduced = 1;\n for(var i=0; i < fraction[0].length;i++) {\n numerator_reduced *= fraction[0][i];\n }\n for(var j=0; j < fraction[1].length;j++) {\n denominator_reduced *= fraction[1][j];\n }\n \nreturn tex.block` \n \\frac{A}{B} = \\frac{ ${numerator} }{ ${denominator} } ${numerator_reduced==numerator? ` ` : ` = \\\\textcolor{${highlight_color}}{\\\\frac{A'}{B'} =\\\\frac{ ${numerator_reduced} }{ ${denominator_reduced} }} ` } ${denominator_reduced == 1? ` = ${numerator/denominator} `: `\\\\approx ${(numerator/denominator).toFixed(5)}`} \n`\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1108,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":1219,"value":"{\n var size_A = fraction[0].length;\n var size_B = fraction[1].length;\n \n if(size_A>1 || size_B>1){ \n return html`Combining these results, we obtain:`;\n } else {\n return html``;\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1146,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":330,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md"},{"id":769,"value":"max_number = 99999999+1","pinned":false,"hidden":false,"mode":"ojs"},{"id":232,"value":"initial_value_A = 4135818*2","pinned":false,"hidden":false,"mode":"ojs"},{"id":801,"value":"initial_value_B = 5960826","pinned":false,"hidden":false,"mode":"ojs"},{"id":1080,"value":"highlight_color = '#02F'","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"A_primeFactors = primeFactors(numerator)","pinned":false,"hidden":false,"mode":"ojs"},{"id":805,"value":"B_primeFactors = primeFactors(denominator)","pinned":false,"hidden":false,"mode":"ojs"},{"id":906,"value":"fraction = {\n var A_reduced = A_primeFactors;\n var B_reduced = B_primeFactors;\n\n for (var i = 0; i < A_reduced.length; i++) {\n var j = 0;\n while(j < B_reduced.length) {\n if(A_reduced[i]==B_reduced[j]) {\n A_reduced = reduce_array(A_reduced,i);\n B_reduced = reduce_array(B_reduced,j);\n } else \n {\n j++;\n }\n }\n }\n return [A_reduced, B_reduced];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"// See also: \n// https://stackoverflow.com/questions/39899072/how-can-i-find-the-prime-factors-of-an-integer-in-javascript\n//\n// Find the prime factors of the natural number 'n'\nfunction primeFactors(n) {\n\n if (n<2) { return [n]; } // For n = 0 or n = 1, we return an array with only one row: [n]\n\n const factors = [];\n let divisor = 2;\n\n while (n >= 2) {\n if (n % divisor == 0) {\n factors.push(divisor);\n n = n / divisor;\n } else {\n divisor++;\n }\n }\n return factors; \n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":656,"value":"function reduce_array(array_in,index) {\n var array_out = array_in.slice();\n array_out.splice(index, 1);\n return array_out;\n }","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}