# Find Common Denominator for 2 Fractions with JavaScript - Simplify & Improve

I wrote a JavaScript that takes 2 fractions and finds the common denominator for both. If the user inputs 2/6 and 1/2 --- the script outputs 2/6 + 3/6. I'm interested in feedback on possibly simplifying it or improving it. Thanks.

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Untitled Document</title>
<script>

// Finds the highest common factor of 2 numbers
function highestCommonFactor(a, b) {
if (b == 0) {
return a;
}

return highestCommonFactor(b, (a % b));
}

// Input fractions to add ////////////////////////////////
// Fraction 1 = 2/6
var fraction1Numerator = 2;
var fraction1Denominator = 6;

// Fraction 2 = 1/2
var fraction2Numerator = 1;
var fraction2Denominator = 2;
////////////////////////////////////////////////////////////////

// Find the highest common factor of both denominators
var factor = highestCommonFactor(fraction1Denominator, fraction2Denominator); // 2

if (factor > 1) { // There's a common factor greater than 1
if (fraction1Denominator > fraction2Denominator) {
// Find out how many times the factor goes into bigger denominator
var temp = fraction1Denominator / factor;

fraction2Numerator  = fraction2Numerator * temp;
fraction2Denominator = fraction2Denominator * temp;
} else {
// Find out how many times the factor goes into bigger denominator
var temp = fraction2Denominator / factor;

fraction1Numerator  = fraction1Numerator * temp;
fraction1Denominator = fraction1Denominator * temp;
}
} else { // There's no common factor greater than 1 so we need to multiple each fraction by each others denominators
// Temp values
var fraction1NumeratorTemp = fraction1Numerator;
var fraction1DenominatorTemp = fraction1Denominator;

fraction1Numerator  = fraction1Numerator * fraction2Denominator;
fraction1Denominator = fraction1Denominator * fraction2Denominator;

fraction2Numerator  = fraction2Numerator * fraction1DenominatorTemp;
fraction2Denominator = fraction2Denominator * fraction1DenominatorTemp;
}

// Display solution
document.getElementById("divSolution").innerText = fraction1Numerator + "/" + fraction1Denominator + " + " + fraction2Numerator + "/" + fraction2Denominator;
}
</script>

<body>
<div id="divSolution"></div>
</body>
</html>


• As a general rule, keep everything as general as you can and don't split your code into different cases unless you have to. From the if (factor >1) part, I knew things could be improved
• At the end, the denominators will be the Least Common Multiple of the two initial fractions.
• Then, you just need to multiply the numerators by the same amount used to multiply the denominators

Here's the corresponding code.

// Finds the highest common factor of 2 numbers
function highestCommonFactor(a, b) {
if (b == 0) {
return a;
}
return highestCommonFactor(b, a%b);
}
function leastCommonMultiple(a,b) {
return a*b/(highestCommonFactor(a,b));
}

// Input fractions to add ////////////////////////////////
// Fraction 1 = 2/6
var fraction1Numerator = 2;
var fraction1Denominator = 6;

// Fraction 2 = 1/2
var fraction2Numerator = 1;
var fraction2Denominator = 2;
////////////////////////////////////////////////////////////////

// Find the highest common factor of both denominators
var commonMultiple = leastCommonMultiple(fraction1Denominator, fraction2Denominator);

fraction1Numerator   *= (commonMultiple / fraction1Denominator);
fraction2Numerator   *= (commonMultiple / fraction2Denominator);

// Display solution
document.getElementById("divSolution").innerText = fraction1Numerator + "/" + commonMultiple + " + " + fraction2Numerator + "/" + commonMultiple;

• Thanks for taking a look at my code. I tried your revised code but had some issues... I inputted the following fractions and got the following incorrect results...Fraction 1 = 1/2 --> 1/6 Fraction 2 = 2/6 --> 6/6; Fraction 1 = 2/12 --> 2/36 Fraction 2 = 1/18 --> 6/36; Fraction 1 = 1/18 --> 1/36 Fraction 2 = 2/12 --> 12/26. Jan 9, 2013 at 5:21
• I changed the following 2 lines of your code: fraction2Numerator *= (commonMultiple / fraction1Denominator); fraction2Numerator *= (commonMultiple / fraction2Denominator); --- TO ---> numeratorMultipler1 = commonMultiple / fraction1Denominator; numeratorMultipler2 = commonMultiple / fraction2Denominator; fraction1Numerator = numeratorMultipler1 * fraction1Numerator; fraction2Numerator = numeratorMultipler2 * fraction2Numerator; And that fixed the issue. Let me know what you think? Jan 9, 2013 at 5:24
• Actually, you just need to change : fraction2Numerator *= (commonMultiple / fraction1Denominator); for fraction1Numerator *= (commonMultiple / fraction1Denominator); (one character is to be changed) Jan 9, 2013 at 6:01
• Also, I think before programming anything, you should try to do your calculation with a pen and paper and try to figure out what you are doing. Then, once everything's clear, you can open your favorite text editor. Jan 9, 2013 at 6:25
• I see it now. Thanks. I started learning JavaScript a few months ago, I appreciate your feedback, especially on how I can make my code clearer and more efficient. I plan on posting a few more similar fraction/decimal codes for review and would like your feedback if you have time. Jan 9, 2013 at 7:20