Simplify a Fraction

Question

How can I simplify a fraction in PHP?

For instance, converting 40/100 to 2/5.

The only way I could think of is to do a prime factor

Answer 1

The algorithm is pretty simple:

• extract both values from a string.
• find their greatest common divisor ($gcd) (with Euclidean algorithm, for example)
• divide both values by $gcd
• rebuild the string with the values found

Answer 2

Here's a simple recursive PHP function

<?php

  function reduceFraction($numerator, $denominator)
  {
    $gcd = findGreatestCommonDenominator($numerator, $denominator);

    return [$numerator / $gcd, $denominator / $gcd];
  }


  function findGreatestCommonDenominator($a, $b)
  {
    return $b ? findGreatestCommonDenominator($b, $a % $b) : $a;
  }
}

usage :

<?php $reduced = reduceFraction(40,100); // returns [2,5] ?>

Answer 3

If you have PHP gmp extension, you can do this.

$num = 40;
$den = 100;
$gcd = gmp_intval(gmp_gcd((string)$num, (string)$den));

$new_num = $num / $gcd;
$new_den = $den / $gcd;

Answer 4

When you simplify a fraction, you divide the numerator and denominator by their greatest common divisor.

So all you need is to calcuate the GCD of the two numbers. There's no built-in function for that, but it's easy enough to implement the euclidean algorithm:

function gcd($a,$b) {
    $a = abs($a); $b = abs($b);
    if( $a < $b) list($b,$a) = Array($a,$b);
    if( $b == 0) return $a;
    $r = $a % $b;
    while($r > 0) {
        $a = $b;
        $b = $r;
        $r = $a % $b;
    }
    return $b;
}

Then just divide the top and bottom by that.

function simplify($num,$den) {
    $g = gcd($num,$den);
    return Array($num/$g,$den/$g);
}
var_export(simplify(40,100)); // Array(2,5)