Addition of Fractions
by Isai Damier, Android Engineer @ Google

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/***************************************************************************
 *  Author: Isai Damier
 * Title: Addition of Fractions
 * Project: geekviewpoint
 * Package: algorithms
 *
 * Statement:
 *   Add the two given positive fractions
 *
 * Sample Input: {5,6}, {7,8})
 * Sample Output: {41,24}
 *
 * Technical Details:
 *   This is the same algorithm you learned in grade school:
 *   1) find the lowest common denominator, which is the same as finding
 *     the lowest common multiplier of the given denominators.
 *   2) Convert the given fractions into equivalent fractions with the
 *     new denominator
 *   3) add the numerators
 *   4) reduce the resulting fraction using the GCD (greatest common
 *     divisor) of its numerator and denominator.
 *
 **************************************************************************/
 public int[] addingFractions(int[] a, int[] b) {
  int denominator = LCM(a[1], b[1]);
  int numA = denominator / a[1] * a[0];
  int numB = denominator / b[1] * b[0];
  int numerator = numA + numB;
  int gcd = GCD(numerator, denominator);
  return new int[]{numerator / gcd, denominator / gcd};
}