/**
 * Calculus with fractionals using gcd and lcm.
 * 
 * @author (Stefan Edelkamp) 
 * @version (2013)
 */
public class Fractional
{
    /**
     * Euclid's algorithm
     * 
     * @param  a   smaller of the two numbers
     * @param  b   larger of the two numbers
     * @return     greatest common divisor of a and b 
     */
    public int gcd(int a, int b) { 
      return a == 0 ? b : gcd(b%a,a); 
    }
    /**
     * Exploiting Euclid's algorithm
     * 
     * @param  a   smaller of the two numbers
     * @param  b   larger of the two numbers
     * @return     least common multiplier of a and b 
     */
    public int lcm(int a, int b) { 
      return a*b / gcd(a,b); 
    }
    /**
     * Performing some calculatoins
     * 
     * @param  a   nominator first fractional
     * @param  b   denominator first fractional
     * @param  c   nominator second fractional
     * @param  d   denominator second fractional 
     * @return     greatest common divisor of a and b 
     */
    public void compute(int a, int b, int c, int d) { 
      System.out.println("(a/b)->("+(a/gcd(a,b))+"/"+(b/gcd(a,b))+")");
      System.out.println("(c/d)->("+(c/gcd(c,d))+"/"+(d/gcd(c,d))+")");   
      int k = lcm(b,d); 
      int s = a*k/b + c*k/d; 
      System.out.println("sum = ("+(s/gcd(s,k))+"/"+(k/gcd(s,k))+")"); 
    }
}