public class Fraction {



	private int numer;
	private int denom;


	public Fraction(int numer, int denom) {

		this.numer = numer;
		this.denom = denom;

		simplify();
	}


	public Fraction(int numer) {

		this(numer, 1);
		/*
		this.numer = numer;
		this.denom = 1;
		
		*/
	}

	public Fraction add(Fraction another) {

	   int newDenom = this.denom * another.denom;

	   int newNumer = this.numer * another.denom
			  + this.denom * another.numer;


	   Fraction answer = new Fraction(newNumer, newDenom);
		
	   return answer;


	}


	public Fraction multiply(Fraction another) {

		int newDenom = this.denom * another.denom;

		int newNumer = this.numer * another.numer;

		Fraction answer = new Fraction(newNumer,
					      newDenom);

		return answer;
	}


	private Fraction negate() {

		return new Fraction(-numer, denom);
	}

	public Fraction subtract(Fraction another) {

		return add(another.negate());

	}

	private Fraction reciprocal() {
		return new Fraction(denom, numer);
	}


	public Fraction divide(Fraction another) {

		return multiply(another.reciprocal());

	}
	public String toString() {

	   return numer + (denom!=1? "/" + denom: "");

	}

	public boolean equals(Object obj) {

		boolean result = obj instanceof Fraction;

		if(!result)
			return false;

		/*
		if(! (obj instanceof Fraction))
			return false;
		*/

		Fraction another= (Fraction) obj;


		return this.numer==another.numer 
		       && this.denom == another.denom;

		
	}
	private void simplify() {
		
	    int divisor = gcd(numer, denom);
		  
	    numer = numer/divisor;
	    denom = denom / divisor;

	}

	//Euclid's algorithm
	private static int gcd(int a, int b) {
		if(b==0)
		    return a;

		else
		    return gcd(b, a%b);
	}

	

/*
 	gcd(anything, 0) = anything

	gcd(a, b) = gcd(b, a%b) 

	
*/

	public static void main(String[] args) {

		Fraction f1 = new Fraction(7, 21);

		Fraction f2 = new Fraction(6, 36);

		System.out.println(f1.add(f2));

		f1 = new Fraction(9, 56);

		f2 = new Fraction(1);

		System.out.println(f2.add(f1));

		f1 = new Fraction(1,2);
		f2 = new Fraction(1, 100);

		System.out.println(f1.multiply(f2));

		System.out.println(f1.divide(f2));

		System.out.println(f2.divide(f1));
	}


}