public class Rational {
	
	// Creating instance variables for the numerator and denominator	
	private long numerator;
	private long denominator;
	
	// Constructor that creates a new Rational object, making sure the denominator is not 0 or negative.	
	public Rational (long numer, long denom){
		
		if (denom == 0){
			throw new RuntimeException("Error, can't have a denominator of 0.");
		}
		
		if (denom <0){
			denom = -denom;
			numer = -numer;
		}
		
		long greatestCommonDivisor = gcd(numer, denom);
		numerator = numer / greatestCommonDivisor;
		denominator = denom / greatestCommonDivisor;
		
	}
	
	// This method takes two rational numbers and adds them together	
	public Rational plus(Rational b){
		Rational answer = new Rational (this.numerator * b.denominator + b.numerator * this.denominator, b.denominator * this.denominator);
		
		return answer;
	}
	
	//This method takes two rational numbers and subtracts them
	public Rational minus (Rational b){
		Rational answer = new Rational (this.numerator * b.denominator - b.numerator * this.denominator, b.denominator * this.denominator);
		
		
		return answer;
	}
	
	//This method takes two rational numbers and multiplies them
	public Rational times (Rational b){
		Rational answer = new Rational (this.numerator * b.numerator, this.denominator * b.denominator);
		
		return answer;
	}
	
	
	
	// This method uses Euclid's algorithm  which calculates the greatest common divisor	
	public static long gcd(long p, long q){
		if (q==0) return p;
		long r = p % q;
		return gcd(q, r);
	}

	// This method produces a string representation of values
	public String toString(){
		if (denominator == 1)
			return numerator + "";
		else
			return numerator + "/" + denominator;
	}
	
	
	// Test client
	public static void main (String args[]){
		Rational p = new Rational (1, 6);
		Rational q = new Rational (4, 8);
		
		Rational r = p.minus(q);
		System.out.println(r);
	}
	

}