public class Rational { 

    private int numerator;
    private int denominator;

    // constructors

    public Rational(int numerator) {
	this(numerator, 1);
    }

    public Rational(int numerator, int denominator) {
	if (denominator < 0) {
	    denominator = -1 * denominator;
	    numerator = -1 * numerator;
	}
	this.numerator = numerator;
	this.denominator = denominator;
	reduce();
    }

    // getters

    public int getNumerator() {
	return numerator;
    }

    public int getDenominator() {
	return denominator;
    }

    // instance methods

    public Rational plus(Rational other) {
	int newDenominator = denominator * other.denominator;
	int newNumerator = numerator * other.denominator;
	int newOtherNumerator = other.numerator * denominator;
	int sum = newNumerator + newOtherNumerator;
	return new Rational(sum, newDenominator);
    }

    public static Rational plus(Rational a, Rational b) {
	return a.plus( b );
    }

    // Transforms this number into its reduced form

    private void reduce() {
	if (numerator == 0) {
	    denominator = 1;
	} else {
	    int common = gcd(Math.abs(numerator), denominator);
	    numerator = numerator/common;
	    denominator = denominator/common;
	}
    }

    // Euclid's algorithm for calculating the greatest common divisor

    private int gcd(int a, int b) {
	while (a != b)
	    if (a > b)
		a = a - b;
	    else
		b = b - a;
	return a;
    }

    public int compareTo(Rational other) {

	int thisNewNum = other.denominator * numerator;
	int otherNewNum = other.numerator * denominator;

	return thisNewNum - otherNewNum;

    }

    public boolean equals(Rational other) {

	if (numerator == other.numerator && denominator == other.denominator)
	    return true;
	else
	    return false;
    }

    public String toString() {
	String result;
	if (denominator == 1) {
	    result = Integer.toString(numerator);
	} else {
	    result = numerator + "/" + denominator;
	}
	return result;
    }

}