public class Rational {

    private int num, den;

    private int gcd(int a, int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    public Rational(int num, int den) {
        int d = gcd(num, den);
        this.num = num / d;
        this.den = den / d;
    }

    /*
     * @param r a Rational
     * @return another Rational that's the result of adding r to the current Rational
     */
    public Rational add(Rational r) {
        int resultNum = r.num * den + num * r.den;
        int resultDen = r.den * den;
        return new Rational(resultNum, resultDen);
    }

    /*
     * @param r a Rational
     * @return another Rational that's the result of multiplying r to the current Rational
     */
    public Rational multiply(Rational r) {
        int resultNum = r.num * num;
        int resultDen = r.den * den;
        return new Rational(resultNum, resultDen);
    }

    public String toString() {
        return String.format("%d/%d", num, den);
    }

    public boolean equals(Rational r) {
        return num==r.num && den==r.den;       
    }

    public static void main(String[] args) {
        Rational r1 = new Rational(3, 4);
        Rational r2 = new Rational(2, 4);
        Rational r3 = new Rational(1, 3);
        Rational result = r1.add(r2).multiply(r3);
        System.out.printf("(%s + %s) * %s = %s%n", r1, r2, r3, result);

        Rational r4 = new Rational(1, 2);
        if (r2.equals(r4))
            System.out.println("r2 is equal to r4");
    }
}