public class FractionAdd {

    public static void main(String[] args) {
        int x1 = 3; int y1 = 5;  // 3/5
        int x2 = 1; int y2 = 2;  // 1/2
        int y3 = y1 / gcd(y1, y2) * y2;
        int x3 = y3 / y1 * x1 + y3 / y2 * x2;
        System.out.printf("结果是%d/%d", x3, y3);
    }

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

------解决方案--------------------

Apache Commons Lang 或者 Apache Commons Math 包，里面有分式计算类。