U10A01

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
Rational.java
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

public class Rational {

    private int num, denum;

    public Rational(int num, int denum) {
        if(denum == 0) {
            // throw new IllegalArgumentException("Fehler: Nenner ist 0");
            System.out.println("Fehler: Nenner ist 0");
        }
        this.num = num;
        this.denum = denum;
        reduce();
    }

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

    private void reduce() {
        final int gcd = ggT(num, denum);
        num /= gcd;
        denum /= gcd;
        if(denum < 0) {
            denum *= -1;
            num *= -1;
        }
    }

    public /* private */ static int ggT(int a, int b) {
        a = Math.abs(a);
        b = Math.abs(b);
        return b == 0 ? a : a >= b ? ggT(a % b, b) : ggT(b, a);
    }

    public Rational add(Rational o) {
        final int denum = this.denum * o.denum, num1 = this.num * o.denum, num2 = this.denum * o.num;
        return new Rational(num1 + num2, denum);
    }

    public Rational sub(Rational o) {
        final int denum = this.denum * o.denum, num1 = this.num * o.denum, num2 = this.denum * o.num;
        return new Rational(num1 - num2, denum);
    }

    public Rational mul(Rational o) {
        return new Rational(num * o.num, denum * o.denum);
    }

    public Rational div(Rational o) {
        return new Rational(num * o.denum, denum * o.num);
    }

    @Override
    public String toString() {
        return num + "/" + denum;
    }

}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RationalTest.java
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

import java.util.Scanner;

public class RationalTest {

    public static void main(String[] args) {
        final Scanner sc = new Scanner(System.in);
        final Rational r1 = new Rational(sc.nextInt(), sc.nextInt());

        Rational result = r1;
        int state = 0;
        for(String input = sc.next(), op = null, num = null, denum = null; !input.equals("."); input = sc.next(), state++) {
            switch(state) {
                default:
                    state = 0;
                case 0: // read operator
                    op = input;
                    break;
                case 1: // read next numerator
                    num = input;
                    break;
                case 2: // read next denumerator and calculate
                    denum = input;
                    final Rational r2 = new Rational(Integer.parseInt(num), Integer.parseInt(denum));
                    if(op.length() != 1) {
                        throw new IllegalArgumentException("expected operator, got " + op);
                    }
                    switch(op.charAt(0)) {
                        case '+':
                            result = result.add(r2);
                            break;
                        case '-':
                            result = result.sub(r2);
                            break;
                        case '*':
                            result = result.mul(r2);
                            break;
                        case '/':
                            result = result.div(r2);
                            break;
                        default:
                            throw new IllegalArgumentException("unknown operator, expected one of +-*/");
                    }
            }
        }
        sc.close();

        System.out.println(result);
    }

}