The class uses the following code, most of which is straightforward.

class Fraction
{
    public long Numerator, Denominator;

    // Initialize the fraction from a string A/B.
    public Fraction(string txt)
    {
        string[] pieces = txt.Split('/');
        Numerator = long.Parse(pieces[0]);
        Denominator = long.Parse(pieces[1]);
        Simplify();
    }

    // Initialize the fraction from numerator and denominator.
    public Fraction(long numer, long denom)
    {
        Numerator = numer;
        Denominator = denom;
        Simplify();
    }

    // Return a * b.
    public static Fraction operator *(Fraction a, Fraction b)
    {
        // Swap numerators and denominators to simplify.
        Fraction result1 = new Fraction(a.Numerator, b.Denominator);
        Fraction result2 = new Fraction(b.Numerator, a.Denominator);

        return new Fraction(
            result1.Numerator * result2.Numerator,
            result1.Denominator * result2.Denominator);
    }

    // Return -a.
    public static Fraction operator -(Fraction a)
    {
        return new Fraction(-a.Numerator, a.Denominator);
    }

    // Return a + b.
    public static Fraction operator +(Fraction a, Fraction b)
    {
        // Get the denominators' greatest common divisor.
        long gcd_ab = MathStuff.GCD(a.Denominator, b.Denominator);

        long numer =
            a.Numerator * (b.Denominator / gcd_ab) +
            b.Numerator * (a.Denominator / gcd_ab);
        long denom =
            a.Denominator * (b.Denominator / gcd_ab);
        return new Fraction(numer, denom);
    }

    // Return a - b.
    public static Fraction operator -(Fraction a, Fraction b)
    {
        return a + -b;
    }

    // Return a / b.
    public static Fraction operator /(Fraction a, Fraction b)
    {
        return a * new Fraction(b.Denominator, b.Numerator);
    }

    // Simplify the fraction.
    private void Simplify()
    {
        // Simplify the sign.
        if (Denominator < 0)
        {
            Numerator = -Numerator;
            Denominator = -Denominator;
        }

        // Factor out the greatest common divisor of the
        // numerator and the denominator.
        long gcd_ab = MathStuff.GCD(Numerator, Denominator);
        Numerator = Numerator / gcd_ab;
        Denominator = Denominator / gcd_ab;
    }

    // Convert a to a double.
    public static implicit operator double(Fraction a)
    {
        return (double)a.Numerator / a.Denominator;
    }

    // Return the fraction's value as a string.
    public override string ToString()
    {
        return Numerator.ToString() + "/" + Denominator.ToString();
    }
}

The Simplify method divides the greatest common divisor (GCD) from the numerator and the denominator. For a description of the GCD function, see the example Calculate the greatest common divisor (GCD) and least common multiple (LCM) of two integers in C#.

I'll leave it as an exercise to figure out why the * operator method makes two intermediate Fractions that mix the numerators and denominators of the operands.