Сделать класс для выполнения арифметических действий с дробями

#include <iostream>
#include <math.h>
#include <string>
 
class Rational
{
public:
    Rational(void);
    Rational(int);
    Rational(double);
    Rational(int, int);
    Rational(int, int, int);
    Rational(const std::string &);
 
    void Reduce(void);
    void Normalize(void);
    void Denormalize(void);
 
    void Show(void);
    bool IsValid(void){ return isValid; }
    unsigned getWhole(void){return whole;}
    unsigned getNumerator(void){return numerator;}
    unsigned getDenominator(void){return denominator;}
    bool getSign(void){return sign;}
 
    Rational operator+(const Rational &);
    Rational operator-(const Rational &);
    Rational operator*(const Rational &);
    Rational operator/(const Rational &);
 
private:
    bool sign, isValid;
    unsigned int whole, numerator, denominator;
 
    unsigned int NOD(void);
};
 
void Check(Rational r)
{
    cout << "Fraction: ";
    r.Show();
    r.Normalize();
    cout << "  Normalized: ";
    r.Show();
    r.Denormalize();
    cout << "  Denormalized: ";
    r.Show();
    r.Reduce();
    cout << "  Reduced: ";
    r.Show();
    cout << endl << endl;
}
 
int main() {
    Check(Rational());
 
    Check(Rational(7));
 
    Check(Rational(1.4));
 
    Check(Rational(7, 2));
 
    Check(Rational(1, 6, 8));
 
    Check(Rational("-3 17/8"));
 
    Rational a(-7.8), b(2,7,9);
    Rational m("-1 2/5"), n(3,2);
    cout << "Sum: ";
    a.Show();
    cout << " with ";
    b.Show();
    cout << " = ";
    Check(a + b);
    cout << endl << endl;
 
    cout << "Multyply: ";
    b.Show();
    cout << " on ";
    m.Show();
    cout << " = ";
    Check(b * m);
    cout << endl << endl;
 
    cout << "Difference between: ";
    n.Show();
    cout << " and ";
    a.Show();
    cout << " = ";
    Check(n - a);
    cout << endl << endl;
 
    cout << "Quotient between: ";
    m.Show();
    cout << " and ";
    b.Show();
    cout << " = ";
    Check(m / b);
    cout << endl << endl;
 
    system("pause");
    return 0;
}
 
Rational::Rational() : sign(false), whole(0), numerator(0), denominator(1), isValid(true) {}
 
Rational::Rational(double in) : sign(in < 0 ? true : false), whole(unsigned(fabs(in))), isValid(true)
{
    in = fabs(in);
    in = modf(in, nullptr);
 
    unsigned d = 1;
    do
    {
        in *= 10;
        d *= 10;
    }while (unsigned(floor(in + 0.5)) % 10 != 0);
    numerator = unsigned(floor(in + 0.5) / 10);
    denominator = d / 10;
//    if (numerator == 0 )
}
 
Rational::Rational(int _whole) : sign(_whole < 0 ? true : false), whole(abs(_whole)), numerator(1), denominator(1), isValid(true) {}
 
Rational::Rational(int num, int denum) : sign(num * denum < 0 ? true : false), whole(0), numerator(abs(num)), denominator(abs(denum)), isValid(denum == 0 ? false : true) { }
 
Rational::Rational(int _whole, int num, int denum) :
    sign(num * denum * _whole < 0 ? true : false), whole(_whole), numerator(abs(num)), denominator(abs(denum)), isValid(denum == 0 ? false : true) { }
 
Rational::Rational(const string &s) :  whole(0), numerator(0), denominator(0), isValid(false)
{
    if (!(s[0] >= 48 && s[0] <= 57) && s[0] != '-')
    {
        isValid = false;
        cout << "bad format, using: \"[w ]n/d\" where w,n,d - integer" << endl;
        return;
    }
    s[0] == '-' ? sign = true : sign = false;
    unsigned int i = sign;
 
    unsigned int ans = s.find(' ');
    if (ans != string::npos)
    {
        while (s[i] != ' ')
        {
 
            if (!(s[i] >= 48 && s[i] <= 57) && s[i] != ' ')
            {
                cout << "bad format, using: \"[w ]n/d\" where w,n,d - integer" << endl;
                return;
            }
            whole = whole * 10 + (s[i++] - 48);
        }
        i++;
    }
 
    ans = s.find('/');
    if (ans == string::npos)
    {
        cout << "bad format, using: \"[w ]n/d\" where w,n,d - integer" << endl;
        return;
    }
    else
    {
        //i = ans;
        while (s[i] != '/')
        {
            if (!(s[i] >= 48 && s[i] <= 57))
            {
                cout << "bad format, using: \"[w ]n/d\" where w,n,d - integer" << endl;
                return;
            }
            numerator = numerator * 10 + (s[i++] - 48);
        }
        ++i;
        while (s[i] != '\0')
        {
            if (s[i] < 48 || s[i] > 57)
            {
                cout << "bad format, using: \"[w ]n/d\" where w,n,d - integer" << endl;
                return;
            }
            denominator = denominator * 10 + (s[i++] - 48);
        }
        isValid = true;
    }
}
 
void Rational::Show()
{
    if (!isValid)
    {
        cout << "incorrect fraction" << endl;
        return;
    }
    if (numerator == 0)
        cout << 0;
    else if (numerator == denominator)
        cout << (sign ? "-" : "") << (whole != 0 ? whole : 1);
    else if (whole != 0)
        cout << (sign ? "-" : "") << whole << " " << numerator << "/" << denominator;
    else if (whole == 0)
        cout << (sign ? "-" : "") << " " << numerator << "/" << denominator;
}
 
unsigned int Rational::NOD()
{
    for (int i = numerator; i > 0; i--) {
        if (numerator % i == 0 && denominator % i == 0)
            return i;
    }
    return 1;
}
 
void Rational::Reduce()
{
    if (!isValid)
        return;
    unsigned int d = NOD();
    if (d > 1)
    {
        numerator /= d;
        denominator /= d;
    }
}
 
void Rational::Normalize()
{
    if (numerator <= denominator || !isValid)
        return;
    whole += unsigned(numerator / denominator);
    numerator -= denominator * unsigned(numerator / denominator);
}
 
void Rational::Denormalize()
{
    if (whole == 0 || !isValid)
        return;
    if (numerator == denominator)
        numerator--;
    numerator += (whole * denominator);
    whole = 0;
}
 
Rational Rational::operator *(const Rational &in)
{
    Rational r = in;
    r.Denormalize();
    this->Denormalize();
    return Rational((r.getSign() ^ this->getSign() ? -1 : 1) * r.getNumerator() * this->getNumerator(), r.getDenominator() * this->getDenominator());
}
 
Rational Rational::operator /(const Rational &in)
{
    Rational r = in;
    r.Denormalize();
    this->Denormalize();
    return Rational((r.getSign() ^ this->getSign() ? -1 : 1) * r.getDenominator() * this->getNumerator(), r.getNumerator() * this->getDenominator());
}
 
Rational Rational::operator +(const Rational &in)
{
    Rational r = in;
    r.Denormalize();
    this->Denormalize();
    return Rational((this->sign ? -1 : 1) * this->numerator * r.getDenominator() + (r.getSign() ? -1 : 1) * this->denominator * r.getNumerator(),
                    this->getDenominator() * r.getDenominator());
}
 
Rational Rational::operator -(const Rational &in)
{
    Rational r = in;
    r.Denormalize();
    this->Denormalize();
    return Rational((this->sign ? -1 : 1) * this->numerator * r.getDenominator() - (r.getSign() ? -1 : 1) * this->denominator * r.getNumerator(),
                    this->getDenominator() * r.getDenominator());
}