#include <iostream>

// THIS IS MORE CHALLENGING
//
// Write a program that implements a simple calculator
// for rational numbers.
//
// A rational number can be written as
//
//     a
//     -,
//     b
//
// where 'a' and 'b' are integers and b != 0.
//
// For this exercise, represent each rational number using
// two integers: a numerator and a denominator.
//
// Ask the user to enter two rational numbers and then
// select one of the following operations:
//
//     1. Addition
//     2. Subtraction
//     3. Multiplication
//     4. Division
//
// If the user enters any integer other than 1, 2, 3 or 4,
// print a message indicating that the selection is invalid.
//
// If the two rational numbers are
//
//     a       c
//     -  and  -,
//     b       d
//
// then calculate the result using
//
//     a   c     a*d + b*c
//     - + -  =  ---------,
//     b   d        b*d
//
//     a   c     a*d - b*c
//     - - -  =  ---------,
//     b   d        b*d
//
//     a   c     a*c
//     - x -  =  -----,
//     b   d     b*d
//
// and
//
//     a   c     a*d
//     - / -  =  -----.
//     b   d     b*c
//
// Print the resulting numerator and denominator with a
// '/' between them.
//
// Do not reduce the result to lowest terms. For example,
//
//     1/2 + 1/2
//
// should be printed as
//
//     4/4
//
// rather than
//
//     1/1.
//
// If the resulting denominator is negative, negate both
// the numerator and denominator so that the denominator
// is positive. For example,
//
//     3/-5
//
// should be printed as
//
//     -3/5.
//
// Remember:
//
//     1. The denominator of a rational number cannot
//        be zero.
//
//     2. Division by a rational number with numerator
//        zero is undefined.
//
// If either input denominator is zero, or if the user
// attempts to divide by a rational number whose numerator
// is zero, print an appropriate error message and
// terminate the program.

// Function declarations
int main();

// Function definitions
int main() {
    return 0;
}









































// Hint:
//
// First read the numerator and denominator of each
// rational number.
//
// Before performing any arithmetic, make sure that neither
// denominator is zero.
//
// Next, use a cascading conditional statement to determine
// which operation the user selected.
//
// Store the numerator and denominator of the answer in
//
//     num
//     den
//
// respectively.
//
// For division, there is one additional issue:
//
//     a   c
//     - / -
//     b   d
//
// requires multiplying by the reciprocal of c/d:
//
//     a   d     a*d
//     - x -  =  -----.
//     b   c     b*c
//
// What happens if c = 0?









































// After calculating the numerator and denominator, there
// is one final issue to consider.
//
// We want the denominator to be positive.
//
// If
//
//     den < 0,
//
// negate both 'num' and 'den'. This does not change the
// value of the rational number because
//
//     num       -num
//     ---   =   ----.
//     den       -den







































// Here is one solution:

/*
int main() {
    int num_m{};

    std::cout << "Enter the left-hand numerator: ";
    std::cin >> num_m;

    int den_m{};

    std::cout << "Enter the left-hand denominator: ";
    std::cin >> den_m;

    // A rational number cannot have a denominator of zero.

    if ( den_m == 0 ) {
        std::cout << "A denominator cannot be zero."
                  << std::endl;

        return 0;
    }

    int num_n{};

    std::cout << "Enter the right-hand numerator: ";
    std::cin >> num_n;

    int den_n{};

    std::cout << "Enter the right-hand denominator: ";
    std::cin >> den_n;

    // Again, the denominator cannot be zero.

    if ( den_n == 0 ) {
        std::cout << "A denominator cannot be zero."
                  << std::endl;

        return 0;
    }

    int choice{};

    std::cout << "Enter 1 for addition," << std::endl;
    std::cout << "      2 for subtraction," << std::endl;
    std::cout << "      3 for multiplication, and" << std::endl;
    std::cout << "      4 for division: ";
    std::cin >> choice;

    int num{};
    int den{};

    if ( choice == 1 ) {
        num = num_m*den_n + num_n*den_m;
        den = den_m*den_n;
    } else if ( choice == 2 ) {
        num = num_m*den_n - num_n*den_m;
        den = den_m*den_n;
    } else if ( choice == 3 ) {
        num = num_m*num_n;
        den = den_m*den_n;
    } else if ( choice == 4 ) {
        // Dividing by zero is undefined. The rational
        // number num_n/den_n is zero exactly when its
        // numerator is zero.

        if ( num_n == 0 ) {
            std::cout << "Division by zero is undefined."
                      << std::endl;

            return 0;
        }

        num = num_m*den_n;
        den = den_m*num_n;
    } else {
        std::cout << "Invalid operation: "
                  << choice << std::endl;

        return 0;
    }

    // Make the denominator positive by moving any
    // negative sign to the numerator.

    if ( den < 0 ) {
        num = -num;
        den = -den;
    }

    std::cout << num << "/" << den << std::endl;

    return 0;
}
*/