multiplicative inverse of rational numbers c++ - c++

Question

My program works fine except when a fraction has a numerator of 0 in the numerator when it does the inverse I get an arithmetic error and it crashes.
I've tried to check for zero int he numerator several different ways but I can't get the program to compile. Can someone give me some pointers.
Here's my code so far:
#include <lab58.h>
using namespace std;
int lcm(int u, int v)
{
if(u == 0 || v == 0)
return 0;
else
return (u * v) / gcd(u, v);
}
Rational rationalAdd(const Rational& augend, const Rational& addend)
{
Rational sum;
int lcm = ::lcm(augend.denominator, addend.denominator);
sum.numerator = lcm * augend.denominator / augend.numerator +
lcm * addend.denominator / addend.numerator;
sum.denominator = lcm;
rationalNormalize(sum);
return sum;
}
Rational rationalAdditiveInverse(const Rational *rational)
{
Rational additiveInverse;
additiveInverse.numerator = rational->numerator * -1;
additiveInverse.denominator = rational->denominator;
return additiveInverse;
}
Rational rationalSubtract(const Rational& minuend, const Rational& subtrahend)
{
return rationalAdd(minuend, rationalAdditiveInverse(&subtrahend));
}
// Function rationalMultiply returns multiplier x multiplicand. The
// result is returned in reduced form.
Rational rationalMultiply(const Rational& multiplier, const Rational& multiplicand)
{
Rational product;
product.numerator = multiplier.numerator * multiplicand.numerator;
product.denominator = multiplier.denominator * multiplicand.denominator;
rationalNormalize(product);
return product;
}
// Function rationalMultiplicativeInverse returns the multiplicative inverse.
// The multiplicative inverse, or reciprocal, of a number a is the
// number that, when multiplied by a, yields the multiplicative
// identity, 1. The multiplicative inverse of the fraction a/b is b/a.
Rational rationalMultiplicativeInverse(const Rational *rational)
{
Rational multiplicativeInverse;
multiplicativeInverse.numerator = rational->denominator;
multiplicativeInverse.denominator = rational->numerator;
return multiplicativeInverse;
}
// Function rationalDivide returns dividend / divisor. The result is
// returned in reduced form.
Rational rationalDivide(const Rational& dividend, const Rational& divisor)
{
return rationalMultiply(dividend, rationalMultiplicativeInverse(&divisor));
}
Here's the lab58.h file:
#ifndef LAB58_H
#define LAB58_H
#include <lab57.h>
using namespace std;
// Function lcm returns the least common multiple of u & v
int lcm(int u, int v);
// Function rationalAdd returns augend + addend. The result is
// returned in reduced form.
Rational rationalAdd(const Rational& augend, const Rational& addend);
// Function rationalAdditiveInverse returns the additive inverse.
// The additive inverse, or opposite, of a number a is the number
// that, when added to a, yields zero. Thus, the fraction a/b is
// returned as -a/b.
Rational rationalAdditiveInverse(const Rational *rational);
// Function rationalSubtract returns minuend - subtrahend. The result
// is returned in reduced form.
Rational rationalSubtract(const Rational& minuend, const Rational& subtrahend);
// Function rationalMultiply returns multiplier x multiplicand. The
// result is returned in reduced form.
Rational rationalMultiply(const Rational& multiplier, const Rational& multiplicand);
// Function rationalMultiplicativeInverse returns the multiplicative inverse.
// The multiplicative inverse, or reciprocal, of a number a is the
// number that, when multiplied by a, yields the multiplicative
// identity, 1. The multiplicative inverse of the fraction a/b is b/a.
Rational rationalMultiplicativeInverse(const Rational *rational);
// Function rationalDivide returns dividend / divisor. The result is
// returned in reduced form.
Rational rationalDivide(const Rational& dividend, const Rational& divisor);
#endif
Lab57.h:
/*
* Prototypes for operations on rational numbers.
*/
#ifndef LAB57_H
#define LAB57_H
#include <iostream>
using namespace std;
typedef struct
{
int numerator;
int denominator;
} Rational;
// Function rationalValid returns true if rational represents a valid
// rational number and false otherwise.
bool rationalValid(const Rational& rational);
// Function rationalNormalize reduces rational to lowest
// terms. Negative rationals should be manipulated so that the
// minus sign goes with the numerator. Zero is represented by zero
// (0) as the numerator and one (1) as the denominator.
void rationalNormalize(Rational& rational);
// Function rationalInput initializes rational from input stream in
istream& rationalInput(istream& in, Rational& rational);
// Function rationalOutput writes rational to output stream out in the
// format rational.numerator/rational.denominator
ostream& rationalOutput(ostream& out, const Rational& rational);
// Function gcd returns the greatest common divisor of u & v
int gcd(int u, int v);
#endif
Lab57main.C:
#include <iostream>
#include <lab57.h>
using namespace std;
int main()
{
Rational rational;
while (rationalInput(cin, rational))
{
if (rationalValid(rational))
{
rationalOutput(cout, rational);
cout << " = ";
rationalNormalize(rational);
rationalOutput(cout, rational);
cout << endl;
}
else
{
rationalOutput(cout, rational);
cout << " is invalid " << endl;
}
}
return EXIT_SUCCESS;
}