Implement a rational class (fractions) that overloads numerous operators. Make the testfile below pass all tests. Use the provided makefile. Refer to cppreference for guidance, particularly their Fractions example. Note, you don’t need a gcd function like they have; our fractions do not need to be “reduced” (e.g., 5/10 does not convert to 1/2).

Here are the rules for various operations:

a/b + c/d = (a*d + b*c) / (b*d)
a/b - c/d = (a*d - b*c) / (b*d)
(a/b) * (c/d) = (a*c) / (b*d)
(a/b) / (c/d) = (a*d) / (c*b)
-(a/b) = (-a/b)
(a/b) < (c/d) means (a*d) < (c*b)
(a/b) == (c/d) means (a*d) == (c*b)

and we'll say *(a/b) means inverse: b/a
e.g., Rational a(5,2); Rational b = *a;
be sure to keep negative in numerator

// this should print as "5/3"
Rational myrational(5, 3);
cout << myrational << endl;


## main.cpp

#include <iostream>
#include "rational.h"
#include "gtest/gtest.h"
using namespace std;

TEST(rational, constructor)
{
Rational a(5, 2);
ASSERT_EQ(a.getNum(), 5);
ASSERT_EQ(a.getDenom(), 2);
}

TEST(rational, minus)
{
Rational a(5, 2);
Rational b(3, 7);
Rational c = a-b;
ASSERT_EQ(c.getNum(), 29);
ASSERT_EQ(c.getDenom(), 14);
}

TEST(rational, plus)
{
Rational a(5, 2);
Rational b(3, 7);
Rational c = a+b;
ASSERT_EQ(c.getNum(), 41);
ASSERT_EQ(c.getDenom(), 14);
}

TEST(rational, negate)
{
Rational b(3, 7);
Rational c = -b;
ASSERT_EQ(c.getNum(), -3);
ASSERT_EQ(c.getDenom(), 7);
}

TEST(rational, complex_math)
{
Rational a(5, 2);
Rational b(3, 7);
Rational c = *a+b*(-b/a);
ASSERT_EQ(c.getNum(), 400);
ASSERT_EQ(c.getDenom(), 1225);
}

TEST(rational, star)
{
Rational b(3, 7);
Rational c = *b;
ASSERT_EQ(c.getNum(), 7);
ASSERT_EQ(c.getDenom(), 3);
}

TEST(rational, comparison)
{
Rational a(5, 2);
Rational b(3, 7);
Rational c(3, 7);
ASSERT_EQ(a == a, true);
ASSERT_EQ(a == c, false);
ASSERT_EQ(a != c, true);
ASSERT_EQ(a < b, false);
ASSERT_EQ(a > b, true);
ASSERT_EQ(a <= b, false);
ASSERT_EQ(b <= c, true);
ASSERT_EQ(a >= b, true);
ASSERT_EQ(b >= c, true);
ASSERT_EQ(c <= b, true);
ASSERT_EQ(a <= a, true);
ASSERT_EQ(a >= a, true);
}

TEST(rational, postincrement)
{
Rational a(5, 2);
Rational b = a++;
ASSERT_EQ(a.getNum(), 7);
ASSERT_EQ(a.getDenom(), 2);
ASSERT_EQ(b.getNum(), 5);
ASSERT_EQ(b.getDenom(), 2);
}

TEST(rational, preincrement)
{
Rational a(5, 2);
Rational b = ++a;
ASSERT_EQ(a.getNum(), 7);
ASSERT_EQ(a.getDenom(), 2);
ASSERT_EQ(b.getNum(), 7);
ASSERT_EQ(b.getDenom(), 2);
}

TEST(rational, postdecrement)
{
Rational a(5, 2);
Rational b = a--;
ASSERT_EQ(a.getNum(), 3);
ASSERT_EQ(a.getDenom(), 2);
ASSERT_EQ(b.getNum(), 5);
ASSERT_EQ(b.getDenom(), 2);
}

TEST(rational, predecrement)
{
Rational a(5, 2);
Rational b = --a;
ASSERT_EQ(a.getNum(), 3);
ASSERT_EQ(a.getDenom(), 2);
ASSERT_EQ(b.getNum(), 3);
ASSERT_EQ(b.getDenom(), 2);
}

TEST(rational, convert_double)
{
Rational a(5, 2);
double b = a;
ASSERT_DOUBLE_EQ(b, 2.5);
}

TEST(rational, ostream)
{
Rational a(5, 2);
cout << a << endl;
SUCCEED();
}

TEST(rational, istream)
{
Rational a(5, 2);
cout << "Enter two integers for numerator and denominator: ";
cin >> a;
cout << a << endl;
SUCCEED();
}


## Makefile

GTEST_DIR = /opt/google-test/googletest
CXX = g++
CXXFLAGS = -std=c++11 -Wall -L$(GTEST_DIR)/lib -isystem$(GTEST_DIR)/include -Wextra -lpthread

all: test

test: main.o rational.o
$(CXX)$(CXXFLAGS) -o test main.o rational.o $(GTEST_DIR)/lib/libgtest_main.a$(GTEST_DIR)/lib/libgtest.a

main.o: main.cpp rational.h
$(CXX)$(CXXFLAGS) -c main.cpp

rational.o: rational.cpp rational.h
$(CXX)$(CXXFLAGS) -c rational.cpp

.PHONY: clean
clean:
rm -rf *.o test