Objectives:

$1.$ Students will apply basic constructs of programming languages to write programs.

$2.$ Students will write correct, will$-$documented and readable programs in a reasonable amount of time.

Problem Description:

Declare and define a class for a fraction number. A fraction in mathematics is defined as a$/$b$,$ where a and b are integers and called numerator and denominator.

Requirements

Task$1$

$$ Define a fraction class that has the following member functions:

o constructor that initializes the fraction by default arguments.

o set function that sets the numerator of the fraction.

o set function that sets the denominator of the fraction.

o get function that returns the numerator of the fraction.

o get function that returns the denominator of the fraction.

o a function that displays the fraction.

$$ Write the class in header and implementation files, and compile it separately from the client program. Name the files as fraction.h and fraction.cpp$.$

$$ Document the class following the example of the point class posted on D$2$L$.$

$$ Write a test program to show all your member functions work before you move to Task$2.$ Name your program as project$1\_$task$1.$cpp$.$

Task$2$

$$ Add the following nonmember functions in your fraction header file and implementation file following the example of modified point class in the file $$newpoint$.$h$$ and $$newpoint$.$cpp$$:

o A function that returns the sum of two fractions.

o A function that returns the difference of two fractions.

o A function that returns the product of two fractions.

o A function that returns the quotient of two fractions.

$[$Note$]$ To make your implementation easier, no need to simplify the calculated result.

Name the modified files as newfraction$1.$h and newfraction$1.$cpp$.$

$$ Write another test program to show all the operations work correctly before you move to Task $3.$ Name the program as project$1\_$task$2.$cpp$.$

A run of this test program might look like this:

$>$a$.$out

Enter the first fraction: numerator denominator

$35$

Enter the second fraction: numerator denominator

$23$

The two fractions entered are

f$1=3/5$

f$2=2/3$

The arithmetic operations on these two fractions:

f$1+$ f$2=19/15$

f$1-$ f$2=-1/15$

f$1*$ f$2=6/15$

f$1/$ f$2=9/10$

Task $3$

Redo the Task $2$ using operators.

$$ Use operator overloading to define the following operations for the fraction class:

o Sum: $+$ as a member function

o Difference: $-$ as a member function

o Product: $*$ as a non member function

o Quotient: $/$ as a non member function

o Output: $<<$ as a non member function

o Input : $>>$ as a friend function of the class fraction

$$ Following the example of the point class for all the documentation.

$$ Write and document the class in header and implementation files, and compile it separately from the client program. Name the files as newfraction$2.$h and newfraction$2.$cpp$.$

$$ Write a program that performs all the operations defined above. Name the program as project$1\_$task$3.$cpp$.$

Please write in C$++$