Write a Fraction class $($

fraction.py$)$ that represents a rational number $($i$.$e$.,$ numbers that can be

expressed in the form of $\frac{a}{b},$ where a and $b$ are integers$).$ For example, a variable with a value

of $\frac{1}{2}$ would be created as follow:

one$\_$half $=$Fraction$(1,2)$

Your class should provide access to the numerator and denominator through the methods

numerator and denominator, and support the following methods$/$operations:

repr$\_\_($self$)$: return a string representation of a Fraction object, e$.$g$.,$ Fraction$(1,2).$

$($self$)$: return a string value of a Fraction object, e$.$g$.,1/2.$

Add, subtract, multiply, and divide fractions. Each method should return a Fraction object with

the answer and be implemented by overloading the appropriate operator.

Comparisons:

Your Fraction class should ensure that your fractions are represented using a canonical $($unique$)$

form. That is$,$ your fractions should be in reduced form. Other questions to consider are $1)$ how

$0$ is represented and $2)$ how a negative number is represented. Handling these questions about

fraction representation are part of robust programming.

Greatest common divisor: To represent a fraction in reduced form, you need to calculate the

greatest common divisor of the numerator and denominator. This can be done using the

Euclidean algorithm. Assume that we want $gcd(a,b),$ where $ab>0.$ Then, using integer

arithmetic, we can calculate the gcd using the following algorithm:

$r=$amodb

while $r$ is not zero:

$a=b$

$b=r$

$r=$amodb

return b

The value $b$ returned by this method is $gcd(a,b).$ For full marks, you need to write your own

version of the $gcd()$ function. The $)$ function is available in the math module, but we want

you to write your own as an exercise. As an added challenge, see if you can write $)$ as a

recursive function; there are no extra marks for a recursive version.

Finally, write a simple program to test your Fraction class. Add your test code at the end of the

file. The text below demonstrates output from sample test code; use it as a guide.

using python