Question

7.

Fractions

You can express a fraction as a list: [numerator, denominator]. For example

1

2

can

be expressed as the list [1,2].

(a) Write a function called

factionAdd()

that takes two fractions as lists and adds

them. For example, fraction([1,2], [3,4]) returns [5,4]

(b) Write a function

fractionMult()

that multiplies two fractions that are passed

as lists.

[HINT: You may use the following function

gcd

(

x

;

y

) to help you calculate the

Greatest Common Divisor, which you will need to reduce fractions to the simplest

form.]

def gcd(x, y):

"""To calculate the greatest common divisor of x and y"""

x1 = abs(min(x, y))

y1 = abs(max(x, y))

gcd_ = x1

if y1 % x1:

gcd_ = gcd(x1, y1 % x1)

Answer 1

Code Screenshot :

Executable Code:

#Function to find the greatest common divisor
def gcd(x, y):
   #Find the absolute values
   x1 = abs(min(x, y))
   y1 = abs(max(x, y))
   gcd_ = x1
   #Computing the GCD
   if y1 % x1:
       gcd_ = gcd(x1, y1 % x1)
   #Return the result
   return gcd_

#Function to multiply fractions
def fractionMult(a,b):
   mul = (a[0]*b[0],a[1]*b[1])
   gcd_mul = gcd(mul[0],mul[1])
   #Finding the simplest form
   simplest_form= [mul[0]/gcd_mul,mul[1]/gcd_mul]
   #Return the result
   return simplest_form

#Function to add fractions
def fractionAdd(a,b):
   gcd_ab = gcd(a[1],b[1])
   m_a = b[1]/gcd_ab;
   m_b = a[1]/gcd_ab;
   sum = ((a[0]*m_a) + (b[0]*m_b),(gcd_ab*m_a*m_b))
   gcd_sum = gcd(sum[0],sum[1])
   #Finding the simplest form
   simplest_form = [sum[0]/gcd_sum,sum[1]/gcd_sum]
   #Return the result
   return simplest_form

#Prompting the user for input
n1 = int(input("Enter numerator for fraction 1: "))
d1 = int(input("Enter denominator for fraction 1: "))
n2 = int(input("Enter numerator for fraction 2: "))
d2 = int(input("Enter denominator for fraction 2: "))

#Printing the result
print("Addition of Fractions :",fractionAdd([n1,d1],[n2,d2]))
print("Product of Fractions :",fractionMult([n1,d1],[n2,d2]))

Sample Output :

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