Adding Fractions in Python

Rationalise (Canonise) the Fractions before Addition

Normally before fractions are added, they are rationalised; i.e., they are put in a form where their denominators become the same. This same denominator is the LCM of the denominators of all the separate fractions.
After this is done, the new numerators can then be added together.

Steps for Addition of Fractions Python code

The following steps will guide us in writing our code.
Let's illustrate with ²/₅ + ⁷/₄

Step 1:

Find the LCM of the denominators.
⇒ LCM of 5 & 4 = 20

Step 2:

In a turn by turn fashion, divide the found LCM from Step 1 by each denominator, multiplying the quotient by the corresponding numerator.
⇒ ^{((2 x 4) + (7 x 5))}/₂₀
= ^{(8 + 35)}/₂₀

Step 3:

Go ahead and add the numerators.
⇒ ⁴³/₂₀

Create a new module file; Call it AddFraction.pm.;
Type out the adjoining Python code for adding fractions.

Note: The code module for finding LCM is from the Primary Category.
Just make a copy of it into the current folder (project).

You can comment out the DivideFraction Python object code in the main class from the previous lesson or simply continue from where it stopped.

So!

Feel free to try out your own set of numerators and denominators for fractional addition.

Python code for AddFraction Module File

# A class
class PlusFraction:

    # Simulate a constructor
    def __init__(self, fractions):

        self.numerators   = fractions['numerators']
        self.denominators = fractions['denominators']

        self.answer = 0
        self.new_numerators = []

    # transforms fractions so they all have same denominator
    # takes a dictionary of a list of numerators and denominators
    #
    # returns a dictionary of the new numerators and new denominator(LCM)
    def canoniseFraction(self):
        # STEP 1:
        from LCM import findLCM
        self.l_c_m = findLCM(self.denominators)
        self.lcm = self.l_c_m.getLCM()

        # STEP 2:
        # make numerators vary(ratio) with lcm
        for count in range(len(self.denominators)):
            self.new_numerators.append(int(self.lcm / self.denominators[count] * self.numerators[count]))

        return None

    # returns a dictionary of the
    # new numerator and new denominator(LCM)
    def doAdd(self):
        self.canoniseFraction()

        # STEP 3:
        # add all transformed numerators
        for num in self.new_numerators: self.answer += num
        return {'numerator':self.answer, 'denominator':self.lcm}

Main class

#!/usr/bin/python
from AddFraction import PlusFraction

##
# Adding fractions
##
numerators = [1, 1, 1, 1]
denominators = [4, 4, 4, 4]
fractions = {'numerators':numerators, 'denominators':denominators}

print('\n    Solving:\n')
# Print as fraction
for numerator in fractions['numerators']: print('{:13d}'.format(numerator), end='')
print('{}{:>12}'.format('\n', ' '), end='')
for wasted in range(len(numerators)-1): print('{}'.format('-     +      '), end='')
print('{:>1}'.format('-'))
for denominator in fractions['denominators']: print('{:13d}'.format(denominator), end='')
print('\n\n')

# use the AddFraction class
add_fract = PlusFraction(fractions)
fraction = add_fract.doAdd()

print('{:25d}'.format(fraction['numerator']))
print('{:>25}'.format('Answer   =   -'))
print('{:25d}'.format(fraction['denominator']))

print('\n\n')

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