Sorting Fractions in Python

Rationalise (Canonise) the Fractions before Sorting

Before fractions are sorted, 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 easily be sorted in a preferred order.

Steps for Sorting of Fractions Python code

The following steps will guide us in writing our code.
Let's illustrate with ⁵/₉, ³/₇, ¹/₂

Step 1:

Find the LCM of the denominators.
⇒ LCM of 9, 7 & 2 = 126

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.
⇒ ^{((5 x 14), (3 x 18), (1 x 63))}/₁₂₆
= ^{(70, 54, 63)}/₁₂₆

Step 3:

Go ahead and sort the numerators in our order of choice.
         ⇒ In ascending order:
         ⁵⁴/₁₂₆, ⁶³/₁₂₆, ⁷⁰/₁₂₆
         = ³/₇, ¹/₂, ⁵/₉

Create a new module file; call it SortFraction.py.
Type out the adjoining Python code for sorting fractions in ascending and descending orders.

Note: You can comment out the SubtractFraction 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 sorting.

Python code for SortFraction Module File

from AddFraction import PlusFraction

# A class with a parent
class ArrangeFraction(PlusFraction):

    # A constructor
    def __init__(self, fractions):
        super().__init__(fractions)

        self.final_numerators   = []
        self.final_denominators = []

    # Returns a dictionary of the new fraction
    def sortAscending(self):
        # STEPS 1, 2:
        self.canoniseFraction()

        self.copy_numerators = []
        for member in self.new_numerators: self.copy_numerators.append(member);

        # STEP 3:
        # the little difference lies here(sort ascending)
        self.copy_numerators.sort()

        # map sorted (transformed) fractions to the original ones
        for numerator in self.copy_numerators:
            # get index using list value
            self.position = self.new_numerators.index(numerator)
            self.final_numerators.append(self.numerators[self.position])
            self.final_denominators.append(self.denominators[self.position])

        return {'numerators':self.final_numerators, 'denominators':self.final_denominators}

    # Returns a dictionary of the new fraction
    def sortDescending(self):
        # STEPS 1, 2:
        self.canoniseFraction()

        self.copy_numerators = []
        for member in self.new_numerators: self.copy_numerators.append(member);

        # STEP 3:
        # the little difference lies here(sort ascending)
        self.copy_numerators.sort(reverse=True)

        # map sorted (transformed) fractions to the original ones
        for numerator in self.copy_numerators:
            # get index using list value
            self.position = self.new_numerators.index(numerator)
            self.final_numerators.append(self.numerators[self.position])
            self.final_denominators.append(self.denominators[self.position])

        return {'numerators':self.final_numerators, 'denominators':self.final_denominators}

main class

#!/usr/bin/python
from SortFraction import ArrangeFraction

##
# Sorting fractions
##
numerators = [1, 3, 5, 9]
denominators = [2, 4, 2, 10]
fractions = {'numerators':numerators, 'denominators':denominators}

print("\n    Sorting in ascending order the fractions:\n")
# Print as fraction
for numerator in fractions['numerators']: print('{:12d}'.format(numerator), end='')
print('{}{:>11}'.format('\n', ' '), end='')
for wasted in range(len(numerators)-1): print('{}'.format('-   ,       '), end='')
print('{:>1}'.format('-'))
for denominator in fractions['denominators']: print('{:12d}'.format(denominator), end='')
print('\n\n')

# use the SortFraction class
sort_fract = ArrangeFraction(fractions)
fractions = sort_fract.sortAscending()

# Print as fraction
for numerator in fractions['numerators']: print('{:13d}'.format(numerator), end='')
print('{}{:>1}'.format('\nAnswer  =  ', ' '), 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')

print('\n\n')

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