How to Reduce Fractions to Lowest Term
Reducing fractions to their lowest terms is all about removing every common factor between the numerator and the denominator.
Reducing Fractions to Lowest Term Code in Python
Let's see this using 12/16.
A common factor to 12 and 16 is 2;
so removing 2 from 12/16 yields
6/8.
Again, 2 is common to both 6 and 8;
removing it yields 3/4.
We stop when nothing else is common (1 does not count).
Create a new module file;
call it LowestTerm.py.
Type out the adjoining Python code for reducing fractions to their lowest terms.
Note: You can comment out the ImproperToMixed 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 numerator and denominator.
Python code for LowestTerm Module File
# A class
class LowTerm:
# A constructor
def __init__(self, fraction):
self.numerator = fraction['numerator']
self.denominator = fraction['denominator']
# set trial_factor to the smaller value between numerator and denominator
if self.numerator < self.denominator: self.trial_factor = self.numerator
else: self.trial_factor = self.denominator
# Returns a dictionary of the new numerator and denominator
def reduceFraction(self):
# We are counting down to test for mutual factors
while self.trial_factor > 1:
# do we have a factor
if self.numerator % self.trial_factor == 0:
# is this factor mutual?
if self.denominator % self.trial_factor == 0:
# where we have a mutual factor
self.numerator /= self.trial_factor
self.denominator /= self.trial_factor
continue
self.trial_factor -= 1
return {'numerator':int(self.numerator), 'denominator':int(self.denominator)}
class LowTerm:
# A constructor
def __init__(self, fraction):
self.numerator = fraction['numerator']
self.denominator = fraction['denominator']
# set trial_factor to the smaller value between numerator and denominator
if self.numerator < self.denominator: self.trial_factor = self.numerator
else: self.trial_factor = self.denominator
# Returns a dictionary of the new numerator and denominator
def reduceFraction(self):
# We are counting down to test for mutual factors
while self.trial_factor > 1:
# do we have a factor
if self.numerator % self.trial_factor == 0:
# is this factor mutual?
if self.denominator % self.trial_factor == 0:
# where we have a mutual factor
self.numerator /= self.trial_factor
self.denominator /= self.trial_factor
continue
self.trial_factor -= 1
return {'numerator':int(self.numerator), 'denominator':int(self.denominator)}
main class
#!/usr/bin/python
from LowestTerm import LowTerm
##
# Reduce fractions to Lowest Term
#
fraction = {'numerator':16, 'denominator':640}
print('\n To reduce to lowest term, simplifying:\n')
# Print as fraction
print('{:45d}'.format(fraction['numerator']))
print('{:>45}'.format('-'))
print('{:45d}'.format(fraction['denominator']))
# use the LowestTerm class
low_term = LowTerm(fraction)
fraction = low_term.reduceFraction()
print('{:46d}'.format(fraction['numerator']))
print('{:>46}'.format('Answer = -'))
print('{:46d}'.format(fraction['denominator']))
print('\n\n')
from LowestTerm import LowTerm
##
# Reduce fractions to Lowest Term
#
fraction = {'numerator':16, 'denominator':640}
print('\n To reduce to lowest term, simplifying:\n')
# Print as fraction
print('{:45d}'.format(fraction['numerator']))
print('{:>45}'.format('-'))
print('{:45d}'.format(fraction['denominator']))
# use the LowestTerm class
low_term = LowTerm(fraction)
fraction = low_term.reduceFraction()
print('{:46d}'.format(fraction['numerator']))
print('{:>46}'.format('Answer = -'))
print('{:46d}'.format(fraction['denominator']))
print('\n\n')