Fractional Numbers
As before, fractional numbers can either be Proper (e.g. 2/5), Improper (e.g. 5/2), or Mixed (e.g. 21/2),
Improper to Mixed Fraction Code in Python
Say we have the fraction 10/3 - which is an improper fraction - we can convert this fraction to a mixed fraction by following a number of steps:
Step 1:
Find the largest number smaller than the numerator (10),
that can divide the denominator - 3 - without remainder.
⇒ 9
Step 2:
Subtract the found number (9) - from Step 1 -
from the numerator (10)
⇒ 10 - 9 = 1;
This yields the whole number.
Step 3:
Divide the found number (9) - from Step 1 -
by the denominator (3)
⇒ 9/3 = 3;
This yields the new numerator.
Step 4:
Reuse the denominator (3) to get our mixed fraction
⇒ 31/3
Create a new python module file;
call it ImproperToMixed.py
Type out the adjoining Python code for converting improper to mixed fractions.
Note: You can comment out the MixedToImproper 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 ImproperToMixed Module File
# A class
class Improper2Mixed:
# A constructor
def __init__(self, fraction):
self.numerator = fraction['numerator']
self.denominator = fraction['denominator']
# Returns a dictionary of the new fraction
def doConvert(self):
# STEP 1:
for dividend in range(self.numerator, 0, -1):
if dividend % self.denominator == 0:
# STEP 2:
self.new_numerator = self.numerator - dividend
# STEP 3:
self.whole_number = int(dividend / self.denominator)
break
return {'whole_number':self.whole_number, 'numerator':self.new_numerator, 'denominator':self.denominator}
class Improper2Mixed:
# A constructor
def __init__(self, fraction):
self.numerator = fraction['numerator']
self.denominator = fraction['denominator']
# Returns a dictionary of the new fraction
def doConvert(self):
# STEP 1:
for dividend in range(self.numerator, 0, -1):
if dividend % self.denominator == 0:
# STEP 2:
self.new_numerator = self.numerator - dividend
# STEP 3:
self.whole_number = int(dividend / self.denominator)
break
return {'whole_number':self.whole_number, 'numerator':self.new_numerator, 'denominator':self.denominator}
Algebra Main class
#!/usr/bin/python
from ImproperToMixed import Improper2Mixed
##
# Convert fractions from Improper to Mixed
##
fraction = {'numerator':10, 'denominator':3}
print("\n Converting from Improper to Mixed the fraction:\n")
# Print as fraction
print('{:55d}'.format(fraction['numerator']))
print('{:>55}'.format('-'))
print('{:55d}'.format(fraction['denominator']))
# use the ImproperToMixed class
imp2mix = Improper2Mixed(fraction)
fraction = imp2mix.doConvert()
print( '{:52d}'.format(fraction['numerator']))
print('{:>48} {} {}'.format('Answer = ', fraction['whole_number'], '-'))
print( '{:52d}'.format(fraction['denominator']))
print("\n\n")
from ImproperToMixed import Improper2Mixed
##
# Convert fractions from Improper to Mixed
##
fraction = {'numerator':10, 'denominator':3}
print("\n Converting from Improper to Mixed the fraction:\n")
# Print as fraction
print('{:55d}'.format(fraction['numerator']))
print('{:>55}'.format('-'))
print('{:55d}'.format(fraction['denominator']))
# use the ImproperToMixed class
imp2mix = Improper2Mixed(fraction)
fraction = imp2mix.doConvert()
print( '{:52d}'.format(fraction['numerator']))
print('{:>48} {} {}'.format('Answer = ', fraction['whole_number'], '-'))
print( '{:52d}'.format(fraction['denominator']))
print("\n\n")