Fraction module in Python

This module provides support for rational number arithmetic. It allows to create a Fraction instance from integers, floats, numbers, decimals and strings.

Fraction Instances : A Fraction instance can be constructed from a pair of integers, from another rational number, or from a string. Fraction instances are hashable, and should be treated as immutable.

  1. class fractions.Fraction(numerator=0, denominator=1) : This requires that numerator and denominator are instances of numbers. Rational and a fraction instance with value = (numerator/denominator) is returned. A zerodivision error is raised if denominator = 0.
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    from fractions import Fraction
       
    print Fraction(11, 35)
    # returns Fraction(11, 35)
       
    print Fraction(10, 18)
    # returns Fraction(5, 9)
      
    print Fraction()
    # returns Fraction(0, 1)

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    Output :



    11/35
    5/9
    0
    
  2. class fractions.Fraction(other_fraction) : This requires that other_fraction is instance of numbers.Rational and a fraction instance with same value is returned.
  3. class fractions.Fraction(float) : This requires the float instance and a fraction instance with same value is returned.
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    from fractions import Fraction
      
    print Fraction(1.13)
    # returns Fraction(1272266894732165, 1125899906842624)

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    Output :

    1272266894732165/1125899906842624
    
  4. class fractions.Fraction(decimal) : This requires the decimal instance and a fraction instance with same value is returned.
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    from fractions import Fraction
      
    print Fraction('1.13')
    # returns Fraction(113, 100)

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    Output :

    113/100
    
  5. class fractions.Fraction(string) : This requires the string or unicode instance instance and a fraction instance with same value is returned.

    Form for this instance : [sign] numerator [‘/’ denominator]
    Here, sign represents ‘+’ or ‘-’ and numerator and denominator are strings of single digits.

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    from fractions import Fraction
       
    print Fraction('8/25')
    # returns Fraction(8, 25)
       
    print Fraction('1.13')
    # returns Fraction(113, 100)
      
    print Fraction('3/7')
    # returns Fraction(3, 7)
      
    print Fraction('1.414213 \t\n')
    # returns Fraction(1414213, 1000000)

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    Output :

    8/25
    113/100
    3/7
    1414213/1000000
    
  6. limit_denominator(max_denominator=1000000) :
    • This method is useful for finding rational approximations to a given floating-point number.
    • This module finds and returns the closest Fraction to self that has denominator at most max_denominator.
    • This module can also be used to return the numerator of a given fraction in the lowest term by using the numerator property and the denominator by using the denominator property.
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    from fractions import Fraction
       
    print Fraction('3.14159265358979323846')
    # returns Fraction(157079632679489661923, 50000000000000000000)
       
    print Fraction('3.14159265358979323846').limit_denominator(10000)
    # returns Fraction(355, 113)
       
    print Fraction('3.14159265358979323846').limit_denominator(100)
    # returns Fraction(311, 99)
       
    print Fraction('3.14159265358979323846').limit_denominator(10)
    # returns Fraction(22, 7)
       
    print Fraction(125, 50).numerator
    # returns 5
       
    print Fraction(125, 50).denominator
    # returns 2

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    Output :

    157079632679489661923/50000000000000000000
    355/113
    311/99
    22/7
    5
    2
    

Performing Mathematical operations on fractions

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from fractions import Fraction
   
print Fraction(113, 100) + Fraction(25, 18)
# returns Fraction(2267, 900)
   
print Fraction(18, 5) / Fraction(18, 10)
# returns Fraction(2, 1)
   
print Fraction(18, 5) * Fraction(16, 19)
# returns Fraction(288, 95)
   
print Fraction(18, 5) * Fraction(15, 36)
# returns Fraction(3, 2)
   
print Fraction(12, 5) ** Fraction(12, 10)
# returns 2.8592589556010197

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Output :

2267/900
2
288/95
3/2
2.8592589556

Fraction-based calculations using various functions of math module

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import math
from fractions import Fraction
   
print math.sqrt(Fraction(25, 4))
# returns 2.5
   
print math.sqrt(Fraction(28,3))
# returns 3.0550504633038935
   
print math.floor(Fraction(3558, 1213))
# returns 2
   
print Fraction(math.sin(math.pi/3))
# returns Fraction(3900231685776981, 4503599627370496)
   
print Fraction(math.sin(math.pi/3)).limit_denominator(10)
# returns Fraction(6, 7)

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Output :

2.5
3.0550504633
2.0
3900231685776981/4503599627370496
6/7

This article is contributed by Aditi Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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