Fraction module in Python - GeeksforGeeks

19 Nov, 2020
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.
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.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)Output :11/35
5/9
0
class fractions.Fraction(other_fraction) : This requires that other_fraction is instance of numbers.Rational and a fraction instance with same value is returned.class fractions.Fraction(float) : This requires the float instance and a fraction instance with same value is returned.from fractions import Fraction  print (Fraction(1.13))# returns Fraction(1272266894732165, 1125899906842624)Output :1272266894732165/1125899906842624
class fractions.Fraction(decimal) : This requires the decimal instance and a fraction instance with same value is returned.from fractions import Fraction  print (Fraction('1.13'))# returns Fraction(113, 100)Output :113/100
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.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)Output :8/25
113/100
3/7
1414213/1000000
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.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 2Output :157079632679489661923/50000000000000000000
355/113
311/99
22/7
5
2

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.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)Output :11/35
5/9
0

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)
Output :
11/35
5/9
0

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

from fractions import Fraction  print (Fraction(1.13))# returns Fraction(1272266894732165, 1125899906842624)
Output :
1272266894732165/1125899906842624

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

from fractions import Fraction  print (Fraction('1.13'))# returns Fraction(113, 100)
Output :
113/100

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.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)Output :8/25
113/100
3/7
1414213/1000000

Form for this instance : [sign] numerator [‘/’ denominator]Here, sign represents ‘+’ or ‘-’ and numerator and denominator are strings of single digits.
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)
Output :
8/25
113/100
3/7
1414213/1000000

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.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 2Output :157079632679489661923/50000000000000000000
355/113
311/99
22/7
5
2

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.
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
Output :
157079632679489661923/50000000000000000000
355/113
311/99
22/7
5
2

Performing Mathematical operations on fractions
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
Output :
2267/900
2
288/95
3/2
2.8592589556

Fraction-based calculations using various functions of math module
import mathfrom 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)
Output :
2.5
3.0550504633
2.0
3900231685776981/4503599627370496
6/7

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