Fraction module in Python

Difficulty Level : Easy
Last Updated : 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 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 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)

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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