Fraction module in Python

In Python the Fraction module supports rational number arithmetic. Using this module, we can create fractions from integers, floats, decimal and from some other numeric values and strings.

There is a concept of Fraction Instance. It is formed by a pair of integers as numerator and denominator.

The class fractions.Fractionis used to create a Fraction object. It takes Numerator and Denominator. The default value of the numerator is 0 and denominator is 1. It raises ZeroDivisionError when the denominator is 0.

At first we will see how the class can create fractions using Numerator and Denominator.

Example code

Live Demo

from fractions import Fraction as frac
print(frac(45, 54))
print(frac(12, 47))
print(frac(0, 15))

Output

5/6
12/47
0

We can provide some floating point numbers as an argument of the Fraction object. If we provide the exact floating point value, it will try to convert it to numerator and denominator value of integer type. In this case, it tries to reach to the approximate value. If the floating point number is provided as a string, it will try to find the exact value as Fraction. From the following examples, you can see the differences.

Example code

Live Demo

from fractions import Fraction as frac
print(frac(33.33))
print(frac('33.33'))

Output

2345390243441541/70368744177664
3333/100

Let us see, some other examples on string type arguments to the Fraction object. It also supports the sign of the numbers. It supports + or - sign.

Example code

Live Demo

from fractions import Fraction as frac
print(frac('5/6'))
print(frac('-25.12'))
print(frac('96.251 \t\n'))
print(frac('3.14159265359'))

Output

5/6
-628/25
96251/1000
314159265359/100000000000

As we have seen, sometimes the denominators are very large in the Fraction object. So we can limit the denominator lengths. The default length is 1000000. It helps to perform rational approximation for floating point data. To limit the denominator, there is a function called limit_denominator().

Sometimes we want only the numerators or the denominators without the whole fraction object. So this method has numerator and denominator keyword to get them.

Example code

Live Demo

from fractions import Fraction as frac
print(frac('3.14159265359'))
print(frac('3.14159265359').limit_denominator(1000))
print(frac('3.14159265359').limit_denominator(100))
print(frac('3.14159265359').limit_denominator(10))
print(frac('36.25'))
print(frac('36.25').numerator)
print(frac('36.25').denominator)

Output

314159265359/100000000000
355/113
311/99
22/7
145/4
145
4

Fractions can also support the mathematical operations, like addition, subtraction, multiplication, division, power etc.

Example code

Live Demo

from fractions import Fraction as frac
print('Add: ' + str(frac('5/4') + frac('9/8')))
print('Subtract: ' + str(frac('15/20') - frac('2/8')))
print('Multiply: ' + str(frac('2/3') * frac('5/7')))
print('Divide: ' + str(frac('80/125') / frac('12/45')))
print('Power: ' + str(frac('5/6') ** 3))

Output

Add: 19/8
Subtract: 1/2
Multiply: 10/21
Divide: 12/5
Power: 125/216

The square root, floor, ceiling and some other operations are also supported by this object.

Example code

Live Demo

from fractions import Fraction as frac
import math
print('Square Root: ' + str(math.sqrt(frac(36, 64))))
print('Square Root: ' + str(frac(math.sqrt(frac(36, 64)))))
print('Floor Value: ' + str(math.floor(frac('22/7'))))
print('Ceiling Value: ' + str(math.ceil(frac('22/7'))))

Output

Square Root: 0.75
Square Root: 3/4
Floor Value: 3
Ceiling Value: 4