# 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.
```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
```
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.
```from fractions import Fraction

print Fraction(1.13)
# returns Fraction(1272266894732165, 1125899906842624)

```

Output :

```1272266894732165/1125899906842624
```
4. 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
```
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.

```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
```
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.
```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
```

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