# 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) `

/div>

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 '````) ` `# 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
```