# 9.5. `fractions` — 分数¶

`fractions` 模块支持分数运算。

class `fractions.``Fraction`(numerator=0, denominator=1)
class `fractions.``Fraction`(other_fraction)
class `fractions.``Fraction`(float)
class `fractions.``Fraction`(decimal)
class `fractions.``Fraction`(string)

```[sign] numerator ['/' denominator]
```

```>>> from fractions import Fraction
>>> Fraction(16, -10)
Fraction(-8, 5)
>>> Fraction(123)
Fraction(123, 1)
>>> Fraction()
Fraction(0, 1)
>>> Fraction('3/7')
Fraction(3, 7)
>>> Fraction(' -3/7 ')
Fraction(-3, 7)
>>> Fraction('1.414213 \t\n')
Fraction(1414213, 1000000)
>>> Fraction('-.125')
Fraction(-1, 8)
>>> Fraction('7e-6')
Fraction(7, 1000000)
>>> Fraction(2.25)
Fraction(9, 4)
>>> Fraction(1.1)
Fraction(2476979795053773, 2251799813685248)
>>> from decimal import Decimal
>>> Fraction(Decimal('1.1'))
Fraction(11, 10)
```

`Fraction` 类继承自抽象基类 `numbers.Rational`，并实现了该类的所有方法和操作。 `Fraction` 实例是可哈希的，并应当被视为不可变对象。 此外，`Fraction` 还具有以下属性和方法：

`numerator`

`denominator`

`from_float`(flt)

`from_decimal`(dec)

`limit_denominator`(max_denominator=1000000)

```>>> from fractions import Fraction
>>> Fraction('3.1415926535897932').limit_denominator(1000)
Fraction(355, 113)
```

```>>> from math import pi, cos
>>> Fraction(cos(pi/3))
Fraction(4503599627370497, 9007199254740992)
>>> Fraction(cos(pi/3)).limit_denominator()
Fraction(1, 2)
>>> Fraction(1.1).limit_denominator()
Fraction(11, 10)
```
`__floor__`()

```>>> from math import floor
>>> floor(Fraction(355, 113))
3
```
`__ceil__`()

`__round__`()
`__round__`(ndigits)

`fractions.``gcd`(a, b)

3.5 版后已移除: `math.gcd()` 取代.

`numbers` 模块