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fractions concept (#3555)
* fractions concept * added links, tried to clarify wording * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Update concepts/fractions/about.md Co-authored-by: BethanyG <[email protected]> * Introduction from About Added some links and edited config.json. --------- Co-authored-by: BethanyG <[email protected]>
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‎concepts/fractions/.meta/config.json

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{
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"blurb": "The fractions module enables working with rational numbers, which preserve exact values and avoid the rounding errors common with floats.",
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"authors": ["BethanyG", "colinleach"],
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"contributors": []
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}

‎concepts/fractions/about.md

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# About
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The [`Fractions`][fractions] module allows us to create and work with [`rational numbers`][rational]: fractions with an integer numerator divided by an integer denominator.
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For example, we can store `2/3` as an exact fraction instead of the approximate `float` value `0.6666...`
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## Creating Fractions
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Unlike `int`, `float`, and `complex` numbers, fractions do not have a literal form.
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However, the fractions constructor is quite flexible.
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Most obviously, it can take take two integers.
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Common factors are automatically removed, converting the fraction to its "lowest form": the smallest integers that accurately represent the fraction.
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```python
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>>> from fractions import Fraction
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>>> f1 = Fraction(2, 3) # 2/3
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>>> f1
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Fraction(2, 3)
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>>> f2 = Fraction(6, 9)
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>>> f2
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Fraction(2, 3) # automatically simplified
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>>> f1 == f2
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True
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```
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The fractions constructor can also parse a string representation:
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```python
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>>> f3 = Fraction('2/3')
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>>> f3
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Fraction(2, 3)
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```
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It can also work with `float` parameters, but this may run into problems with the approximate nature of representing the decimal value internally as binary.
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For more on this representation issue, see the [0.30000000000000004][0.30000000000000004] website, and [Floating Point Arithmetic: Issues and Limitations ][fp-issues] in the Python documentation.
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For a more reliable result when using floats with fractions, there is the `<fraction>.limit_denominator()` method.
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[`.limit_denominator()`][limit_denominator] can take an integer parameter if you have specific requirements, but even the default (`max_denominator=1000000`) can work well and give an acceptable, simple approximation.
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```python
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>>> Fraction(1.2)
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Fraction(5404319552844595, 4503599627370496)
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>>> Fraction(1.2).limit_denominator()
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Fraction(6, 5)
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```
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## Arithmetic with Fractions
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The usual [`arithmetic operators`][operators] `+ - * / **` work with fractions, as with other numeric types.
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Integers and other `Fraction`s can be included and give a `Fraction` result.
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Including a `float` in the expression results in `float` output, with a consequent (possible) loss in precision.
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```python
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>>> Fraction(2, 3) + Fraction(1, 4) # addition
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Fraction(11, 12)
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>>> Fraction(2, 3) * Fraction(6, 5) # multiply fractions
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Fraction(4, 5)
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>>> Fraction(2, 3) * 6 / 5 # fraction with integers
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Fraction(4, 5)
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>>> Fraction(2, 3) * 1.2 # fraction with float -> float
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0.7999999999999999
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>>> Fraction(2, 3) ** 2 # exponentiation with integer
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Fraction(4, 9)
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```
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## Conversions to and from Fractions
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Fractions are great for preserving precision during intermediate calculations, but may not be what you want for the final output.
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It is possible to get the numerator and denominator individually or as a tuple ([`tuples`][tuple] will be discussed in a later Concept):
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```python
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>>> Fraction(2, 3).numerator
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2
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>>> Fraction(2, 3).denominator
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3
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>>> Fraction(2, 3).as_integer_ratio()
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(2, 3)
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```
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Various standard Python numeric functions also give the result you might expect from working with `int` and `float` types:
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```python
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>>> round(Fraction(11, 3))
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4
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>>> from math import floor, ceil
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>>> floor(Fraction(11, 3))
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3
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>>> ceil(Fraction(11, 3))
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4
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>>> float(Fraction(11, 3))
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3.6666666666666665
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```
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[fractions]: https://docs.python.org/3/library/fractions.html
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[0.30000000000000004]: https://0.30000000000000004.com/
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[fp-issues]: https://docs.python.org/3/tutorial/floatingpoint.html#tut-fp-issues
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[tuple]: https://docs.python.org/3/tutorial/datastructures.html#tuples-and-sequences
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[operators]: https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex
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[rational]: https://en.wikipedia.org/wiki/Rational_number
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[limit_denominator]: https://docs.python.org/3/library/fractions.html

‎concepts/fractions/introduction.md

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# Introduction
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The [`Fractions`][fractions] module allows us to create and work with [`rational numbers`][rational]: fractions with an integer numerator divided by an integer denominator.
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For example, we can store `2/3` as an exact fraction instead of the approximate `float` value `0.6666...`.
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Unlike `int`, `float`, and `complex` numbers, fractions do not have a literal form.
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However, the fractions constructor is quite flexible.
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Most obviously, it can take take two integers as arguments.
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Common factors are automatically removed, converting the fraction to its "lowest form": the smallest integers that accurately represent the fraction:
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```python
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>>> from fractions import Fraction
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>>> f1 = Fraction(2, 3) # 2/3
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>>> f1
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Fraction(2, 3)
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>>> f2 = Fraction(6, 9)
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>>> f2
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Fraction(2, 3) # automatically simplified
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>>> f1 == f2
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True
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```
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The fractions constructor can also parse a string representation:
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```python
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>>> f3 = Fraction('2/3')
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>>> f3
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Fraction(2, 3)
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```
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Fractions can also work with `float` parameters, but this may run into problems with the approximate nature of representing the decimal value internally as binary.
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For more on this representation issue, see the [0.30000000000000004][0.30000000000000004] website, and [Floating Point Arithmetic: Issues and Limitations ][fp-issues] in the Python documentation.
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For a more reliable result when using floats with fractions, there is the `<fraction>.limit_denominator()` method.
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## Arithmetic with Fractions
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The usual [`arithmetic operators`][operators] `+ - * / **` will work with fractions, as with other numeric types.
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Integers and other `Fraction`s can be included in the equation and give a `Fraction` result.
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Including a `float` in the expression results in `float` output, with a consequent (possible) loss in precision:
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```python
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>>> Fraction(2, 3) + Fraction(1, 4) # addition
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Fraction(11, 12)
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>>> Fraction(2, 3) * Fraction(6, 5) # multiply fractions
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Fraction(4, 5)
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>>> Fraction(2, 3) * 6 / 5 # fraction with integers
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Fraction(4, 5)
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>>> Fraction(2, 3) * 1.2 # fraction with float -> float
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0.7999999999999999
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>>> Fraction(2, 3) ** 2 # exponentiation with integer
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Fraction(4, 9)
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```
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Various standard Python numeric functions also give the result you might expect from working with `int` and `float` types:
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```python
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>>> round(Fraction(11, 3))
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4
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>>> from math import floor, ceil
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>>> floor(Fraction(11, 3))
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3
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>>> ceil(Fraction(11, 3))
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4
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>>> float(Fraction(11, 3))
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3.6666666666666665
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```
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[0.30000000000000004]: https://0.30000000000000004.com/
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[fp-issues]: https://docs.python.org/3/tutorial/floatingpoint.html#tut-fp-issues
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[fractions]: https://docs.python.org/3/library/fractions.html
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[operators]: https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex
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[rational]: https://en.wikipedia.org/wiki/Rational_number

‎concepts/fractions/links.json

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[
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{
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"url": "https://docs.python.org/3/library/fractions.html/",
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"description": "Documentation for the Fractions module."
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},
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{
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"url": "https://docs.python.org/3/tutorial/floatingpoint.html#tut-fp-issues",
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"description": "Limitations of Floating Point Arithmetic."
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},
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{
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"url": "https://leancrew.com/all-this/2023/08/decimal-to-fraction/",
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"description": "And now it's all this: Decimal to fraction."
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},
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{
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"url": "https://nrich.maths.org/2515",
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"description": "History of Fractions."
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}
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]

‎config.json

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"uuid": "565f7618-4552-4eb0-b829-d6bacd03deaf",
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"slug": "with-statement",
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"name": "With Statement"
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},
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{
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"uuid": "000e7768-38b9-4904-9ae2-9a4e448f366c",
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"slug": "fractions",
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"name": "Fractions"
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}
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],
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"key_features": [

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