fractions concept (#3555)

* fractions concept

* added links, tried to clarify wording

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Update concepts/fractions/about.md

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

* Introduction from About

Added some links and edited config.json.

---------

Co-authored-by: BethanyG <BethanyG@users.noreply.github.com>

concepts/fractions/.meta/config.json

@@ -0,0 +1,5 @@
+{
+  "blurb": "The fractions module enables working with rational numbers, which preserve exact values and avoid the rounding errors common with floats.",
+  "authors": ["BethanyG", "colinleach"],
+  "contributors": []
+}

concepts/fractions/about.md

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

concepts/fractions/introduction.md

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

concepts/fractions/links.json

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

config.json

@@ -2567,6 +2567,11 @@
       "uuid": "565f7618-4552-4eb0-b829-d6bacd03deaf",
       "slug": "with-statement",
       "name": "With Statement"
+    },
+    {
+      "uuid": "000e7768-38b9-4904-9ae2-9a4e448f366c",
+      "slug": "fractions",
+      "name": "Fractions"
     }
   ],
   "key_features": [