fracture

Convert decimals to fractions in R

Installation

You can install the released version of fracture from CRAN with:

install.packages("fracture")

or the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("rossellhayes/fracture")

Usage

Convert decimals to a character vector of fractions

fracture converts decimals into fractions.

fracture(0.5)
#> [1] 1/2

fracture((1:11) / 12)
#>  [1] 1/12  1/6   1/4   1/3   5/12  1/2   7/12  2/3   3/4   5/6   11/12

Math with fractures

fractures are implemented using an S3 class. This means we can perform mathematical operations on them like real fractions.

fracture(0.25) * 2
#> [1] 1/2

fracture(0.25) + fracture(1/6)
#> [1] 5/12

Stylish fractures

frac_style() uses Unicode to provide stylish formatting for inline fractions.

`r frac_style(pi, mixed = TRUE, max_denom = 500)`

3 ¹⁶/₁₁₃

Arguments

Additional arguments help you get exactly the result you expect:

Set denominator

fracture((1:12) / 12, denom = 100)
#>  [1] 8/100   17/100  25/100  33/100  42/100  50/100  58/100  67/100  75/100 
#> [10] 83/100  92/100  100/100

Common denominators

fracture((1:12) / 12, common_denom = TRUE)
#>  [1] 1/12  2/12  3/12  4/12  5/12  6/12  7/12  8/12  9/12  10/12 11/12 12/12

Base-10 denominators

fracture(1 / (2:12), base_10 = TRUE)
#>  [1] 5/10             3333333/10000000 25/100           2/10            
#>  [5] 1666667/10000000 1428571/10000000 125/1000         1111111/10000000
#>  [9] 1/10             909091/10000000  833333/10000000

Maximum denominators

fracture(sqrt(1 / (1:12)), max_denom = 100)
#>  [1] 1/1   70/99 56/97 1/2   17/38 20/49 31/82 35/99 1/3   6/19  19/63 28/97

Mixed fractions

fracture((1:9) / 3, mixed = TRUE)
#> [1] "1/3"   "2/3"   "1"     "1 1/3" "1 2/3" "2"     "2 1/3" "2 2/3" "3"

Convert decimals to a fraction matrix

For more advanced work, you may prefer to work with a fraction matrix:

frac_mat((1:11) / 12)
#>             [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
#> numerator      1    1    1    1    5    1    7    2    3     5    11
#> denominator   12    6    4    3   12    2   12    3    4     6    12

frac_mat() accepts all the same arguments as fracture().

When mixed fractions are used, frac_mat() has three rows:

frac_mat((1:9) / 3, mixed = TRUE, common_denom = TRUE)
#>             [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> integer        0    0    1    1    1    2    2    2    3
#> numerator      1    2    0    1    2    0    1    2    0
#> denominator    3    3    3    3    3    3    3    3    3

Just a fun example

Use fracture to find the best approximations of π for each maximum denominator.

unique(purrr::map_chr(1:50000, ~ fracture(pi, max_denom = .x)))
#>  [1] "3/1"          "6/2"          "9/3"          "12/4"         "15/5"        
#>  [6] "18/6"         "22/7"         "333/106"      "355/113"      "103993/33102"
#> [11] "104348/33215"

Isn’t is interesting that there’s such a wide gap between ³⁵⁵/₁₁₃ and ¹⁰³⁹⁹³/₃₃₁₀₂?

Advantages