Splitting multiple columns of text into different columns in R

I have a column that looks like the following dataset:

Initial_Data 3Mo_Data 6Mo_Data Irrelevant_Col1 Irrelevant_Col2
18/24        14/14    NA       1               1
4/24         NA       6/14     0               0

df <- structure(list(Initial_Data = c("18/24", "4/24"), `3Mo_Data` = c("14/14", 
NA), `6Mo_Data` = c(NA, "6/14"), Irrelevant_Col1 = 1:0,     Irrelevant_Col2 = 1:0), class = "data.frame", row.names = c(NA, -2L))

And I'd like to split it in such a way to identify all the columns of "Data" and then split them into three columns:

1. One with the fraction (originally a character variable), expressed as a decimal.
2. Second column with the numerator
3. Third new column with the denominator

while ignoring the irrelevant columns so as to look like the following:

Initial_Data 3Mo_Data 6Mo_Data Irrelevant_Col1 Irrelevant_Col2 Inial_Data_Numerator  Initial_Data_Denominator 3Mo_Data_Numerator 3Mo_Data_Denominator 6Mo_Data_Numerator 6Mo_Data_Denominator 
0.75         1        NA       1               1               18                    24                       14                 14                   NA                 NA
0.17         NA       0.43     0               0               4                     24                       NA                 NA                   6                  14

I tried something like the following just to generate the numerator and denominator columns:

test <- df %>%
  mutate(across(contains("Data"),
         ~ paste0(.x, "Numerator") = str_extract(., "^\\d+"),
         ~ paste0(.x, "Denominator") = str_extract(.,"(?<=\\D)\\d+"))

But gives me errors with the equal sign, perhaps I'm not able to use paste0 in this way?

Thanks for your help in advance!

A tidyverse workflow:

library(dplyr)
library(tidy)

df %>%
  separate_wider_delim(ends_with("Data"), delim = '/',
                       names_sep = '_', names = c("Num", "Denom")) %>%
  mutate(across(ends_with("Num"), as.numeric, .names = "{sub('_Num', '', .col)}") /
         across(ends_with("Denom"), as.numeric),
         .before = 1)

# # A tibble: 2 × 11
#   Initial_Data `3Mo_Data` `6Mo_Data` Initial_Data_Num Initial_Data_Denom `3Mo_Data_Num` `3Mo_Data_Denom` `6Mo_Data_Num` `6Mo_Data_Denom` Irrelevant_Col1 Irrelevant_Col2
#          <dbl>      <dbl>      <dbl> <chr>            <chr>              <chr>          <chr>            <chr>          <chr>                      <int>           <int>
# 1        0.75           1     NA     18               24                 14             14               NA             NA                             1               1
# 2        0.167         NA      0.429 4                24                 NA             NA               6              14                             0               0

Another presentation of mutate() that uses cur_column() within across():

df %>%
  separate_wider_delim(ends_with("Data"), delim = '/',
                       names_sep = '_', names = c("Num", "Denom")) %>%
  mutate(across(ends_with("Num"),
                ~ as.numeric(.x) / as.numeric(get(sub("Num", "Denom", cur_column()))),
                .names = "{sub('_Num', '', .col)}"),
         .before = 1)

Here's one way, using separate_wider_delim:

library(tidyverse)

df <- separate_wider_delim(df, cols= c("Initial_Data", "3Mo_Data", "6Mo_Data"), delim = "/", names_sep = "_")
colnames(df) <- str_replace_all(colnames(df), c("_1$" = "_Numerator", "_2$" = "_Denominator"))