First I’l comment on your code which may help you understand text item delimiters a little better…
set numberInch to get every text item of fractionNum as list
Invoking text items returns a list of items, so you do not need to coerce the result “as list”. It’s already a list.
set numerator to get 1st text item of numberInch
Since numberInch is a list it has components called item 1, item 2 and so on. So this line should be “item 1 of numberInch” or “first item of numberInch”. When you say “first text item” you are invoking “text items” again and thus are trying to turn the items in the numberInch list into more lists rather than getting the actual items of numberInch… and of course you’re not trying to make more lists.
Now here’s how I would use text item delimiters to solve your question…
set myData to "1-2/15, 3-11/13, 7/23, 5-1/6, 12"
set text item delimiters to ", "
set numbersList to text items of myData --> {"1-2/15", "3-11/13", "7/23", "5-1/6", "12"}
set finalList to {}
repeat with aNumber in numbersList
set {wholeNumber, numerator, denominator} to {missing value, missing value, missing value}
if aNumber contains "-" then
set text item delimiters to "-"
set thisList to text items of aNumber
set {wholeNumber, fraction} to {item 1 of thisList, item 2 of thisList}
if aNumber contains "/" then
set text item delimiters to "/"
set fractionList to text items of fraction
set {numerator, denominator} to {item 1 of fractionList, item 2 of fractionList}
end if
else if aNumber contains "/" then
set text item delimiters to "/"
set fractionList to text items of aNumber
set {numerator, denominator} to {item 1 of fractionList, item 2 of fractionList}
else
set wholeNumber to aNumber
end if
if wholeNumber is not missing value then set wholeNumber to wholeNumber as number
if numerator is not missing value then set numerator to numerator as number
if denominator is not missing value then set denominator to denominator as number
set end of finalList to {wholeNumber:wholeNumber, numerator:numerator, denominator:denominator}
end repeat
set text item delimiters to ""
return finalList
--> {{wholeNumber:1, numerator:2, denominator:15}, {wholeNumber:3, numerator:11, denominator:13}, {wholeNumber:missing value, numerator:7, denominator:23}, {wholeNumber:5, numerator:1, denominator:6}, {wholeNumber:12, numerator:missing value, denominator:missing value}}