Is there any way to create fractions that are not listed on the pop-up list?
For Gboard: Just enable longpress for symbols in Gboard settings. Than find textbox and in lower left corner of keyboard switch to symbols, than longpress on some numbers will give you fraction or exponent.
With the SwiftKey keyboard navigate to your Numeric keys and long-press the number 5 to get ⅝ as an option.
Go to numerical keys in bottom left and long press 1-3, 5 and 7. It will give you options if there is more than one available fraction for that number, for instance long pressing 1 will offer ⅛, ¼, ⅓, ½. Otherwise it will just give you the one available fraction for that number. Just choose the first number you want. So if you needed ⅝ you'd long press 5, ⅞ you'd long press 7 etc.
For MessagEase keyboard, there only seems to be three values supported out-the-box via the combine function: ½, ¼, and ¾. To input them, type out the numerator followed by the denominator, then swipe up-left on the