While iOS can display a full range of characters the iOS keyboard is unable to type many of them.
There are several methods to work around this limitation, the easiest of which uses the built-in keyboard shortcuts.

It does require a little bit of setting up to use this method, but once done will yield the quickest typed fractions possible.

1. Search the web for a page that includes the fractions and/or characters that are most important to you

2. Copy each character one at a time and perform the following steps

3. Go to settings, general, keyboard and finally shortcuts

4. Choose Add new shortcut

5. In the Phrase field paste the character. eg. ‘½’
In the shortcut Field type the shortcut. eg. 1/2
(return to step 2)

Other methods, all of which require copy and paste, include;

Creating a note (using the note app) that includes all the characters you might use, then copying and pasting from the note each time a fraction is needed.

Or, searching the web each time you need a character.

Or, using a webapp known as Glyphboard which allows fast access to a range of characters

Or, use text expander to create and store your shortcuts. (Text expander shortcuts can be shared and edited with multiple devices).