Is a dependent clause considered a fragment? Are all fragments considered to be a dependent clause? Or is fragment like an umbrella where dependent clauses and phrases can be found? Thanks for any and all help.
"Fragment" has no technical meaning.
It means a chunk of language that someone disapproves of, for some reason.
Generally, the reasons for the disapproval are spurious.
Consequently, there is no ISO Standard definition for a "fragment",
so there can be no answer to your questions, alas.
My advice is to ignore "fragments", and concentrate on learning to recognize clauses.
If anyone tells you that something is a "fragment",
be sure to ask them to state precisely
- what the rule is that applies
- what it is a fragment of
- what it should be
- why it is inappropriate
Take notes. Be sure to ask for rule citations at every step, so you can look them up. Be very polite.
Nine times out of ten they won't have any citations, and can't state the rules.
So you needn't pay attention to them.