With-construction: I can't work with all the children crying.
"with + a participle construction" expresses a special circumstance of the main clause.
Sometimes "with" can be dropped. But sometimes the connection between main clause and participle construction can become unclear as in this case:
I can't work, all the children crying.
Added: An old post of mine on another forum:
with-construction (with + noun + participle)
If you don't know this special construction, you have difficulty to understand it.
A typical example: I can't work | with all the children crying.
The sense of it is: I can't work when all the children are crying.
This construction is very old and was already in use in Latin (ablativus absolutus).
You can choose whether you consider "crying" as a participle or gerund. Grammars treat it as participle.
I tend to see it as gerund and explain the sentence as
- I can't work with all the children (in the act of) crying.
Of course, it will take you quite a time till you can think in such constructions. The advantage of the
with-construction is you can add in a shortened and elegant way circumstantial facts for which
you normally need a subclause with a conjunction.
This is a whole chapter in grammars and you should have a lot of examples as there are some variants of this with-construction (My name as there is no standard term for this construction).