Because my children were sick and I was up all night.

[Biro]

"Because my children were sick and I was up all night." Why is this a fragment ? It has a dependent clause "Because my children were sick" and an independent clause "I was up all night". Where do I go wrong ?

[Beeesneees]

This sentence needs the context. The main phrase is missing.
For example:
I didn't come to the meeting because my children were sick and I was up all night.

Although when speaking we might start parts of dialogue with 'because + a reason', this is not a complete sentence. It is in a way a follow-on from the question that was asked.
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Cheers m' dears!

[Alan]

Hi Biro,

The problem with your sentences is that they do not lead to a consequence. If you include the conjunction 'and', you are really giving two reasons for an action that isn't mentioned. If you want to describe a reason and a consequence, you have to leave out the conjunction 'and'.

Because my children were sick, I was up all night.

Alan
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English as a Second Language
You can read my ESL story Present Simple