"Wrap up" has 4 definitions. For most of these definitions, "wrap up" can be separated.
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Definitions
1. To cover or surround something in paper, cloth or other material.
["wrap up"] + [something]
["wrap"] + [something] + ["up"]
"Have you wrapped up the presents yet?"
"If you want to bring some cake home, I can wrap it up for you."
"Wrap" vs "Wrap up"
"Wrap" and "wrap up" have the same meaning.
"I wrapped the presents yesterday."
"I wrapped up the presents yesterday."
To me, both of these sentences sound natural and grammatically correct. However, I have read that "wrap up" should not be used in the first person, like "I" or "we." So just be aware that native English speakers have different opinions about this.
2. To dress someone in warm clothes.
["wrap up"] + [something]
["wrap"] + [something] + ["up"]
"Look at you! All wrapped up in a big jacket and woolly scarf."
"It's starting to get cold. Make sure you wrap the baby up properly."
3. To finish or conclude something.
["wrap up"] + [something]
["wrap"] + [something] + ["up"]
This could refer to a presentation, event, meeting, certain tasks or projects.
"Let's wrap up the meeting and get some lunch."
"The stage performance will wrap up the national event."
You can also use this to mean completing or concluding something successfully or in a satisfactory way.
This could refer to a negotiation, an agreement, a job, or a match.
"The senior staff were able to wrap up the meeting early today."
4. To spend so much time doing or thinking about something that you do not notice anything else.
["wrap up in"]
"Don't get so wrapped up in playing games that you forget to eat!"
"He's been so wrapped up in his new girlfriend. I haven't seen him the past month."
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Related expressions
"Wrap it up" - to get to the point, or hurry up.
"Wrap it up. You've been talking for 30 minutes."
"If you can't wrap it up in the next 5 minutes, I'll have to ask you to move on."