fold up - fold multiple times?


Senior Member
Dear all,

(At an inn, an employee is explaining one of its rules to a guest)
When you wake up in the morning, please fold up your blanket and put it away in the closet over there.

I made up the sentence. Does 'fold up' imply folding the blanket multiple times? I'm wondering if any connotations would be added when 'up' was attached to 'fold.'

I would appreciate any comments.
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