A dance class/routine.
What does this sentence mean? Is it meant that this is a routine dance class? And why use / between the words 'class' and 'routine'?

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A dance class is the event you attend.
A dance routine is a specific sequence you learn :"Let's do the Beyonce dance routine"!
It does not mean 'routine' = regular.

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The me of this / is “or”. The sentence simply means;
A dance class “or” A dance routine