"Ordinary" Compound Meter
I was taught that 6/8 time, for example, meant "six beats in a measure; the eighth note (quaver) gets one beat." Similarly, 9/8 would be "nine beats in a measure; the eighth note gets one beat."
Arriving at this website (SE MP&T), I encountered the approach in which 6/8 time is "two dotted quarter-notes (dotted crotchets) in triple divisions", and 9/8 is "three dotted quarter-notes in triple divisions."
"Irregular Compound"1 Meter
The method by which I learned to understand compound time remains consistent for, say, 5/8 or 7/8: five (or seven) beats per measure; the eighth note gets the beat.
The "dotted quarter-note per beat" approach cannot remain consist for 5/8 or 7/8, so how does a "dotted quarter-note beat" teacher explain irregular compound meters like 5/8 and 7/8 to a student?
1 There's no such thing as "irregular compound" meter. I've invented the term for use in this post as a shorthand for "irregular meters that have an 8 on the bottom".