A piano teacher gives lessons that are each 3/4 hour long. How many piano lessons can the teacher fit into a 12-hour work day?

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3/4 of an hour each lesson

12 hours

12 x 3 = 36

36/4 = 9

The teacher can fit 9 piano lessons in a 12 hour work day

hope this helps
multiply 12 by 60 minutes and divide by 45 minutes.  The answer is 16 lessons in a 12 hour work day.