What is the period of a water wave if 4.0
complete waves pass a fixed point in 10. seconds?

Use your units . . . "period" is time, so you know that you have to
set up your fraction with time in the numerator.

                     10 seconds / 4 waves  = 

                         (10/4)  sec/wave  =  2.5 seconds per wave.


Notice how the first answer set it up exactly backwards.
He would have seen his mistake immediately if he had
kept the units.

He started out by saying . . . .    P  =  N / t

Keeping the units,                  P  =  (waves) / (second)

The answer will have units of      "waves per second" .

That's frequency, not period.

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