A kid on a playground swing makes 6 complete to-and-from swings each 30 seconds (a) the frequency of the swinging is? (b) the period of the swinging is?

The frequency is how many per second:

(6 swings) / (30 sec) = (6/30) swing/sec = 0.2 per sec = 0.2 Hz.

The period is how long each one takes, or seconds per swing.

It's exactly the flip of frequency.

So we could just take the frequency, flip it, and find 1 / 0.2,

but let's do it the long way:

(30 sec) / (6 swings) = (30/6) sec/swing = 5 seconds.