How to convert degrees minutes seconds to hour minutes seconds (and viceversa)?

Question

I'm reading the book "Practical Astronomy with your Calculator or Spreadsheet 4th Edition" and I want to implement formula 22: Converting between angles expressed in degrees and angles expressed in hours. It says that:

To convert between angles expressed in decimal hours and angles expressed in decimal degrees, simply multiply or divide by 15.

So, I have to convert a angle in degrees minutes and seconds into decimal degrees and then multiply it 15 (or divide it by 15?).

When do I have to multiply and when do I have to divide by 15?

Or

How to convert degrees minutes seconds to hour minutes seconds (and viceversa)?

Answer 1

In one day = $24$ hours the sky ''rounds'' $360°$, so: $$ 24:360=h:\alpha° $$

Answer 2

Each hour is $360^\circ/24=15^\circ$. Each minute of time is $15^\circ/60=15^\prime$, i.e. $15$ arcminutes. Each second of time is $15^\prime/60=15^{\prime\prime}$, i.e. $15$ arcseconds.

Answer 3

Most clocks feature a $12$ hours dial and a full turn is $360°$. Hence an hour is $30°$ !

Answer 4

Nope! 360 degrees is 24 hours. 360 divided by 24 is 15. So 15 degrees is 1 hour of right ascension.