There are 60 minutes in an hour. This is the simple, man-made concept to keep in mind when calculating minutes as a fraction of an hour. The best way to understand the calculation of minutes as fractions of an hour is to first visualise some common hour-fractions which we see every day.
Visualising the Fraction
Visualise the face of a clock as a pie, seeing the quarters that mark 15 minutes, 30 minutes, 45 minutes, and 60 minutes in your mind's eye. When you imagine the 15 minute mark, what do you see? It is a quarter (or 1/4) of a pie! Thus, 15 minutes equate to 1/4 hour. Now, if you further halved the quarter pie, what would you get? Yes, one-eighth of a pie. Thus, seven-and-a-half minutes equate to one-eighth (1/8) of an hour.
Understanding the Unit
To calculate fractions of hours for other numbers of minutes, we need to understand the unit of calculation. If 60 minutes make an hour, then each minute is one-sixtieth (1/60) of an hour. Therefore, this is the unit of calculation, and forms the basis of converting other numbers of minutes into fractions of an hour.
Applying the Unit to Calculations
Now that we have established the unit of calculation as one minute, which equals one-sixtieth of an hour, we can apply this to other quantities. If one minute is one-sixtieth of an hour, then five minutes must be five times as much. Therefore, five minutes equals five times one-sixtieth (i.e., 5 x 1/60), which is one-twelfth (5/60 = 1/12) of an hour. Similarly, six minutes equals six times one-sixtieth (i.e., 6 x 1/60), which is one-tenth (6/60 = 1/10) of an hour. And twenty minutes equals twenty times one-sixtieth (i.e., 20 x 1/60), which is one-third (20/60 = 1/3) of an hour.
We have now mastered the art of calculating minutes as fractions of the hour.