There are 60 minutes in an hour. This is the simple, manmade 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 visualize some common hourfractions which we see every day.
Visualizing the Fraction

Visualize 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, oneeighth of a pie. Thus, sevenandahalf minutes equate to oneeighth (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 onesixtieth (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 onesixtieth of an hour, we can apply this to other quantities. If one minute is onesixtieth of an hour, then five minutes must be five times as much. Therefore, five minutes equals five times onesixtieth (i.e., 5 x 1/60), which is onetwelfth (5/60 = 1/12) of an hour. Similarly, six minutes equals six times onesixtieth (i.e., 6 x 1/60), which is onetenth (6/60 = 1/10) of an hour. And twenty minutes equals twenty times onesixtieth (i.e., 20 x 1/60), which is onethird (20/60 = 1/3) of an hour.
We have now mastered the art of calculating minutes as fractions of the hour.
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