Dividing by a fraction seems anomalous in the set of arithmetic operations inasmuch at it appears to have no analog in the physical world.
Is this the case? Or is there some physical analog to the arithmetic operation of division by a fraction?
Analog: Place one pebble on the ground. Place a second pebble on the ground beside the first. Count the pebbles. That is an analog for the addition operation.Subtraction
Analog: Place three pebbles on the ground. Remove one pebble. Count the remaining pebbles. That is an analog for subtraction of 3 minus 1.Multiplication
Analog: Take a group of x pebbles. Place n of those groups on the ground. Count the pebbles. That is an analog for multiplication of x times n.Division
Analog: Take an apple. Slice it into six pieces. Give one piece to each of six friends. That is an analog for division by six.
One can construct examples of other arithmetic operations. Even powers. But in the world of simple arithmetic, for division by fractions, there seems to be no analog.
Or have I overlooked something?