Actually, my theoretical answer to this theoretical question is both “Yes” and “No”, but since I have to take sides, I randomly chose “Yes”.
Just as you cannot extract something out of nothing, so also, you cannot divide something with nothing. This is the short and sweet answer.
According to the Law the Conservation of Matter and Energy: Matter & Energy is neither created nor destroyed; they can only be transformed, even Matter into Energy and vice-versa.
The prerogative of creating something out of nothing remains that of God who, according to the Bible, spoke the Universe into existence. He can do it because He is the only “Unmoved Mover”.
Mathematically, division by zero will end up with such a big number that will bust your computer if not your mind as it becomes as inexpressible as the Universe.
If you divide a number bigger or equal to 1 with a number smaller than 1, you will always get a bigger number. For example, 1 over 0.5 will give you 2, because 1 apple divided by one half a person will yield 2 halves of an apple for 1 person.
While this might seem bizarre given there cannot logically or functionally be “half a person”. I chose this example on purpose to illustrate the conservation principle.
1 divide by one half equals 2. This is conceptually possible but not necessarily in other forms other than mathematics.
1 divided by an even smaller number will yield a even bigger number: 1 divided by 0.05 will give you: 20, 0.005: 200, 0.0005: 2000, 0.00000000002: 20000000000
See the pattern? Yes, for ever 0 after the 0 in the denominator, you get an additional 0 after the 2 in the result.
It follows therefore that as the denominator tends towards a number that is so small until it becomes “nothing”, you will get a yield of a number that is so big that it tends to infinity.
So, when you divide something with 0, you should get an infinitely big number concomitant to the infinitely super nano-ly small entity of the divider, to bring us back to the beginning of 1 apple divided between 2 halves of a person will yield 2 pieces of a whole apple for 1 person.
Were there more whole apples when shared with more pieces of a whole person? No of course, because matter is conserved. How do you get more apples then? Simple, by acquiring or harvesting more whole apples, never by halving a whole person sharing it.
It may interest many of us that 0 (Arabic “zephirum” from which “cipher” and “zero” derive) is a rather recent invention of man, perhaps only as recent as 771 AD through and Indian traveler in Baghdad who introduced a new set of “Arabic numerals” 1,2,3…0 that we still use today that includes the “0”. It is more interesting that the the concept of “0” could even have originated from Hindu numerals, which may have come from China (Ideas, Peter Watson, The Orion Publishing Group Ltd, Page 268)
Pondering over such oddities in Mathematics and Science could be rather enriching mentally, and perhaps, that is where the value of the exercise ends, in the head, since it may not have any practical value in promoting the material and spiritual welfare of the common people.
The moral of the story of division by zero?
You get nothing, yes, “0” for doing that, so go create something, grow something, do something to add value and then when you have more, you can divide by the same positive number of denominator or even with more people and you still get the same or even more of the same per person!