What question are we actually asking when we ask “what is 8 divided by 2”? We’re asking “If I have 8 jellybeans and break then into two groups, how many jellybeans are in each group?”
So Consider the question for 8/0: “If I have 8 jellybeans and break them into zero groups, how many jellybeans are in each group?” The question itself is invalid. Answering with any number wouldn’t make sense, the only response that would make sense would be “what do you mean? There are no groups!” It’s almost like it stops being a math problem at all, hence no mathematical answer.
The problem with this explanation is that I should perfectly well be able to divide my jellybeans into 0.5 or -1 groups, though those also make no real sense in this example.
Exactly. And I find this is also the best explanation to give to people who don't have a maths background, but who still want to know "Why does the calculator say ERROR?"
What question are we actually asking when we ask “what is 8 divided by 2”? We’re asking “If I have 8 jellybeans and break then into two groups, how many jellybeans are in each group?” So Consider the question for 8/0: “If I have 8 jellybeans and break them into zero groups, how many jellybeans are in each group?” The question itself is invalid. Answering with any number wouldn’t make sense, the only response that would make sense would be “what do you mean? There are no groups!” It’s almost like it stops being a math problem at all, hence no mathematical answer.