Have you ever known someone who did not know the rules for adding and multiplying even and odd numbers?

This is not something that typically comes up in conversations, but I have been doing some math tutoring and I have come across students in junior high school who do not know the rules. For example, one student thought that 4×8=33. When I mentioned that 33 can’t be right because multiplying by an even number gives another even number, they said that in learning the rules for positive and negative numbers, they had forgotten the rules for evens and odds.

When I mentioned this to my brother and SIL, my SIL said that she also did not know the rules. I know that she has difficulties with math, but this seems so obvious. I do not recall being taught rules for evens and odds.

One dramatic way that the rules for multiplication could be demonstrated would be to ask if the numbers in a 10 by 10 multiplication table are mostly even, mostly odd or the same for each. Immediate intuition would most likely be that the numbers of odd and even products are the same, but this is not the case, since even times even, odd times even, even times odd all give even numbers and only odd times odd gives an odd number. That means that ¾ of the entries are even.