Why in the multiplication table, different characters such as 如，得，歸，中 are used?

Question

It seems to me that the following rules apply:

1. When the answer is a one-digit number, the character 如 is used.
2. When the answer is 10, the character 得 is used.
3. When the answer is a multiple of 10, other than 10 itself, the word 中 is used.
4. When it is 3×3=9, the character 歸 is sometimes used (though not on this picture here).
5. In all other cases, no additional character is inserted.

I am wondering why there are such rules? Do we use these rules anywhere else?

Answer 1

九因歌 using synonyms words instead of using one character universally is to make it 押韻 rhyme better, easier for children to 'sing' to remember it better

如 = as same as

得 = get

中 = together

~

二五得一十 ( 2 X 5 get 10 )

二三如六 (2 X 3 is as same as 6)

四五中二十 (4 X 5 together is 20)

歸 = end up with

三三歸九 (3 X 3 end up with 9) is a variant of 三三如九. No other set of numbers is using 歸