Yup (but sometimes up to 10x10)

Of course, we would only need to memorize (10-x) items for the x table, except 1x anything, which is trivial

so, know 2x2, 2x3, 2x4, 2x5, 2x6, 2x7, 2x8, 2x9 from 3, you can begin at 3x3, then 3x4, etc

to be more advanced you only need to know up to 5, and do the rest with math... 97? easy peasy. (5+4)(5+3) = 55 + 53 + 45 + 43 -> 25 + 15 + 20 + 12 = 72

(there are other tricks you can do)

Well, that's an example of the time-memory tradeoff, right? It takes a lot longer to calculate 9·7 that way than it does if you've just memorized it. The real question is where to draw the line with respect to diminishing returns on memorizing products for larger and larger numbers.

> where to draw the line with respect to diminishing returns on memorizing products for larger and larger numbers

Everything from 2 * 2 to 9 * 9 where the second number is greater or equal to the first, i.e. 36 combinations. But it would also be good to memorize sums from 3 + 2 to 9 + 8 where the second number is less than the first, i.e. another 28 combinations. So we'd need to memorize 64 combinations from 2,2 to 9,9 where we'd know whether the result is addition or multiplication from the ordering of the numbers.

all 9s..in multiplication take second muliplicand subtract one and that is the first digit of the answer..now take that first multiplicand and subtract that first digit of the answer and that is the second digit of the answer

memorizing without knowledge is for chumps!

you wrote 9 * 7 then proceeded to calculate 9 * 8. I find the 9s easy to remember. simply take the other number, reduce it by 1, then add the complementary that together sum to 9. for 9 * 7, this is 63,

Ouch, true

Yeah, I know this trick for multiplying by 9, but I wanted it to be generic

(As pointed by several commenters, this is the multiplication of 9x8 not, 9x7)

Yup, but it's easy to forget. Most Chinese can remember 9x9 up to a very old age.