![]() In multiplying 2-digit numbers by 2-digit numbers, the longest string we need to visualize is three digits (9 x 9 + 9 x 9 = 162), so in context of adding columns we mostly operate on two digits at a time, at most four. I could proceed normally (the way we’re taught in the West) from right to left by first multiplying 7 x 9, add to that 7 x 50, 20 x 9 and so on, but addition like this involves strings of digits that only get longer as we progress from units to tens to hundreds etc., so it didn’t feel convenient for me, as in it felt terribly inefficient considering how long the strings we’re operating on quickly become. It is of course a trivial procedure, but the problem with mental calculation for me has been the visualization. I now know that this is called cross-multiplication. I looked at the diagonal spacings and figured that a much more convenient way to express the steps would be to directly get the partial product-sums Īnd stack them over each other like this Īnd then add the columns, which gives us 1593. I used the following Chinese method of multiplication as the base: My apologies for the redundancy I try to be thorough, perhaps sometimes to the detriment of clarity. I’ll elaborate and extend on it a bit just in case someone is working on the same things. ![]() I hope you didn’t have high hopes for my method as it is very basic. Does it work? Are you happy with it?Ī convoluted 2D grid is too vague for me to comment on… I developed my own algorithm for multiplying 2- or 3-digit numbers (where both multiplicands had the same number of digits) from some redundant Chinese system that used a convoluted 2D grid. Something to practice on while I wait for my new toy. Thanks for the input, time to look for a soroban on eBay. Currently I have high hopes for the abacus, hoping its simplicity would turn out more approachable and efficient. I’m not sure if there is a shortcut, other than multiplication tables. I was essentially still building a 2D grid (a pyramid shape) of the numbers when I was multiplying mentally, and mostly it was difficult to visualize for me. Later when I was reading up on Vedic math or Trachtenberg they had pretty much exactly the same system, only I didn’t ever go to 4-digit numbers because it became too much of a mess for me. I figured even after knowing the rules, the process wouldn’t have been much easier to carry out mentally than improvising. It was just arbitrary data for me - my number sense didn’t extend to those rules. I was mostly frustrated with having to remember rules that I didn’t intimately understand. IIRC I got from multiplicand 1 to 6 and eventually 7 and 8 pretty fast, but when I was drilling 8 I had already forgotten about the earlier ones, and all I had in my head was a big mess. ![]() I may have rushed, being impatient and all. I am going to take a stab in the dark and say that this could be caused by trying to do too many different things.
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