Lattice Multiplication

[davidn]

Why on earth didn't anyone teach me about this when I was in school! I've been covering the whiteboard in these ever since I saw this going past on Facebook (I haven't yet found definitive proof that it's of Japanese origin).

After a couple of fascinated scribbles (please excuse the mouse handwriting), I realized that by counting the intersections, you're doing exactly the same thing as the normal long multiplication method of multiplying each position by each other position, just laying it out visually... but it's so satisfying to see it fall out of a tartan picnic rug like that. Besides, it's prettier than a column of numbers.

I will have to remember this for when I next have paper to hand but not a calculator, which in today's environment will be round about never.

Comments

[igorium.livejournal.com]

I never understood the exact algorithm behind it, nor why it works.
For 97x46 for example

[xaq.livejournal.com]

It basically breaks the numbers being multiplied into their 10s and 1s, makes 2 bunches of sticks in each color in those same numbers, then lays them out so they intersect.

Red sticks: 10s in the left bunch, 1s in the right bunch. In this case, we've got 9 sticks in the left and 7 in the right.
Blue sticks: 10s in the top bunch, 1s in the bottom. 4 on top, 6 on bottom.

Then, you simply multiply the number of sticks in each corner.

Top left corner: 10s x 10s, giving you your 100s result
Top right corner & bottom left corner: 10s x 1s, giving you 2 sets of 10s results
Bottom right corner: 1s x 1s, giving you your 1s results.

For the 97 x 46 example:
Top left: (9 x 4) 100s = 3600
Top right: (9 x 6) 10s = 540
Bottom left: (7 x 4) 10s = 280
Bottom right: (7 x 6) 1s = 42

Once you got that, you just add up your results.

3600 + 540 + 280 + 42 = 4462.


...Come to think of it, this basically works the same way as cross-multiplying an algebra equation.
(90+7)(40+6) = (90x40)+(90x6)+(7x40)+(7x6) = 3600 + 540 + 280 + 42 = 4462.

Heh. Definitely gonna have to show my mom this trick so she can pass it on to the math teachers up in Nome. Could prove quite useful to the kids up there...or at least keep their interest long enough to actually do their homework.