Elegant visual way to multiply numbers by hand | Hacker News Reader

Elegant visual way to multiply numbers by hand

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Cute but it does kind of predictably fall down when you're doing 9s and 8s instead of 2s and 3s.

This method essentially converts the typical tabular calculations into a lattice, where the x-axis is the 10's coefficient.

Cool way to think about it, but I doubt it would give any extra insight to someone learning how to multiply.

It also loses a lot of the "elegance" when you have to carry over sums > 10.

Maybe not insight but it gives you an approach to multi-digit multiplication that you can use even if you're still sketchy on single digit.

I know as a kid I'd occasionally resort to just adding a number up the appropriate number of times. and while that works for 67 * 5 it's super error prone for a 6 year old if that 5 is a 9 or worse a 30. This might (might) give 6 year old me an approach to that, sure it doesn't change the need to be able to count and do a little addition but it's a way to break the problem down that I sure wouldn't have thought of.

That's like saying it gives you an approach to running that you can use even if you're still sketchy on walking.

There's only one proven way to teach arithmetic, and that's drill and repetition of the basic number facts and the standard algorithms. It's worked for centuries.

Just because somebody hasn't mastered step A yet doesn't mean they won't occasionally need/want step B.

So playing around with this it also works for multiplication with decimals using say a dashed line between the appropriate digits. The location can be read off by finding the intersection of the dashed lines and putting it in front of that column's digit. It's significantly less elegant, particularly when that column yields a multi-digit count but it does work visually.

I'm sure I'm not the first person to realize this, but it's cool that decimals can be integrated into the method while keeping vaguely in the spirit of the idea.

It also works with binary numbers.

how does one work this out if there is a zero in one or in both numbers... I played around with this on a napkin at a bar and couldn't figure it out...

I guess you'd just have to figure out some way to represent it, say a squiggly line or something, then remember not to count it's intersection, or you could just leave a big blank spot, but too many big blanks might throw off the ease of vertical grouping

Imagine (or draw) a dotted line where the zeroes are..Count the dotted intersections as contributing zero to the diagonal addition step.

123 * 312

Using the first example I would have thought it would be 371376, but no using some math "voodoo" 7 is added to 1 making it 38376.

How are we supposed to know where these numbers are merged? Gotta buy the book, I guess.

I'm wondering if you are serious or not - it's hard to tell. It's really pretty obvous why the "1" from one column goes into the next column over to the left, isn't it?

If you have to use the same rules as the standard multiplication method then how is this anymore elegant than doing it the old fashioned way. So instead if counting numbers now you count dots, how revolutionary

because to perform 312 * 123 you draw 12 lines, count a total of 36 intersections and perform a single addition.

you did not have to actually know any multiplication. and the rules for are hung on a visual framework instead of just being "the rules."

No one said it was revolutionary (well maybe some youtube commenters..)

No, fuck you. The rules aren't just "the rules". They are directly derivable from the property of distributivity of multiplication over addition. E.g., 12 * 39 = 12 * (30 + 9) by the property of place value, and hence 12 * 39 = (12 * 30) + (12 * 9) by distributivity. Then you do the same thing again with the 12s to get the two subresults, and... well, you get the idea. This is the basis of the standard algorithm, and it is derived directly from the properties of multiplication itself.

But this line thing... this is a trick. And, might I add, a trick that may actually cause more work and use up more scratch-paper space for the figurer. Using a "visual framework" without meaning is no way to teach math. The point is that the standard algorithm is the shortest path from point A to point B, and that is why it should be taught first and foremost.

Easy there. (This isn't actually a youtube comment thread!)

This is just a visual metaphor for standard mutiplicaton process. They are fundamentally the same thing. I personally think the way in the video has the potential to help children assimilate the process faster and/or better than otherwise.

Wow, I'm sorry, did cross hatching molest you as a child or something?

But please explain to a child the difference between abstract rules and directly derivable properties of distributivity of multiplication over addition. See how much of a difference there is to a first grader between "It's a fundamental property of mathematics" and "Because I said so."

>But this line thing... this is a trick.

Yes, yes it is. And seeing as all any one has said is it's a elegant (under certain circumstances) trick, why are you so hostile. No one here has proposed replacing the k-12 math curriculum with happy fun line counting time.

EDIT: okay the sibling post may have said something that could possibly be construed as supporting the addition of this to the standard curriculum. Still not advocating replacement.

You have to 'carry the one' just like the regular multiplication algorithm they teach in schools.

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