A simple way to multiply

Things that don't belong anywhere else. (Check first).

Moderators: Moderators General, Prelates, Magistrates

Spider
Posts: 27
Joined: Tue Sep 12, 2006 3:48 pm UTC

A simple way to multiply

Postby Spider » Wed Oct 18, 2006 7:52 am UTC

I was shown this method a week or so ago, and I just think it's brilliant.

Basically, you take your two numbers which you want to multiply, and write them side by side as two columns. The number on the right is doubled, and the number on the left is halved until you reach 1. If the number on the left is odd then you simple subtract one and then halve it.

So say we take 18 and 21, you would get a table like this:

Code: Select all

18    21
 9    42
 4    84
 2   168
 1   336


Once you have this table, you cross off all the rows in which the number on the left is even, so now we're left with:

Code: Select all

 9    42
 1   336


And then you simply add up the numbers in the right hand column, so we have:

Code: Select all

42 + 336 = 378


Which you can easily verify on a calculator.

The great thing about this is that because you're halving the number on the left each time it doesn't take long to reach 1 (if your smallest number is 2047 or less it will take at most 10 steps), so you can very quickly multiply very large numbers and it doesn't require any difficult maths really :)

User avatar
Gelsamel
Lame and emo
Posts: 8237
Joined: Thu Oct 05, 2006 10:49 am UTC
Location: Melbourne, Victoria, Australia

Postby Gelsamel » Wed Oct 18, 2006 7:58 am UTC

Handy if you're not great at multiplying.

User avatar
Kas
Posts: 41
Joined: Sun Jul 09, 2006 9:24 am UTC
Contact:

Postby Kas » Wed Oct 18, 2006 8:24 am UTC

I'm quite proficient at multiplcation, but I think I'm going to have to try this method for a while just because it is so damn nifty.
"I love all those who are heavy drops, falling one by one out of the dark cloud that hangs over men: they herald as the advent of lightning, and, as heralds, they perish."
-Nietzsche

Hix
Posts: 364
Joined: Sun Oct 15, 2006 5:46 pm UTC

Postby Hix » Wed Oct 18, 2006 3:05 pm UTC

I was shown the following method over 20 years ago, and I find it works just as well. :P

Basically, you take your two numbers which you want to multiply, and write them side by side as two columns. The number on the right is multiplied by 10, and the number on the left is divided by ten, until you reach a single digit number on the left. If the number on the left is not a multiple of 10, you ignore any remainder upon dividing.

Once you have this table, you cross off all digits in the left column except the one's digits. Now perform the simple multiplications in each row (they're all multiplications by a single digit), and add the results to get your final answer.

(Try it... the whole process should feel somehow familiar!)

Of course, this also works if you replace "10" with any other integer greater than 1 (also replacing "digit" with the new base-appropriate term).

rlo
Posts: 92
Joined: Wed Oct 04, 2006 11:43 am UTC

Re: A simple way to multiply

Postby rlo » Wed Oct 18, 2006 5:13 pm UTC

Spider wrote:I was shown this method a week or so ago, and I just think it's brilliant.... Basically, you take your two numbers which you want to multiply, and write them side by side as two columns.

Spider, that is excellent.

holyyakker
Posts: 16
Joined: Mon Sep 18, 2006 9:30 pm UTC
Contact:

Postby holyyakker » Thu Oct 19, 2006 5:32 am UTC

That is nifty, but I'm a huge fan of mental math and I could do 18 * 21 in my head faster via mental means then using the halving trick. Is there an application for it outside of how spiff it looks when you do it?

(btw, the mental way I'd tackle that is 18*20+18=36*10+18=360+18=378. About 3 or 4 seconds of mental manipulation.)
7, 8, 9 - the punchline to the worst joke ever.

User avatar
SpitValve
Not a mod.
Posts: 5130
Joined: Tue Sep 26, 2006 9:51 am UTC
Location: Lower pork village

Postby SpitValve » Thu Oct 19, 2006 5:55 am UTC

See I did 18*21 = 10*21+8*21 = 210+168 = 378 but hey :)

rlo
Posts: 92
Joined: Wed Oct 04, 2006 11:43 am UTC

Postby rlo » Thu Oct 19, 2006 7:43 am UTC

Reminds me of another multiplication trick, which I've known since I was very young but forgot about until recently.

I just tried to describe it myself, but it begs for illustrations. Luckily it's on the web elsewhere (of course):

http://www.cofc.edu/wallacegurganus/

Cool thing is I have no idea why it works.

User avatar
Verysillyman
"Do me! Do me!"
Posts: 1442
Joined: Sat Aug 19, 2006 11:25 am UTC
Location: Drinks Cabinet.
Contact:

Postby Verysillyman » Thu Oct 19, 2006 9:49 am UTC

Wow! that one's pretty cool. i was expecting the 9s multiplication thing which I think is gay.

I was pleasantly surprised.

Spider
Posts: 27
Joined: Tue Sep 12, 2006 3:48 pm UTC

Postby Spider » Thu Oct 19, 2006 10:22 am UTC

holyyakker wrote:That is nifty, but I'm a huge fan of mental math and I could do 18 * 21 in my head faster via mental means then using the halving trick. Is there an application for it outside of how spiff it looks when you do it?

(btw, the mental way I'd tackle that is 18*20+18=36*10+18=360+18=378. About 3 or 4 seconds of mental manipulation.)


Sadly the method is slow, and unless you really struggle to multiply single digit numbers the standard "10's" method is by far the fastest, even if you can't do mental maths it's much quicker on paper too.

I just think this is really neat, and it does simplify the calculations, at the cost of efficiency.

rlo
Posts: 92
Joined: Wed Oct 04, 2006 11:43 am UTC

Postby rlo » Thu Oct 19, 2006 6:05 pm UTC

Verysillyman wrote:Wow! that one's pretty cool. i was expecting the 9s multiplication thing which I think is gay. I was pleasantly surprised.

Thanks, VSM (can I call you VSM?). Any idea why it works? I guess that's a puzzle in and of itself.

Hey, you know what? I'll post that question as a puzzle over in the puzzles forum.

User avatar
Verysillyman
"Do me! Do me!"
Posts: 1442
Joined: Sat Aug 19, 2006 11:25 am UTC
Location: Drinks Cabinet.
Contact:

Postby Verysillyman » Thu Oct 19, 2006 8:48 pm UTC

rlo wrote:Thanks, VSM (can I call you VSM?).


You can call me anything you like ;) Just so long as you call me.

I don't know why things work, so long as they do.

As for the original post, it seems to me that I'd need paper to do all that working. So why not do it the normal way if I have paper handy? And a pen/pencil/sharp knife dipped in my own blood.

User avatar
Peshmerga
Mad Hatter
Posts: 2061
Joined: Wed Oct 04, 2006 1:56 am UTC
Contact:

Postby Peshmerga » Thu Oct 19, 2006 10:54 pm UTC

A simple way to multiply


Image

Zomg! D:
i hurd u liek mudkips???

User avatar
thomasjmaccoll
Posts: 541
Joined: Thu Oct 19, 2006 11:27 pm UTC
Location: cupar, fife, scotland
Contact:

Postby thomasjmaccoll » Thu Oct 19, 2006 11:45 pm UTC

SpitValve wrote:See I did 18*21 = 10*21+8*21 = 210+168 = 378 but hey :)


hmm, i think i would do 18*21 = (18*10)+(18*10)+(18*1)=180+180+18=378

which is probably the simpleton way to do it but also seems easiest to me...

(and yes, i probably would've tried to work out 18*1)
slow down, you move too fast

User avatar
hermaj
Posts: 6139
Joined: Sun Oct 15, 2006 10:37 am UTC
Location: Sydney, Australia
Contact:

Postby hermaj » Thu Oct 19, 2006 11:53 pm UTC

thomasjmaccoll wrote:
SpitValve wrote:See I did 18*21 = 10*21+8*21 = 210+168 = 378 but hey :)


hmm, i think i would do 18*21 = (18*10)+(18*10)+(18*1)=180+180+18=378


Yeah, I'd probably do it that way too. But this is great... even better than that thing with multiplying by 11!

rrenaud
Posts: 47
Joined: Fri Jul 28, 2006 12:34 am UTC

Postby rrenaud » Mon Oct 23, 2006 9:01 pm UTC

This repeated doubling for multiplication reminds me of doing repeated squaring for exponentiation.

See http://www.algorithmist.com/index.php/Repeated_Squaring

When combined with modular arithmetic, it makes for a practical algorithm for computing remainders of powers, eg 3^7 % 10.

3 % 10 = 3
3^2 % 10 = 9
3^4 % 10 = (3^2 % 10) * (3^2 % 10) = 9 * 9 % 10 = 1

So 3 ^ 7 % 10 = ((3^1) % 10 * (3 ^ 2) % 10 * (3^4) % 10) % 10 = (3 * 9 * 1) % 10 = 7

This is actually useful in cryptography, for things like the RSA algorithm.

http://en.wikipedia.org/wiki/RSA

User avatar
Narsil
Ask me about my junk!
Posts: 2995
Joined: Thu Oct 26, 2006 6:59 pm UTC
Location: Columbus.

Postby Narsil » Sat Oct 28, 2006 3:24 am UTC

Someone needs to make one o' them damn machines do au' work.


Return to “General”

Who is online

Users browsing this forum: No registered users and 34 guests