Math Lesson: A new way to multiply
WOW!!!!!!!! 
Thats sick!!!
I gonna try use that on a math test at school one time.
Thats sick!!!
I gonna try use that on a math test at school one time.
omg, wish i'd been taught that at school 
coolio
coolioWell, this isn't really new. It's just a visualisation, of what we learned in primary school. 
| TomS wrote: |
| Well, this isn't really new. It's just a visualisation, of what we learned in primary school. |
Yeah it's only a visualisation, but a nice one. I have never think of it this way and it can be helpful for that people having trouble with discalculi disease.
| TomS wrote: |
| Well, this isn't really new. It's just a visualisation, of what we learned in primary school. |
I see it today, not in past, i am very surprised. Did you see it or similar thing in primary school really? this is awesome.
No. As I said. It's just visualized with the lines.
At frist you take the last number of the first factor and multiplicate it with the second factor.
21 * 45
1*5 = 5
1*4 = 4
=> 45
2*5 = 10
2*4 = 8
Then you add the numbers.
045
10
8 ___
945
So you have 945.
We called that "in writing multiplication"
At frist you take the last number of the first factor and multiplicate it with the second factor.
21 * 45
1*5 = 5
1*4 = 4
=> 45
2*5 = 10
2*4 = 8
Then you add the numbers.
045
10
8 ___
945
So you have 945.
We called that "in writing multiplication"
Sometimes when I got lasy and didn't want to do all the carries.. I just added lines underniegth. It was faster than tracking the carries sometimes. In the example... if all the digits multiplied to dual digit numbers... you likely would have used 4 lines instead of 3.
funny thing... but now, there are no problem to use calculator on math classes because it's faster... there are harder things than "x" and ":" 
integral? ... :]
because it's faster... there are harder things than "x" and ":" integral? ... :]| b4r4t wrote: |
| funny thing... but now, there are no problem to use calculator on math classes because it's faster... there are harder things than "x" and ":" integral? ... :] |
Yea, I think I haf somewhat forgotten all the tricks to calculate multiplications and stuff in a shorter time as after going to secondary sch, u basically get to use the calculator and depend on it heavily.
| orcaz wrote: | ||
Yea, I think I haf somewhat forgotten all the tricks to calculate multiplications and stuff in a shorter time as after going to secondary sch, u basically get to use the calculator and depend on it heavily. |
according to me, code optimizers use this method, because number of interoperations is lower.
For integer math as in this case... it really uses the more standard technique.
What this technique offers is that you don't track carries directly. You do this by writing the individual results on separate lines.
Since a computer uses binary... there are no carries as you mulitply by 0 or 1. So the techniques become effectively the same. However, many computer processors have hardware support of multiplication... and the compiler doesn't have to optimise, just code for the optimised hardware.
What this technique offers is that you don't track carries directly. You do this by writing the individual results on separate lines.
Since a computer uses binary... there are no carries as you mulitply by 0 or 1. So the techniques become effectively the same. However, many computer processors have hardware support of multiplication... and the compiler doesn't have to optimise, just code for the optimised hardware.
| b4r4t wrote: |
| integral? ... :] |
You can't manually compute integrals?
| dooble.doodles wrote: |
| For integer math as in this case... it really uses the more standard technique.
What this technique offers is that you don't track carries directly. You do this by writing the individual results on separate lines. Since a computer uses binary... there are no carries as you mulitply by 0 or 1. So the techniques become effectively the same. However, many computer processors have hardware support of multiplication... and the compiler doesn't have to optimise, just code for the optimised hardware. |
hardware support ? do you mention arihtmetical logic unit (ALU). where is the multiplication doing? please describe. For example, in asm
MUL AX
what kind operations are carried out ? Which hardware is used ?
First time seeing this lol. That takes way too much time, I'll just stick to the old one, which is way faster for me. 
| Tools and Cheese wrote: |
| First time seeing this lol. That takes way too much time, I'll just stick to the old one, which is way faster for me. |
For human, you are right but for the machines, grid is the perfect solution.
I have never seen that kind of "visualisation" before. Quite a good method to calculate if you are not very fast the "normal" way.
It is funny!
I think that I would likely work in binary
OK .... this is likely best to explain by example. Why don't we try by using 7*5. Sounds like I might be trying to over simplify by using single digit numbers. But binary comes to the rescue. This will be sufficient to explain the method. So we have:
111
* 101
====
so first we want to multiply by 1!... welll it has to be a 1 or a 0.
111
* 1 being the right most 1 in the 101 term
------
111 and gives us a 111 as a result. No big surprise.
so next we shift the top number to the left and the bottom number to the right (from the original problem) and we have
1110
* 10
-------
lets take a little segway and explain this. It should be obvious because we do this normally, but rarely explain it when we do it. The bottom # shifts right because we have already done the multiplying by the right most number and it falls off, or we just ignore it normally. The top number shifts left because we are using a higher digit from the bottom. Typically we just shift it when we right it in the summation. This is true with the method described above or the one we used before dinosaurs.
done with segway. here we multiply by the right most digit in the bottom number. Forturnately multiplying by 0 is easy! we get 0000. So then again we do the same shifts as before and we have
11100
* 1
---------
11100 and end up with an easy multiplication as such.
Now we have to go back to add up all the terms as before.
111
0000
11100 hopefully this look OK since it is proportional spacing?
---------- but now we add in binary
100011
converting to decimal is 35. Hmmmm, I think it works. Remember that 1+1=0 -- carry the one!
acient toaster processors I think microcoded this function. It increased speed significantly over assembly languages... and no -- C could not optimise faster than proper assembly for this simple of a problem.
Larger processors may have placed this hardware in differently. I have not checked since the time of dinosaurs.
Calculators are a great tool, but there are times that it helps to understand the hows and whys. You may not always have access to this level of computing.
OK .... this is likely best to explain by example. Why don't we try by using 7*5. Sounds like I might be trying to over simplify by using single digit numbers. But binary comes to the rescue. This will be sufficient to explain the method. So we have:
111
* 101
====
so first we want to multiply by 1!... welll it has to be a 1 or a 0.
111
* 1 being the right most 1 in the 101 term
------
111 and gives us a 111 as a result. No big surprise.
so next we shift the top number to the left and the bottom number to the right (from the original problem) and we have
1110
* 10
-------
lets take a little segway and explain this. It should be obvious because we do this normally, but rarely explain it when we do it. The bottom # shifts right because we have already done the multiplying by the right most number and it falls off, or we just ignore it normally. The top number shifts left because we are using a higher digit from the bottom. Typically we just shift it when we right it in the summation. This is true with the method described above or the one we used before dinosaurs.
done with segway. here we multiply by the right most digit in the bottom number. Forturnately multiplying by 0 is easy! we get 0000. So then again we do the same shifts as before and we have
11100
* 1
---------
11100 and end up with an easy multiplication as such.
Now we have to go back to add up all the terms as before.
111
0000
11100 hopefully this look OK since it is proportional spacing?
---------- but now we add in binary
100011
converting to decimal is 35. Hmmmm, I think it works. Remember that 1+1=0 -- carry the one!
acient toaster processors I think microcoded this function. It increased speed significantly over assembly languages... and no -- C could not optimise faster than proper assembly for this simple of a problem.
Larger processors may have placed this hardware in differently. I have not checked since the time of dinosaurs.
Calculators are a great tool, but there are times that it helps to understand the hows and whys. You may not always have access to this level of computing.
| dooble.doodles wrote: |
|
..... |
Great post, thank you.
i didn't knew about it, but the traditional way is easier anyway i think... or at least shorter.
I don't think either of my kids, who are doing well in gr. 9 and gr. 7 respectively could multiply 13 x 21 without a calculator. this might be good for them if they're ever without a calculator.
my little one.... now 18 could multiply 3 digit numbers before he started kindergarten... all with the help a a silly little toy called "Math to Go".
As someone said:
converting to decimal is 35. Hmmmm, I think it works. Remember that 1+1=0 -- carry the one!
acient toaster processors I think microcoded this function. It increased speed significantly over assembly languages... and no -- C could not optimise faster than proper assembly for this simple of a problem.
But this form of math is purely geometrical how can something like this be achieved with simple lines and calculating angles.
converting to decimal is 35. Hmmmm, I think it works. Remember that 1+1=0 -- carry the one!
acient toaster processors I think microcoded this function. It increased speed significantly over assembly languages... and no -- C could not optimise faster than proper assembly for this simple of a problem.
But this form of math is purely geometrical how can something like this be achieved with simple lines and calculating angles.
I think you either need a sliderule or a Smith Chart
Wow thank you, this is definitely very helpful. It does become a burden if the lines you have to draw are 5+. None the less, this is a great way to do multiplication. I'll try to do this with decimals.
Like others have said, not a new way to multiply, but it IS more interesting.
I want to see someone turn that in as their scratch work on some math homework or exam and see what the teacher comments.
I want to see someone turn that in as their scratch work on some math homework or exam and see what the teacher comments.
wow thats pretty cool...
very easy and thought ful
Great visual and would be neat to show people, but not practical.
Hye!
I think multiplication is nothing more than repeated addition.
Technically, In mathematics, multiplication is an elementary arithmetic operation. When one of the numbers is a whole number, multiplication is the repeated sum of the other number.
For example, 7 × 4 is the same as 7 + 7 + 7 + 7.
Fractions are multiplied by separately multiplying their denominators and numerators: a/b × c/d = (ac)/(bd). For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.
Multiplication can be defined for real and complex numbers, polynomials, matrices and other mathematical quantities as well. The inverse of multiplication is division.
Source: http://en.wikipedia.org/wiki/Multiply
About, the link, well don't you think it is only for symmetric numbers?? Like
12 x 21 or 123 x 321??
Easier, and faster methods of multiplication cane be found in Vedic Mathematics, http://en.wikipedia.org/wiki/Vedic_Mathematics
I don't I should quote something from there as this will not be morally correct to just increase my points. But, I recommend you to have look at it!
Thanks!
- Mayank
I think multiplication is nothing more than repeated addition.
Technically, In mathematics, multiplication is an elementary arithmetic operation. When one of the numbers is a whole number, multiplication is the repeated sum of the other number.
For example, 7 × 4 is the same as 7 + 7 + 7 + 7.
Fractions are multiplied by separately multiplying their denominators and numerators: a/b × c/d = (ac)/(bd). For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.
Multiplication can be defined for real and complex numbers, polynomials, matrices and other mathematical quantities as well. The inverse of multiplication is division.
Source: http://en.wikipedia.org/wiki/Multiply
About, the link, well don't you think it is only for symmetric numbers?? Like
12 x 21 or 123 x 321??
Easier, and faster methods of multiplication cane be found in Vedic Mathematics, http://en.wikipedia.org/wiki/Vedic_Mathematics
I don't I should quote something from there as this will not be morally correct to just increase my points. But, I recommend you to have look at it!
Thanks!
- Mayank
Thanks for posting, I am going to send to my friend who is a math teacher...
that is pretty kool. Ive only been taught the regular way and that seems to provide a pretty good shortcut, im going to show it to my friend who is crazy at math.
WOW, thats great. I agree with others though, its not very practical, in my opinion its far quicker and easier to do the multiplication the old fashioned column by column way.
| muhendisabi wrote: |
| http://www.glumbert.com/media/multiply |
This is purely elementary stuff
i think the purpose of that method is just for amusement, i've shown that method before to my cousin and he was astonished haha.
I'm definately showing this to my math class who will be blown away and totally not realize this is just a visualization. (I still love em though) 
. Neat idea for putting it down on paper. I can see this being use when teaching multiplication. The only trick would be breaking the habit and getting them to do it the real way.
. Neat idea for putting it down on paper. I can see this being use when teaching multiplication. The only trick would be breaking the habit and getting them to do it the real way.i should talk to my math teacher about that one
HOLY #$&@$
I need to learn this, that was amazing!
I always have trouble multiplying >,<
I feel close to retarded without a calculator
I need to learn this, that was amazing!
I always have trouble multiplying >,<
I feel close to retarded without a calculator
Because this is so practical. Why even bother drawing it out like that? What a waste of time. And do any of you know how old this video is? And it's just now making it onto Frihost...sad.
And it's just now making it onto Frihost...sad.It is really nice, how would you figure this out since this is really nice to do. You don't need a calculator!
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