Multiply numbers graphically

joedirtsays...

It is just doing what you do long form.
    431
   x 32
-------
&nbsp;&nbsp;&nbsp; 86<B>2</B> (or 2 lines intersecting 4, then 3, then 1)
&nbsp; <B>12</B>93 (or 3 lines intersecting 4, then 3, then 1)
-------
13|7|9|2

pull right side off [one intersect two line] (2)
add middle right ones (2 intersect 3 plus 3 intersect 1) (9)
add middle left ones (2 intesect 4 plus 3 intersect 3) (17) ==> 1 carries, (7) stays
pull left side off [three intersect four lines] (12) ==> add carries


leeweeksays...

i am a student taking precal in highschool right now an i have started using this all the time now, great for those times when it's a no-calc quiz or test. oh! i also figured you can divide with it.. ill try to make a vid and post it on youtube or the like!

HistNerdsays...

Farhad: Am astonished I was never ever taught this in any level of academia...

My girlfriend is tutoring at an elementary school, and she tried telling me about this stuff which neither one of us have ever heard of. I think it's pretty new, along with math in bases other than 10, which I've noticed at the school I work at. Math is crazy these days!

This video talks about doing math in different bases:

http://www.videosift.com/story.php?id=18388

sometimessays...

while cute, that's a more complicated and convoluted way of doing plain old regular multiplication.
your solve-time is affected by both the number of digits, and the value of those digits.
regular boring multiplication solve-time is only affected by the number of digits.

It's kinda like that phone number puzzle that's been going around. at first it seems clever, but if you think about it for more than a second, it should become clear that it's not particularly special.

1. Grab a calculator. (You won't be able to do this one in your head.)
2. Key in the first three digits of your phone number (NOT the area code).
3. Multiply by 80
4. Add 1
5. Multiply by 250
6. Add the last 4 digits of your phone number
7. Add the last 4 digits of your phone number again.
8. Subtract 250
9. Divide number by 2

Do you recognize the answer?

joedirtsays...

DC, you said 99*99, right?

Well you would have a diamond with four intersecting areas, all of them having 81 "dots". So using this method.

right most number:
add one intersection area ==> 81 (the 8 carries)
"1"

middle number:
add two ares plus carry (81+81+8) => 170,
"0"

left most areas:
add 81 to carry ==> 81+17 = 98
"98"

9801 -- tada.
(distributive powers .. you are doing digit math 91 is "9" for tens digit, "1" for ones digit)
left [tens*tens] + middle ([ones*tens]+[tens*ones]) + [ones*ones]

deathcowsays...

I love it Joe, screw the impracticality of counting all those groups of dots and drawing the lines in a feasible method, just discuss using the dots and lines and you're there without the mess.

rottenseedsays...

Abaci are definitely a more useful visual tools. By using the abacus one will be able to physically construct a mental "image" of numbers in his/her head and eventually the use of a physical device becomes less necessary.

Trancecoachsays...

No.

It was 1200 too low.

>> ^sometimes:

while cute, that's a more complicated and convoluted way of doing plain old regular multiplication.
your solve-time is affected by both the number of digits, and the value of those digits.
regular boring multiplication solve-time is only affected by the number of digits.
It's kinda like that phone number puzzle that's been going around. at first it seems clever, but if you think about it for more than a second, it should become clear that it's not particularly special.
1. Grab a calculator. (You won't be able to do this one in your head.)
2. Key in the first three digits of your phone number (NOT the area code).
3. Multiply by 80
4. Add 1
5. Multiply by 250
6. Add the last 4 digits of your phone number
7. Add the last 4 digits of your phone number again.
8. Subtract 250
9. Divide number by 2
Do you recognize the answer?

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