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Once you figure this out it'll blow your mind...

"The lines over the circles are color coded. Notice the single red line and 3 blue lines representing "13" grouped together while the single green and 2 black lines take their own group. [Simply] draw your first group of lines in one direction then your second group of lines going over the first, count the groups of intersections and there's your answer."


Further Explanation:

Julian Wollmann's profile photoAysha Noble Goins's profile photoSravan Buddhu's profile photoFidan Gasimova's profile photo
Elisa T
Wait... I need to test this.
A lot.

counts on fingers
Lauren Hill
Luckily the Japanese invented the calculator for the rest of the world. #whew  
omg.  It actually works.  I'm... flabbergasted!
Jess Nut
That's not really learning to multiple, that's just another trick, the same as doing it the western style of 13 over 12 then multiplying the individual numbers versus the places. It's a different process, but still a process.
It works very nicely for 13x12.  When you try to make it work for 67 x 81 it gets messy.
For intersections where you get 10+, carry the tens digit backward and add it to the preceding number. 

So with 14x5, you'd end up with Top Left = 0, Top Right = 5, Bottom Right = 20. Carry to the 2 backward to Top Right, add it to the 5 and you end up with 70. :D 

Yes. Not impossible, just messy.
My calculator still faster, but definitely not as #cool  
3 digit x 3 digit numbers ? Any volunteers?
Just did 123 x 456 and got the right answer
^^^^^ I do admire you all!

I did 11x11 all on my own and it worked, I then tried 35x27 and my brain developed a bleed....
Okay, I'm about to try 4 digits. If you don't hear from me in the next few minutes, my brain exploded.
It will burn like a bitch then Kaboom! .... It really isn't worth the risk +Christy Ramsey .. please don't do it!!
+Elisa T Won't be back. While practicing, she used string to represent the circles and tied her fingers together.
And I thought counting multiples of 9 with your fingers was cool! That is astonishing!!
Wow, I forgot about this one...
Is there a way to get this to work with fractions of numbers? (That would really blow my mind)
Nobody tried 2 x 2 and ended up playing Noughts & Crosses ?
How about 53x22 please answer
+Joltrast . I can make it work with small numbers like 4.5x2 but it doesn't look like a pattern or standard.
It would be super hard to be a valedictorian there! Thanks for sharing!
what do u mean by count the groups of intersections??? some1 pls tell me cuz I wanna try it...!
Not really, we are doing almost the same thing in the tradition way, and the traditional way works with any number of digits not just 2x2 digits
Maybe it helps if you speak Japanese... lol This does not work for me.
You're doing the exact same thing as long multiplication.
For bigger numbers, it still helps if you can multiply the smaller subset numbers. In the example above, the intersections are 1X1, (1x2 + 1 X3), and 2x3. 
My kids are learning all sorts of cool algorithms to do basic arithmetic. This is one of them. It's a close cousin of the lattice method.
It is kinda logical but time consuming.. try 99* 99 with that.. ! better even 999*999 ;)
+Will More Funny you should say that because I'm an Aircraft Engineer and I use that method. I had assumed that everyone did until I had a conversation with my wife about it.
It still comes out to the same answer. What's the draw here?
Pow! That was cool and so creative.
67x81 equals multiply first two last two inside two outside two
Add together

4800 7 560 and 60
Does this work for something like 123 X 4567 ?
I tried it with 47x68 = 3196 and just ended up with lots of lines and intersections - in which order and how do you count them?
Sad thing is they don't teach math in England anymore, against the children's human rights making their brain work at such a young age. Look it up, it happened a parent complained!
Saeed N
من که نفهمیدم چی شد؟ میشه توضیح بدین؟ what? I no undrestand
That's pretty clever.  It is the exact same process performed visually.  I like it.
If you multiply on paper, what you do?
    1  3  
    1  2       x
- - - - - - -   =
    2  6          (2x3=6, 2x1 = 2)
1  3              (1x3=3, 1x1 = 1)
- - - - - - -   +
1  5  6          (count together)
And graphical interpretation is the picture above
S Mann
I don't get it :-$
I can never be a Japanese kid :,(
Wow that is impressive. It takes a litlle looking at it, but the more I did it the more it stuck. Geeeez wish I had know this in school.
I'm unimpressed. It's nearly the same method we were taught as a students in the US with a slightly different visual representation. 
Being an aspiring teacher, I must say that I find this really cool! 
Just look at the circles. I tested this over ten times and it works - what a cool conceptual. 
(ab) x (cd) = (ac)x100 + ((ad)+(bc))x10 + bd.  The four intersections of the sets of lines are ac, ad, bc and bd.  Notice the 6 is actually 2x3, and the 5 is 1x2 + 1x3.

This is a very clever visual expression of the same technique we use to multiply columns of numbers.  This very clever visual technique does not scale well.  After your numbers get past three digits, it is probably error prone.  Our technique will let me multiply a pair of arbitrarily large numbers.
remember algebra (a+b)(c+d) = ab+ad+bc+bd?  those lines are a clever visual way of doing the exact same thing (10+3)(10+2) = 10*10 (upper left), 10*2 and 3*10 (middle), 3*2 (right).  also good way to do arithemetic in your head...
It's a lot easier to just draw a grid for 3 digits by 3 digits

1. 9. 6
9. 90000. 81000. 5400 176400

8. 8000. 7200. 480 15680

4. 400. 360 24 784

So 196 x 984 is the sum of all these numbers which is 192864

+Toby Hoover
Take two horizontal lines and three vertical lines. How many intersections are there assuming each horizontal and vertical line is unique? Six, same as the product of the number of horizontal lines (2) and vertical lines (3).

Take this a bit further, into a two digit number and a one digit number. Now you have to group the lines by order of magnitude (1s and 10s). Let's try 13 x 2. First we have the 10 line from 13. That's one line by itself. Then we have the 3 from 13, which is another line in the same direction, but in a separate grouping. That leaves 2, which we run across both the (1) 10 line and the (3) 3 lines. This gives us the results of both 2x10 (20) and 2x3 (6). Put the two together and you have your result, 26.
The abacus is like a calculator: 
 it makes you do it fast, but doesn't let you learn how to calc, just how to use the abacus itself.
at a glance it looks like it only works for NxN, where N<100.   IE only double digits allowed.  There might be a way to form a 3x3 matrix for integers up to 1000 though.  
wow - your post is actually just as true as you said it would be. that calculation works out effectively - i thought for abit damn - how does this work - -its very simple though
Just put'n it out there that if any ya are stuck with me on Mars...don't count on Math + Me = Save You

*reference to Mission to Mars movie
Am I the only one looking at this, and after 10 minutes, I still don't get it? lol
Bryce C
I don't get. 
I tried 16x15 and it doesn't work. Is this for only certain #'s? or what I'm I doing wrong?
Thank you it's easy but give us another tough example and see how to draw those circles like if you want to multiply 123*23*45??
Bryce C
Oohhhhhhh! I see!
Derrr...uh...that's it...the United States is doomed!

JK---actually, this is VERY cool...I GOT it...thanks for the share!

Nifty little technique I must admit :)
I used to have to do grid method, thats all they teach us at where I went. I learnt the Italian multiplication method at school when I was teaching my year 6 pupils. I found it very easy, suprisingly.
Yep, and if you think about it, it makes sense. If the numbers are A and B, drawing the lines with A as horizontal lines and B as vertical lines, with gaps between tens and ones, makes a pattern with intersections in four quadrants. The number of intersections in each quadrant is the multiple of the two numbers that intersect there. For example, in the example, 2 lines intersecting 3 lines gives six intersections. The top left is A's tens times B's tens, the bottom right has A's ones times B's ones, and the other two quadrants are A's ones times B's tens and A's tens times B's ones. So the top left quadrant is the resulting hundreds digit, the bottom right quadrant is ones, and the other two are tens.

This strategy works fine for small digits, which is why they used 1, 2 and 3 in the example. But it would be annoying for large digits. Imagine, for example, drawing 76 x 89, drawing 15 horizontal lines and 17 vertical lines, and counting all of the intersections. Memorizing the multiplication tables, while boring, is more efficient in the long run. :-)
+Rodrigo Eilert  red and green intersect once = 1 black and red intersect twice plus green and blue intersect 3 times so 5 black and blue intersect 6 times so 1 5 and 6 or 156
+Chris Miller but what its good for is getting kids to view math and numbers in more than just the traditional sense (if that is how it was taught, and I hope it is).  I think the important part is for them to see that the numbers do work out the same and why!  they can always learn the method that scales better later.
This is the coolest thing ever! I even did it with three digit numbers and it works! :D
You realize they teach this method in the USA and have for multiple years now right? There is nothing inherent to this method and Japan per say. 
mike m
I probably won't forget it or use it.
Harder than just rrgular multiplying
My father was very fast at estimating business sums (price per item X # of items, yards of fabric, etc.) and would try to get me to estimate my homework multiplication problems first, then nail down the actual answer from the estimate. Then I'd go back to school and try to do it that way. Nuns would freak out!!
Worked for 16X15, just need to understand how to carry the numbers...
haha suckers u still dont get it? (i dont either)
awesome!!! Sad it came across me so late :)
thats stupid u should know that simple math in your head
Hey I figured this out. It sucks for larger numbers such as 17x19 took me awhile to count the intersections. 323! Interesting.
+Elijah Gil You still need to learn things like this, sweetie. Just wait a few months.
Ok, somebody do 1024 x 1024, then explain how you keep up with the zeros in the hundreds places?
S Mann
Ok I get it now.phew
It works you just have to do the spacial concept correctly (15 x 16 = 240)


Larger numbers require more space. Broaden your horizon:)
cool..never knew of this quick trick
Yes. Wow, when you think about it, it is quite simple really (:
yes it works, but it really not that much fun when you start dealing with numbers that contain 7s, 8s, or 9s. Not sure how it scales with more than 2 digits either. Seems the traditional US method is more efficient for those scenarios.
+Bernardo Ramirez Once you get groups over 9, you have to start carrying them over to the next group. In your case, you had these three groups: 1 (for 100s), 11 (for 10s), and 30 (for 1s). Put all those together and you'll get 240, which is the correct answer.
Nick S
I'm confused o.O
as a closet maths fan this just blew me away....amazing
I was just showing a co-worker this the other day.  Very awesome way to do multiplication, however, large numbers get very tedious.
the same is true with your fingers and multiples of 9, look at palms with hands open, put thumb down(9x1) 0 fingers to the left and 9 to the right...put first finger down(9x2) 1 finger to the left and 8 to the right...18...put second finger down(9x3) 2 to the left and 7 to the right..27 ...third finger down (9x4) 3 to the left 6 to the right... 36... easier if you count thumbs as fingers so the finger number matches the number you're multiplying.
+Bernardo Ramirez: I tried a while ago, and it still works. The trick is to multiply the top left by 100, the diagonal by 10 and the bottom right by 1, and then add them up. In this case, 1(100) + 11(10) + 30(1) = 100 + 110 + 30 = 240.
Wait... There are more than two colors of lines? 
I would have understood that back then and would have actually learned to use math, not hate and despise it.
It is really cool that there's is a new way to multiply
Would anyone mind adding me? (:  I'm not one of those silly teenagers, who swear. I'm a year 6 teacher, aged 23. NOT LOOKING FOR DATING.
Crazy I actually understand this, I'm terrible at math. Maybe they should adopt the same thing in Canada....

that seems way more complicated than the american way...
Does not work. For anything that has a carry, eg. 13x14, the carry needs to be added to the previous digit manually. Count can be quite  cumbersome. eg. 29*39.  Regular multiplication would be much faster. 
Wow that's cool.

How do you carry the numbers?
Anyone know the italian method? Where you do a grid box, but with diagonal lines across each one? Then put the calculations along the top and side and times together and add the diagonals together? (:
I taught my kids multi digit multiplication the same exact way.  You can learn it on +Khan Academy It's called lattice multiplication.
+Paul Mathews This is regular multiplication, just displayed graphically instead of numerically. You have to worry about carrying in both methods.
I don't see what's mind blowing about it. n lines intersecting m lines gives n*m . Gets really unwieldy when the digits are large.
Try 98 X 87.  You till need multiplication to figure it out quickly.
+Will More I'm no engineer, but that's what I do, and am teaching my daughter. All these lines and intersections...way too much work :-) 
Just take it diagonally, so start in the bottom right and work up and left. I just did it for 2112*325 (drew random lines and then checked after) and got the right answer. Pretty cool.
I really don't understand this madness.........
Or since you know 12*12 is 144, just add another 12 to get 156.
I understood how it worked for 3 digits and 4 digits before I got how it worked for 2 digits. Brilliant method though.
Still complicated that way. For me its easier knowing 12 x 12 = 144 then add 1 more 12.
I doubt this is how they learn to multiply, because for numbers greater than two digits you need a new system. It's a neat little trick on certain occasions I guess.
I tried it. Really does work.
kumon? needs theoretical testing... not sold
+Pippa Drought I think you can google proofs. I've seen it proven and it's not actually that interesting or even useful for larger numbers.
Dont like figures please get me apoem
Ok I get the lines and that's cool but someone make me understand what the circles are for???
I tried it. It works but is complicated. Easier to round and do it in your head than with a handful of colored pens.
really? is this how did we learn math? never heard of.
Gee, we just learn to use calculators, slide rules or computers...
Nice. However it doesn't scale well as many pointed out. It quickly becomes too complicated (read: messy).
+Nathan Ehresmann You need a new system not because this one doesn't work necessarily but because it becomes cumbersome.
+Kimberly Woodruff, you add the number of intersections within the circles.  There is 1 intersection in the first circle, 5 intersections in the 2nd, and 6 intersections in the 3rd circle.  
I just tried it and... how can 16 x 14 work?  I keep getting 1 then 10 then 24.. but the answer is 224?
Try this one. Add any 3 numbers across like 947. 9 + 4 + 7 = 20. Subtract the total from what ever 3 numbers you choose. The anwser will always be 9 or 18 no matter which 3 numbers you use.
I think this will cause division by zero and end space/time as we know it so I'm sorry - can't do it.
Wow thats actually fairly simple
Be like 5 + 5 + 5 = 15 then 555 - 15 = 540. Then 5 + 4 + 0 = 9. No matter which 3 you choose its always 9 or 18.
And the point of this is...what?

I like the American way. I actually use multiplication in my brain as opposed to counting intersecting lines on a piece of paper. 
This is Vadic mathematics and in ancient india is not a  unexpected....and magic....
+Will More not just engineers, that's the way it instictively came to me as a child....and yeah, I was one of those kids always in trouble for not showing work

cool hangin'out with most intelligent human spicies in this planet keep on keeping on we are waiting for the best:lifesaver Milez;;;
+Emil Georgiev  of course. The three numbers you get represent how much is in their respective digit places. For example: in the example you have 1 in 100-digit-place, 5 in 10-digit-place and 6 in 1-digit-place, which gives you number 1×100+5×10+6×1=156. But in your case, you have 1, 10 and 24, which means the number will be 1×100+10×10+24×1. You could also imagine it this way: keep only one digit in each number and move the rest to the higher-order numbers: 1+1, 0+2, 4+0 gives you 224.
+Jerry Feldmesser - just do it the long way, and you'll see the correspondence between the numbers that you have to add up to get your answer in each method.
Just did it with 78x89 and it worked, but really, unless I'm doing 5 digits by 4 digits, it's just easier and faster for me to use mental math.
Amazing, never heard about it but bit complex technique for large numbers.
it works great with these numbers but it gets messy with say 64 x 76
I tried 67×81 and it works. It is a bit complicated but if u stick to the rule of carry the 10s digit backward then it is piece of cake. Though u need to stay focus
+David Perry  2*2 is 4 because you remembered so. Try remembering two-digit multiplications. that gives you ~100^2=10.000 combinations.. not that easy, eh?
just tried 27 x 14 and it failed miserably.  I must not get it.
How American children learn to multiply in primary school:

pulls out calculator
cool hangin'out with most intelligent human spicies in this planet keep on keeping on we are waiting for the best:lifesaver Milez;;;
cool hangin'out with most intelligent human spicies in this planet keep on keeping on we are waiting for the best:lifesaver Milez;;;
As other already mentioned, conceptually this is the same as the usual long multiplication method, with a couple of differences in the process:
1. It replaces doing calculation in order by drawing lines, which is more visual and probably easier for some people.
2. It replaces memorizing single digit multiplication table (requirement in long multiplication) by counting the number of intersection, which some people may more comfortable and/or faster with.
does this work with non-base-10 number systems?
this is what is wrong with education, crap like this.
what about bigger numbers, for example 16 x 16, or 19 x 19...???
I have seen the kids here do that, I still do not understand how it it done
I've seen this "trick" so many times now and I still can't believe people consider this to be simpler than 10x12 + 3x12.
What's your plan here? Take out your post-it block when someone asks you a simple math question?
That's really interesting.  I didn't read a link or anything explaining it, finally figured it out but I do have questions about it.   (edit) just read the description with the pictures.  beans.
Its the exact same thing as long multiplication, nothing mind blowing. If it helps people understand it easier, more power to them though.
+Rob Alvarenga, geometry, 2 x 3 basically 2 rows of 3 column, which crossing of 2 and 3 lines represent. So just count the number of crossing, it will be the product of the multiplication.
that's ancient math
I've seen variations of it in many ancient cultures particularly the recently erroneous Mayans :)
I get it, but how do you define the lines being strewn across? 
It's a matter of counting lines that touch the circles....
+Catherine Wakeling 
This is a easy way to do 35 x 27 in mind
35 x 27 = (35 x 30) - (35 x 3) = 1050 - 105 = 945

Break down to nearest known multiples and then add/subtract those.
This is close to what I learned from a friend in 4th grade. 
That's maddeningly simple. Why don't we all learn like this?

I once bought a book on the Trachtenberg System of Speed Mathematics but I never got the chance to use it and I forgot how to do it.
This is actually no different than the way we do it. Just graphical.
I'll try another time when my mind is refreshed.
It's called vedic multiplication, I believe.
It works fine. Just tried 34 x 763. Its a lot of lines!
No wonder the US ranks so low in math
Understand the 13 & 12 not sure how they are getting 156 out of it though
+Sayth Renshaw 1 crossing between lines representign 10s (10x10), 5 crossings between lines for 10 and 1 (10x1x5) and 6 crossings between lines representing 1s (6x1).
Simply doing THAT in your head instead of writing it down would be way faster though.
I tried it on a white board and it really works...
For example 24 x14 you get the answer 21216 and that is not correct but above 10 line you have to count the 2+1 =3 and the following 2+1=3 and left over is the 6 Then the answer is 336 and that is indeed correct.
I remember that i saw this trick in a google blogspot (google employer) one year ago,   
This is awesome. I've noticed that other countries have such cool methods for teaching math.
I say do 1+ 5 + 6 = all together 156!!!......... my way of saying: wha????? lolz 
Well I gotta say that's kinda flawed. How do you get that the two middle groups go together instead of being 2 groups? Is there a missing step or rule? Cuz you could come out with 1326 just as easily...
oh wow dats so cool
It is not "Counting" the intersections. It is multiplying the corners. That's why it is drawn at a angle, so you take the first angle (1x1) for the first digit, the second two angles [(2x1)+(3*1)] for the second digit, then the right angle (3*2) for the last digit. Just adding the corners would come out to 155. +Christy Ramsey 
I would have multiplied 13*10, then added 13*2...but I REALLY would have used a calculator, because I would have been hypothetically living in modern Japan when given this problem.  
Seems like a good way  to master math and swordsmanship at the same time.  Always useful to see how other people solve the problems that we are all presented with.
i think the fact that so many people are amazed by this "visualization" of long multiplication speaks volumes to the quality of math education in various places... ;)  just sayin'!
Nice pitures I see
Mian umar

Nice, figured it out.  I can do it in my head too.  It's fun. 
It's nothing but a graphical representation of the common calculation we do by numbers.
...sounds like the same thing to me. both descriptions yield 156.
+Steve Weldon, it is calculating intersection, but one group at the time. Each digit drawn as different group of lines, then the each crossing of one group of lines with another group of lines treated as one group of crossing. It does not need to be drawn in angle, see +Christy Ramsey's screen-shot of her own calculation above, the lines were perpendicular to each other.
It works for decimals too! Just count the number of significant digits to the left of the decimal and insert that many places from the left. 
Brilliant math Tec,(toke me longer 2 find coloured pens to show my G-friend) hear's a way of doing or remembering ur 9 x tables. Write ur 9x table out(up too 10) the answers from 1 too 10.(as it would be normally) Looking down the line from 09 too 90,( add a 0 too the first 9 & u C 09 ie;1x9=9 add the 0 & it should look like 1x9=09 (0,9,8,7,6,5,4,3,2,1 on one side, then start by going back up the other side from 90 (9,8,7,6,5,4,3,2,1,0) put a line downe the middle of the answers too the 9xtable?!. An other tip if u don't C this simple way "Don't eat Yellow Snow"
Doing this seems to take longer than actually doing the multiplication
Hour do you use number that ends in zero? Example 10 * 10
What a waste of time. Either use a calculator it do it the traditional way. Who the hell would sit and draw lines all over? Are you insane?
Bryan I
Ddefinitely cool, but doesn't seem any faster. 
Cool = Yes. Useful = IDK.
I was taught that once soooooo confusing
OMG! It really does work with everything, i just tried extensively to dissprove it, you can't! It's fantastic!!
Seems the american way is better in this particular case.  It's cool but kind of a pain and when you deal with 0's or more digits then a real pain and a lot of chicken scratch.
Once I figured the bounce back or carry over it became clear... cool trick
i learned to multiply in grade school, just differently
Wait I'm gonna confirm this...

Uses Google Now
I don't understand this and while (if it really works) itmight be handy at times it doesn't really teach multiplication, does it.
Visual math!  That looks like an expansion of one I use frequently; to multiply N by 9 (where 0 <= N <= 10), fold down the Nth finger.  Fingers before the Nth finger are the tens, fingers after the Nth finger are the ones.
I'm too busy killing my brain with alcohol to need this.
add a comment about color coded way of mathematics
That's awesome. I need to try this on other factors. 
I take it they do not teach spelling it is colour not color 12*12 is 144 and add 12. Do you not teach your children the times tables. 
This would be fantastic for tests where you aren't allowed a calculator.
Ali M.
It's like the abacus or roman numerical math. 
           = 156
In the conventional way you do this. 13 x 12, you really end with (10+2)13, or (2 * 13) + (10 * 13)
13       * really 130.

In this method, you are really doing the foil method.

So, in this case (10+3) (10+2)
10 * 10 = 100
10 * 2 = 20
10 * 3 = 30
2 * 3 = 6

Either way of doing it is correct.  Both let you break up the problem in a methodical way.  Both help to obscure the power of ten you are dealing with during the calculations to some extent.
4 got 2 say"nice one sweety that's cooler than penguin piss" Will teach my nieces & nephews that little trick as it seems in schools now adays, the Kids know more than the teachers":~} L8trs Mr 
+Nasrin Khalilzadeh +Hamed Mir Abolghasemi 
+Mohammad Doroudgari 
چناب درودگري ...فكر كردم از اين به بعد شديدن برا ي پول هاي نداشته و كاهش قدرت خريد و .....در هر روز ديگه متوسل به انگشت دست و پا نشين ...بخصوص تو خواب ...اونوقت  همه فكر مي كنن حركت انگشت هاي پاتون يعني اين كه بيدارين و متوجه نمي شن  چه عمليات مهمي در حال انجامه.....اين كار ساده تره )))
I like this. Now how do they devide.
Indian kids just do it in their head. Visual mathematics.
1= x times lines intersect within the circle; 5= x times lines intersect within the oblong; 6= x times lines intersect within the much bigger circle. but i don't know how they come up with circles and oblongs or even how the lines where placed in such ways.
Reading the comments is more fun! Many people should pass the elementary school again! It just works exactly the same way we multiply two numbers on the paper and people still think they need to test it on 100 cases to make sure it works :))
Are we really that dumb? I did it in my head in split second simply using common calculations and operating brain. Are you serious? Or lost?God help us. 
Mayans used this method, it's awesome that this method is till being use.
What about multiply 3 numbers without association? A xyz plane (3D) crossing x, y and z parallel planes. It works for 2 x 2 x 2, which is a cube of 8 corners
this is just a visual way to (10+3)*(10+2)

(10*10) = 100
(10*2) + (10*3) = 50
(2*3) = 6
Just multiply two numbers with any number of digits. It works as long as you don't have carry when adding up:
          1 2 1
*        1 2 3
         3 6 3
+    2 4 2
+ 1 2 1
   1 4 8 8 3
It is just replacing the digits with lines
I tend to forget the internet is nerdy.
why don't they just use their toes like me?
My mind has been blown by how much sense this makes
I learned it in primary school... ;)
I see where they got they 1 and 6 from but
 where the 5?
Hey thanks to all of you who shared such  easy method..
da faq?!
im in algebra and i hav no fugding idea what that is!!!
Really Where did the 5 come from. I only know where the 1 and 6 came from.
A sort of arithmetic tic-tac-toe  !!@@!!
its wherever the lines cross.  look at the circles made by the pencil.  
This is totally fast and yet lazy...gotta try this
I haven't seen this before. Both of my daughters learned a kind of sing-song chant for their times tables. For example, the 4 table would be like "4 1 4, 4 2 8, 4 3 12,..." (but in Japanese). Interestingly, they only memorize up to 9x9=81, and they're amazed that I had to learn up to 12x12=144 in US elementary school. 
Nick W
That's actually really cool. I always used to revert to lattice multiplication but now that I have seen this...
Steve D
Neat but I prefer my good old MS Excel
the 5 comes from the intersecting of red and black lines (2) plus (+) the intersecting of blue and green lines (3)
red x green = 1, [diagonal] green x 3 blue + red x 2 black = 5, and  2 black x 3 blue = 6    Total 1,5,6

I guess this is how it works.
it goes to show that there are more way then one way to solve a problem...
Windows, Mac, Linux...
but all the solutions came from the human mind.
This is interesting for 2 digits by 2 digit multiplication, though larger value digits would get more unruly. The colors aren't critical, you can just think of the four quadrants (drawing with the extra gap helps). Notice that there's more adjustment needed when one of the areas you "count" is greater than 9.
why the hell did nobody tell me this earlier in life?
They use the number of intersections that are circled?
55 x 76 = 35 + (30+35) + 30 = 356530?  

So, it's flawed. (I won't even go into multiplying larger numbers...) 
Multiplication is used as a shortcut for addition.
5+5+5+5+5+5 = 5 x 5.

So instead of a quick 26+130=156, the mind has to count lines, and get them in the right order.  
was hard to get it working with 17x25 wich is the first I tried.. Got 2 + 19 + 35.. so I ended with the basic and old sum to the left. 2 + "1"9 (3) 9+"3"5(12) 3 + "1"2 (4) 2 5.
ctrl+r:calc did work at first attemp
jeff i
We dont have to multiply anymore we just let the Japanese do it for us
It looks cool,like Tic Tac Toe,but nothing beats like memorizing by heart the multiplication table.In my humble opinion.
Want to blow your mind?
How to add fractions:
A/B + C/D = (A x D) + (B x C) / (B x D), then simplify.
(razzafrackin math teachers didn't show us this shortcut until Algebra II (Tenth Grade)!)
It gets confusing when there are numbers that carry over but yes it works like a mofo
mmm fractions.. (thinking in pie)
Please I dont get how you arrived at your answer. More explanations with the diagram
H. Lane
makes so much since! maybe i should try their way of doing math cause it is so confusing here!
?  What's so difficult about basic multiplication?  And how is this more efficient?  The time it takes to figure out the answer is at least twice as long as the method taught in American schools.  Heck... this problem I can do in my head in less than five seconds.
I have to say though. Why not just think it up in ur head? How should kids learn to do math? Without pen and paper! Writing everything down makes you so reliant on pen and paper, while in the mean time your actual brain isn't doing much.
+William Hamilton
17X19=(17*20)-17. My way  may not seem as cool, but it's neater on paper. Easy to do mentally. Only very efficient near multiples of 10.
Easier mentally:
13x2 = 26
13x10 = 130
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