Multiply Numbers And Algebra Equations By Drawing Lines

Some people say this is "how the Japanese multiply." Others say this is "Vedic Math." I'm not sure of the origin, but this is a visual way to multiply two numbers and it does work. The video also shows how to use the same method to multiply algebraic expressions like (x + 2)(x + 3).

Here's a blog post I wrote on this: http://mindyourdecisions.com/blog/2012/01/27/multiplicating-with-lines-math-trick-how-it-works/

Many people asked me to write a reference guide. So I wrote a book "Multiply Numbers By Drawing Lines." https://www.amazon.com/gp/product/1500866148/

I've made a few follow-up videos you might like.

Multiply by lines (advanced examples)
https://www.youtube.com/watch?v=DUop79ZKxmc

Multiply by lines (why it works)
https://www.youtube.com/watch?v=bL5eUQIMaek

Multiply by lines (the rotation trick)
https://www.youtube.com/watch?v=scCfeJhJ2TA

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: http://mindyourdecisions.com/blog/
Twitter: http://twitter.com/preshtalwalkar
Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965
Google+: https://plus.google.com/108336608566588374147/posts
Pinterest: https://www.pinterest.com/preshtalwalkar/
Tumblr: http://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: http://www.patreon.com/mindyourdecisions

Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r

My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

"Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/

"Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/1517596351/

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/

---

Closed Caption:

Hi this is Presh Talwalkar and today I am going to explain a math trick
of how you can multiply numbers just by
drawing lines.
Let's say you want to multiply 12 by 13
For this one we will draw one line
and for the two we will leave a little bit of space
and we will draw two lines.
For the other number, we will draw lines in the other direction.
Now we will group together different lines and we will count the dots.
Here we have six different dots.
In the middle we have five different dots.
And on the other side we have one dot.
And that's the answer 156.
We will do another example.
For 15 by 21,
we start out by drawing one line.
Then we'll leave a little bit space and draw five lines.
For the other number we draw lines in the other direction.
We draw two lines here and one line here.
We will again group the different lines
Here we have five dots.
In the middle we have eleven dots.
And the other end we have two dots.
We will need to make one adjustment
because we have 11.
We will need to carry this one over which will make 3.
And our answer is 315.
We can even do this for bigger numbers.
For 123 we start out with one line and with some space two lines. And with some more space three lines.
And we draw the other lines for the other number in the other direction.
We again group the lines.
We have three dots here,
eight dots here,
fourteen,
eight,
and three.
Once again we're going to have to carry
this one over (from the 14).
So that's our answer.
It'll be 39,483.
You can even use this trick when a number includes 0.
But one thing is when you draw this line
you should still draw the line, but
put it in a different color or different
marking.
And the trick will be that we don't count any of the dots for that line
So when we make the grouping, we have three dots here.
For the second arrangement,
we're only going to count the dots for
the non-zero lines.
So we have six dots here. We don't
count any of the intersections for the zero line.
In the middle, we again ignore the zero line, which makes seven.
Here we have two dots.
And two dots here.
So you can even use this method when you have a number that includes zero.
The reason it works is you can even use it
for algebraic equations.
Let's say you have x plus 2y times x plus 3y.
We will draw one line for the x,
and we will draw two lines for the 2y
and we will draw the lines in blue.
We will put all the x lines in black and all the y lines in blue.
The other number we draw the lines in the other direction
And again we make groupings.
So here we have six dots and because
both of the lines are blue that means it's y-squared.
In the middle we have five dots,
and these are the intersections of a black and blue line,
which means it will be an x and a y.
On the end we just have one dot and
that's for two black lines so it's x-squared.
So that's the answer.
I hope you enjoyed this trick. Please subscribe to my channel. I make videos on math and game theory.
You can follow me on Twitter @preshtalwalkar, and get my ebooks on Amazon.com