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  • 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

Hi this is Presh Talwalkar and today I am going to explain a math trick

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