The magic of Vedic math - Gaurav Tekriwal

Nameste. I'm from India, and India is one of the oldest civilizations in the world. It has contributed to the world concepts such as yoga, ayurveda, spicy chicken tikka, and Vedic math. Vedic math is one of the world's easiest and simplest ways to do math.

We are going to combine together and do some number crunching today. So what we are going to first do is multiply by 11. We're going to do it together, so if you blink, you're going to miss it. So just watch it, OK? So we're going to do 32 times 11, OK? So we split 3, and we split 2, and we add 3 and 2 and paste it on top, and we get the answer as 352. That's it.

Let's try another sum. 45 times 11. Let's hear it. Exactly, that's 495. And 75 times 11. So it gives you 7,125, 1 gets carried over, and it becomes 825. That's how simple it is. OK, this is the principle behind it where a is the coefficient.

Let's move on. OK, now what we're going to do is the base method. OK, this is used to multiply numbers very close to the powers of 10, like 10, 100, 1,000, and so on. So we have a sum here, say 99 times 97. OK, now tell me, is 99 more than 100 or less than 100? Less by how much? So we write minus 01. And 97 is less than 100 by how much? So we write minus 03.

So what we're going to do is we're going to cross subtract and get the first part of the answer, like this. We're going to do cross subtraction. 97 minus 01 would give us 96, and we multiply 03 times 01 vertically, and we get an answer of 03. Let's check another sum. Try and do it yourselves. We got 98, which is, is it more than 100, less than 100? By how much? And 97 is 3.

So we got 98, we go crosswise, we got 98 minus 3, or we can do 97 minus 2, they'll all give you the same answer. So that would give us 95. And the second part would be 06. So that's our answer. OK, let's take a bigger number. Let's try this one. Here the base is 1,000.

So we got -004, and 997 would be -003. We go crosswise like this, and we get 996 minus 003 would give us 993, and 004 times 003 would give us 012. And that's our answer. Thank you. 14 times 12. OK, here the base is 10.

OK, so is 14 more than 10 or less than 10? More, so we got plus 4, and 12, we got plus 2. Again, we apply the same rule, so we do 12 plus 4, which gives us 16, like this. And we multiply 2 and 4, that gives us 8.

So now, all of us here, we're going to do mental squaring, OK? Everybody is going to participate here, and we're going to do squares of numbers more than 100 mentally right now. So we got 101, OK? Now visualize on the board, what's going to be on the right-hand side. Plus 01, so we got that. OK, now we add plus sides, right? Yes? No?

So we got 101 plus 01, that would give us 102, and see here, like this. And 01 is getting squared, right? So that would give us 01, and that's your answer. Try the next one. Let's try 102 squared. Let's try, everybody. So 100, so 102 would be 10404.

OK, now the next one, try it everybody together. I'll give you 5 seconds. OK, let's say it together, let's say it together, OK. [10609] 10609 and that's the answer. Woo! 104 squared, how much would that be? Calculate it, 5 seconds. Come on, girls in the back.

OK, so the answer would be 10816. OK, let's do the next one: 105 squared. Oh, no, no, no, no, we're going to try over, we're going to try over, OK? OK. I'll give you 5 seconds, just think about it. OK, now we're going to go, OK? 11025.

OK, let's going to do the next one, 106 squared. Try it, come on, everybody, it's simple and easy. [11236] OK, let's do it one more time. 11236. Now 107, think, hold on, don't say anything out loud, just think mentally, 107 squared.

OK, now let's say it out loud. 11449. And 108 squared. [11664] Fantastic, give yourself a round of applause, come on! And this is the principle behind this, where a and b are the excesses or the deficiency from the base.

I'm going to teach you in Vedic math, there are 16 sutras, or word formulas, OK? They are very visual and one of them is called, "vertically and crosswise," through which you can multiply any number by any number in a single line. So I'm going to do a two-digit by a two-digit multiplication.

Let's do this. So we got 31 times 12. OK, so we're going to apply the vertically and crosswise sutra. So we're going to do like this: vertically, and then we're going to go crosswise, and then we're going to do vertical again. So, 2 times 1 gives us [2], 2 times 3 gives us [6], and 1 times 1 gives us [1].

6 plus 1, [7]. 1 times 3 gives us [3]. And that's it, and that's our answer. No more tedious calculations, no more going through the rough work, it's simple in one line. I want to show you a sum again, this time with carry-overs. The same formula, all of us here can do this, OK? Same formula.

So let's get started. 4 times 2 gives us [8]. OK, now we go crosswise like this, so we're going to multiply 4 times 1, [4], and 3 times 2, [6] 4 plus 6 gives us [10]. So we put down 0, carry the 1. And 3 times 1 gives us [3], plus 1, [4]. Exactly, that's our answer, 408.

OK, thank you for being such a participative audience, and we had a great time number crunching. Now I want to end with a question: whether you'd like math to be dull or boring, or fun and interesting? The choice is yours.