Vedic Multiplication - Fastest and Easiest Mental Multiplication Techniques

1. Technique_1 :: Multiplying Numbers Near To 100 within 10 seconds: Hi. Welcome to the courts. A Vedic mathematics. In this lecture, we're going to learn what kind off simple multiplication we can do when the numbers are near 200,000 or 10,000. Or for that case, any power off then. So let's start with a smaller numbers First on, then we will see how their techniques has been done on. We will be able to scale it up to the higher numbers. So we're starting with two numbers. 98 on 92. So 98 has to be multiplied with 92. So let's start with a convincing. All mattered. Then only you'll be able to see that how much time were ableto save using the vedic matter . So here, when we multiply, we say toe aged 16 61 carried for 2 90 18 plus 1 19 then 98 to 72 to seven. Captured on 9 1981 plus seven is 88. Then we comfort addition. We say this is 69 plus two is 11 again one carried. So this becomes eight plus 19 plus 1 10 01 carried eight plus one is a court tonight. So this is the whole step we need to do in a convincing ometer invaded matter. The things are quite simple. How? Let's see. First thing we need to figure out in this mysteries, these numbers are near toe. Which number on? We call that us based. So, in our case, the basis 100 Because these numbers are near 200 the step two is that find out how bigger are all smaller. The numbers are compared to the best. So 98 is do less than 192 is eight less than 100. A next step is that just multiply eight on to which gives 16 and then do a cross substructure in that is either 98 minus eight or 90 to minus toe. Whatever you do, that is, it is 90. So my answer is 9016 that's all. So look at the simplicity off this metal on. Look at the time saving that we're going to do to this matter on the complex calculation that we're doing here were ableto award in this matter. No complex calculation, no addition. Just do some few ah, simple subtraction and multiplication, and you have the result in your hand on. I'm pretty much sure that if you practice this mentally, you know, to write all the steps as well. Okay, so those are the key benefits off this Reddick meter Select do distinct with another set off numbers as well. So here I have taken an example of 100 well multiplied by 100 7 So here, again, our basis 100 because the numbers are near 200. And here the boat, the numbers are more than 100. So 100 well is 12 more than 100 107 is seven more than 100. So now we do 12 70 84 somewhere. Duplication on. Then we want toast aren't here. We do not drink cross obstruction rather to do across. Addition, because the numbers are more than the base. So why don't you do 100 well, plus seven or you do 107 plus 12. Whatever you do, you will get the result. US +119 So our answer these 11984 Let's stick this using a calculator multiplied by one Tzeitel seven. The answer These double 1984 for that soul is our answer as well. So look at the simplicity here. I think the time that you will take toe type this numbers in a calculator you can actually calculate in your brain or mental. You can calculate and figure or dancer so that this way we say that if you are going toe master this techniques, you can do a lot of things mentally. You don't need even pendant paper or some Calgary it or something like that. So that's the power of a dick Met appendix. So here, one more thing I want to tell you is that it has a inbuilt technical. So to figure out, if you have done some mistakes, sometimes we can say that 112 plus seven is 118 120 year 119. Whatever we can make some mistake death. Instead of telling 119 we can tell something else. But when you try to do the same addition in a different way, 107 plus 12 their higher tenses that you'll figure out Oh understand, plus 12 is under 19 not under dating, right? So there is a building methodology here, toe cross check your answer as well, or to figure out if you have done some mystic so that is the key difference and key benefits off Reddick mint products. So let's revise what we have done. Fasting that we did is that we found out the base. So in case off multiplication between 98 90 to the base was 100. Then we figured out how far the numbers are compared to the base. So 98 waas do less than 100 on 92 was eight list 1000. Then we did some multiplication off the deficiency or die access, whatever it is. So in case it was in in our kissed or deficiency toe to multiplied by 8 16 and then we did across sub strapped or art. So cross obstruction means 98 minus eight on 90 to minus toe. Whatever you do know, reserve this 90 sort of answer this 9016 So this early cap off what we have done. So I hope this concept is clear. So this is really small thing that we're doing. I don't want toe introduce into really big numbers and things gets complicated and you guys get confused. So I want to introduce with using the smaller numbers, do a practice and you were going to jump into bigger numbers as well. Andi, if you do a proper practice, bigger numbers really quite simple. I'm pretty much sure. So now, before closing, I know you'll have questions. So you might be thinking What happens if the multiplication of red officiant ear that exists? It's a single number, or acri digit number, like the blue example like when you say 85 multiplied by 93. So we get here 15 less 1000 this is seven less than 100. So 15 multiplied by seven becomes 105 on. Then when you do across obstruction, it comes 78. So is 78,000 105 has done so off this multiplication or how do you do it? Similarly, for 98 multiplied by 97. Also, you get when you multiply two on three, you get a single digit six. So is 9 56 is dancer. So I know this kind of questions might be coming to your mind is good if it has come into your mind. If it is not coming to your mind, then look at this hand figure or that yes, usually, as the scandal questions. So don't worry. We're going to see in the next lecture that how this kind of things can be addressed. Stitches. Thank you. 2. Technique_2 :: Multiplying Numbers Near To 100 within 10 seconds: welcome back. So we have left our last lecture with these two questions. If your pride of you would have faced a problem that we have already described. So let's see how we can solve this situation using the same technique but with a little bit off modification. So 85 has to be multiplied with 93. That's how question so fasting, you start about base. So in this case, also the basis 100 because 85 on 93 both a near 200 85 is 15. Less than 100 on 93 is seven less than 100. So the fasting that we need to do is multiply 15 on seven. So 15 7 gia is 10 Fife, that's all about our rights. Eight part the left side part. How do you find out is a cross subtraction. So that means either you need to do 85 minus seven or 93 minus 15. So whatever you do, you get the answer. A 78. So is our answer. 70 8105 Let's take that now. Using a calculator 70 Sorry. 85 multiplied by 93. Sudan today is 790 Fife. So whatever, we got this wrong. So what happened wrong here? So the modification that I'm going to talk about is a letter to that. So always remember that our base is 100 on 100 Hostile Geo's. So on your right side, you have to keep two numbers. You cannot keep more than two numbers or you cannot keep less than two numbers. I'm pretty much sure that the question will be coming to mind wide, So I will answer to that. Why? For sure. Okay. This course is all about giving you that technique on also telling you why this technique works. Okay, I love you. Lose something blindly so But in this point of time, please be presents. Understand the technique that I'm telling. But I get into you or I promise you that incoming lectures. I'll give you the technique that why it works like this week. So what they were seeing is that ah, when our basis 100 always try to keep only two numbers on your right state. So here the cases that we have already got three numbers. So what to do with the turnover? You just carry it to the other side So now it's just like normal addition. You do 78 plus fun, so it becomes 79. Underwrites Sadie. Still zero faith. So answer is 7905 That's what we saw in the calculator. Got it? Simple, really simple modification. You're still getting the same answer. Let's do it with 103 100 to and you'll be able to figure out this again. For here. Our bases again 100 103 multiplied by 100 to so 103 is three more than 100 on 102 is two more than 100 fast epi's multiply tree. And to this will give you six. But if you immediately remember, I want I told you before that you must keep two numbers on right state. But here I'm getting only one number. What to do? Just put a zero before that. So my right side is 06 Keep it as it is. The left side is gross. Addition 100 to plus 303 plus two or 102 plus tree. Whatever you do, you get +10 Fife. So our answer is one D +0506 Let's see. +103 multiplied by 10 So 10506 That's a little answer. So you see how easy it is? Know how, how much time saving it is happening. So if we extend this technique toe higher numbers still we can use the same technique and figure out the answer much faster. Andi, In the coming lectures, I'm going to show you how this technique forfeit. Bigger numbers also will be really amazed to see how this technique is so useful for Big Anonymous. I just started to explain you the technique with a smaller numbers because I want you to understand this technique totally so pleased. To understand the technique, I have attached some practice quizzes. Please do those. You have any question put forward? I want you to be an export in this ants. Once you learn this, you'll find mathematics fun on. You will find mathematic interesting. So let's do it on. Let's meet in the next lecture. Thank you. 3. Technique_3 :: Multiply 998 and 576 within few seconds: Okay, let's get started with some bigger numbers. Okay? We have done little or a smaller numbers. I hope you guys have practiced it on ur mastered the smaller numbers. Now let's see with the bigger numbers which will actually give us more time saving. So here I'm trying to do 998 multiplied by 567. If you want, give it a try using noble matter convince No matter on, I will do it in Vedic matter. Pause the video here. If you want to give it a try in convinced limiter on, then come back. Once we're done with her answer and we will do it The Vedic metal. So 9 98 is how much less than the nearest power off then So nearest part off 10 here is 1000 which is over Beth. So now 9 98 is too less tan 1000. So I'm writing is 002 Because, as we have discussed in our last lectures, we have to keep three numbers on the right, say, because the base has three zeros 5 67 how less is it from 1000? It is 400 33 less now The first procedure is, what we need to do is multiply two on 433. So simple manipulation to three there six two threes a 6 to 4 to eight. That's always my right side, nor coming to the left side. Either I need to do 998 minus 433 or I need to do 567 minus do so. Off course, 567 minus two is easier, so let's do it. So it is 565. So multiplication off 998 on 5 67 gives answer. 565 A double six. Just thing you are multiplying a three digit number with another three digit number on your getting the multiplication result in a single line. Can you do this using their convince limiter? No. So this is the power of Reddick meant critics just stick using a calculator. Border answer. 567 multiplied by 998 The answer is 5658 double six, That's all. So you see how simple it is and how, if activities you safe strain. It's unnecessary interest as well. So let's try. Oh, dis mattered. Using some more bigger numbers on you will be still able to appreciate more about how much time to deceive. 4. Technique_4 :: Bigger the numbers .. More Fun: Okay, so here I have taken still very big numbers like the first number is 999,987. On the second number is 999,991. He felt multiplied This two numbers on you need to do it and conventional method. You will really go crazy. I'm pretty much sure, but see, in Vedic matter how simple it is, how easy it is on, I will just do it in a single line. So as we have discussed, we have toe first figure out what is my nearest tend to dip our number. So here the nearest number is 2000. That means one for Lord by six zeros on day. So here we have 123456 numbers. So the sister nearest tend to dip our number, which is nearest to these two numbers. Now we need to figure how small or big this numbers are. So of course, these numbers has smaller than 2000. So how small it is? This number is actually 13 small, But has we have discussed previously? We should always make sure that how many Jiro is that they're in the base. Same number should be here on my right side. So if I put only 13 that it's not only two digit number. So I need to put four zeros. 12340 on, then 30 on, then here. Similarly, this is just nine less than 100,000. But I need to put all zeros before that to make sure that I keep six digit on here. So 123 full five on nine. So now things are simple. I need to multiply 13 on nine, which is 117 So I died 117 here on off course. I need to keep six numbers on this side. So I will put three zeros before this 123 So my diet say job is done now coming to the left side. But we need to substructure either 999,987 minus nine or 999,991 minus 30. So whatever if we do, the result is 999,000 978. Right? So now you see, this is my answer. Let's check with a culture. The first dinner will come to the saving part. So 1234 nines 87 multiplied by one door 34 Faith nine one. So the answer is 999 nine, 7843 zeros 117 Right, So our answer is absolutely correct. Do you just think off that I have multiplied a six digital number with another six digit number? I ain't got on answer with double digits on I'm doing in a single line. So that is stop our road that Easter benefit that we're going to get if you practice predicament. Critics. I'm not saying that it is applicable to all them with because we are discussing about the specific way we're numbers and year to 10 to depart number. So I know this is a special case, but still, if you can think off in this direction for other cases as well, you can actually figure out your own formulas because I'm going to tell you that. Why distinct walks? Okay, that also I'm going to tell you so I hope this is helpful. I will put some practice exit. Please do it on DA Master. The technique on amaze your friends, your relatives Onder do well in your exam. Thank you. 5. Technique_5::Multiplying Numbers Near To 100 within 10 seconds: Okay, so in this section, we're going toe do little different and tricky thing, or I would say what we have missed it. Now I I'm sure that you guys might have guessed that till now. Whatever we're doing, it's Whatever multiplication we're doing is one side of the base. That means let's say we're doing 96 multiplied by 94 or something like 108 multiplied by 109. All these things are one side of the basic. Both numbers are either Ah, smaller here, Andi here. Both numbers are bigger late, but there are also cases when numbers are on either side of the base. Right. So this is a case 96 multiplied by one dear seven. So here our basis 100 and 96 Ys four less than 100 on 97 is it's a sorry 107 is seven more than 100. So what we do, we follow the same process. 74 the 28. Then what happens on this? Say it again. The same process. We do it cross addition or cross a subtraction based on the symbols. So 96 plus seven or 107 minus four. So based on the symbol 96 plus seven cross addition or gross subtraction, which is 107 minus four. So whatever we do that answer this 103 But our actual and sort of multiplication, that is 96 multiplayer 107 is not one Jiro tree to it. What we need to do here for this case is that we need to write this as 103 double Jiro because we have based with two zeros. So we died that on. Then we subtract minus 28 soda and studies desist, then minus eight is too nine minus two e seven. So we have borrowed 10 from here. So now this is to a zero on one. So answer this one Genital 70. So this is just the last mortification that you need to do to figure out this answer. Let's do it one more time so that the procedure is quite clear. So here I will do 85 multiplied by 109 So in this scenario again, our bases 100 with two zeros. 85 is 15 less than 100 on one Jiro nine is nine more than 100. So now if you multiply 15 multiplied by nine. The answer. This 1 35 right? Keep it as artists. Then we need to do. I did across addition here or across subtraction. Whatever you do. 85 plus nine or 109 minus 15. Whatever they do, the answer is 94. But that we have already discussed our answered isn't not 94,135. What we need to do is 94 double Jiro. I need to put because my base has two zeros on. Then I need to say, minus 135 If I do that, this is from here IRB or open. So 10 minus five is five nine minus three is six here. Remaining is three. So three minus one is to under this night. So this is simple subtraction. We're doing nothing else. So only that were writing. It has 9400 minus 135. Unanswered is 9 to 65 So this is just one more additional step we need to do when the numbers are on either side of the base. There's secretary calculator for her confirmation. If we're doing correct or not. 85 multiplied by 10 tonight. The answer is 9 to 65 right? So that's all Are all the techniques where we have discussed that if the numbers are near toe and me 10 to the power number, then we can actually figure out it in a very simple way. Even very big numbers also. Right? So whatever doing the next lecture is that I will sum up all the techniques. So we have discussed about something to side off the base single side of the base. When we multiply, numbers are higher. All those criterias are all those modifications, whatever you have discussed. So I will put sum it up in one video and put it in the next lecture so that Ah, whatever the concert we had discussed still long, you can get it at one place and compare that. Okay, fine. So this is the base technique. If this variation is that I need to do little variation here and I'll get dancer. So that's the whole idea. So let's join the next lecture, go through it. Any questions? You have any doubt you have? Please feel free to put it in our question section or a common section. I will surely get back to you. I'll clarify the top. My intention is that you should understand this. Taking totally on you sort of master this technique get actual benefit off technique. Do you need to apply it at many places? You need to understand. Why does it work as well? I hope from Hey, inventiveness Clear. I want you to be a mad genius. Yes. Or put the questions Whatever comes to your mind, please feel free to put it. I will surely answer. You will see the clarify your dope. Thank you. 6. Let's Revise All The Techniques: will come back again. So here we are going to see the techniques. Whatever we have discussed. Still now, at one place here, you can clearly visualize how the base technique and we modify a little bit on. Then you can start using it for doing the multiplication in a very fast rate. So fast it's 92 multiplied by 97. This is a normal metal. 92 is eat list. 1000 on day 97 is three less than 100. So we just multiply eight on three, which will give us 24. That is made. I'd say Number 100 has two D rose. I got two numbers on the right side, so I have to do nothing. Then I just need to do cross obstruction here 90 to minus tree or 97 minus eight. So whatever I do, I get the answer at 89. So my answer is 89 do for So now, this one, the next one where again the numbers aren't one side of the base. But when we multiply the right say numbers, I get the lesser number. Donde geos in the base. What do I mean? I mean here this is do more than 100. On 103 is three more than 100. Sophie Name Multiply two and three. It gives me six. But 100 is our base in this case on 100 house two zeros. So I have tohave to numbers on this. Right Said so. What I will do is I will put one, dear Oh, before this. So my right state part is done now moving to the left side 102 plus three, that is across addition or 103 plus toe. Whatever you do, you get one Jiro five. So the answer is +10506 Then moving to the next case where when you multiply the number, Stan number of digits is higher than the Jiro is in the best. That means 85 is 15. Less than 100 on 93 is seven less than 100. When a multiply 15 I'm seven, it becomes one Jiro Fife. But in this case, also my basis 100 so on the right side actually can keep only two numbers. So what will happen is that the remaining number has to go as a carry for or to the other side. So let's first finish our left say, then we'll do it. Carry forward. So 85 minus seven grow subtraction or 93 minus 15. So whatever I do, I get 78 after that. Since I can only keep these two numbers on this side, I will carry number one here on. I will just add it on the side. So what? My answer comes as 79 zero. Got it. I hope all the things that clear here. So we're done with the numbers at one side of the base Now we heard discussed also another case where the numbers are on both side of the best. Like either side of the base there. Stick that out also. So here, if you look at it, the numbers I don't either side of the base 85 is a number which is lesser than 100. On 107 is the number which is more than 100. So 85 is 15 less than 100 find 107. He's seven more done 100 When you multiply 15 and seven, it gives 105 keep it does thirties, then coming to the lips said Either you do 85 plus seven or 107 minus 15. So this is again crossways. We need to do either subtraction or addition based on the signed here. So 85 plus seven is 92. So if you do the same thing, that 107 minus 15 a little get 92 anywhere. That's a verification step. So now from here, how need Howie will derive the answer so simple here. If it is on either side of the base, I write 92 on two zeros because my basis to zeros on, then minus 10 Fife. So if I do the subtraction normal subtraction you just carried in here and do the subtraction. Once you get you get five, nine Zito me So dancer is 9095 I hope all these things are clear now. So we have summed up all the techniques that we have discussed in long. So please do practice it. Come back to me if you have any kind of question. I'm here to help you on. Make sure that you understand their techniques. You get rid off Matt phobia Andi become Imagine yous so be very free. And frank, if you cannot understand something that frankly speaking frankly, give me in comment. So that is nothing called a silly question. If you do not understand something, it's absolutely fine it so that everybody can understand everything. So if you don't understand something, put a question if required, I can continue with you for you and give it to you so that you understand that your own way and own pace. So that is absolutely fine. But speak out. Tell the thing that you are not able to understand or tell that thing that you are able to understand. But you need some kind of variation if you have a different kind of question, so feel very free to put all your questions and I will answer it to your satisfaction, for sure, thank you. 7. Mathematical Proof Of How the Technique Works?: Hi. So now it's the time toe Reveal the secret that how this technique works. So as you can see, there are three formulas I have written here. X minus e multiplied by x minus B is called Toe X whole, multiplied by X minus a minus. B plus a B. Similarly, that a formula for explosive a multiplied by X plus B under the formula for X minus a multiplied by X plus B. So let's see that first, we will see that how we come from this side to the site. How does being derived? Then we'll see the application offer it so X minus a multiplied by X minus. B is called toe this. So let's first derived that. So I'll start from my left hand side, which is X minus a multi blood work x minus b. If they do that, this recall toe X multiplied by X minus B minus a multiplied by X minus B. So they're distributed. Property is a quarto X multiplied by X. It gives me X squared on then x minus be multiplied in minus B X. Then my nurse a multiplied by X. Give me minus a X on minus a multiplied by minus B minus minus. Multiplication becomes plus a in Toby. I can write us a B. So now, from these four street terms, if I take X as common. So what happens is X minus B minus a plus. Hey, baby. Freight. So now you're clear that from this state how we came to the site. So this is a simple proof arithmetic proof. Okay, so beyond this, let's see how this is applicable. We have seen that. Okay, how you derive although stuff. But how? Using this formula, we are able to do those things there. See that? So here I'm multiplying 90 to 97. So 92 I can write us 100 minus eight on then this I can 97. I can write that 100 minus three. So if they put it into formula in this case, my ex is 100 great and is a call to eight. Andi B is a cool little tree. So as put the formula, I need to write X minus a multiplied by x minus B is X holding toe. That means 100 holding toe 100 minus a, which is minus eight on minus beef which is minus three rocket close plus a multiplied baby , which is nothing but 24. So if I saw this, this is 100 multiplied by 100 minus eight minus tree, which is nothing about 89 plus 24. So this is +89 double Jiro 8900 plus 24. So my answer is 89 to 4. How did it map your technique? I hope you got it. But I will. I will tell it again so that it's pretty much clear. So in our technique, what we do, we first multiply eight into three on. Just keep it as it is. Then we do a cross subtraction. That is 90 to minus tree or 97 minus eight. We're actually doing that here. So if you first take these two numbers 100 minus eight, this becomes 92 minus three. So 90 to minus tree. This is one other ways. If you take this on this number faster, this 100 minus tree, which becomes 97 on then minus eight. So this is this record cross subtraction. So whatever you do, we get in 89. So that is that this rather question plays a role here. Or you can clearly see that why that gross subtraction technique works and it gives the same result on. Then the next thing is that we write 89 here on directly. We say, Okay, 24 in this side, so answered is a name to four. Because we know that whatever is our base, we're multiplying that with this number. Andi, Since base has two zeros at the end, it will always have two zeros. So if I get a two digit number, I need not added explicitly because I know that last two digits off the side is 00 So whatever I get here on my right side, I can directly later don't. So 89 to 4 or 8932 Whatever it comes. Because my last two digits zero. So I hope this technique is clear. So how, using this formula, we are able to explain this technique on actually the sister main just behind the Stickney . So my sedition to use that always whenever doing some kind off algebraic expression, always try to look forward if you can apply it some way to our numbers or our normal multiplication division. addition, subtraction or something else. Okay, so that kind of mind city should have. So now you can clearly see that. Okay, X minus a multi blood makes minus. B gives me any question, but if I just thinking little different way than you can actually apply to the numbers and see great results. So I'll be showing you this kind of techniques going for their also that how? By applying some off the algebraic identities, you are able to figure out answers very fast. Okay, So stay tuned. Ask questions. If you don't understand, Do not hedge. It'd absolutely. And in next picture, we're going to discuss. Ah, the technique. What? How the technique works when the numbers are on either side of the base. So, during I decided the base, I told that joke right down to with the roast and do a minus, and all right, I think you'll be able to visualize it. But I will explain it again so that it is pretty much clear. Okay, so stay tuned. Thank you. 8. Applying the Mathematical Proof: Hi. So here we're seeing how the technique works or why their technique works when the numbers are on either side of the base. So the formula that we use here he's explosive, multiplied by X minus B is called toe X, multiplied by X plus a minus B minus a B. So our example is 85 multiplied by 107 So 85 I can write has 100 minus 15. He's 85 on 807. I can write 100 plus seven so you can easily visualize here. My 87 and B is 15. So as the formula goes on, of course, excess 100 so 100 multiplied by 100 plus seven which is a minus 15 which is B on, then minus a multiplayer baby which is 15 multiplied by seven is one Jiro Faith. So now here What we do is that 100 multiplied by 100 plus seven minus 15. So how how much it comes to it comes to 90 to minus 10 Faith So which is nothing but 92 multiplied where 100 is nine to the ball. Jiro minus 10 Faith on this is exactly what we do at the last step when the numbers are on either side of the base. Right? So let's do it in a warm it hard and just map it. I think you are already able to map it. I'll just tell it again so that if you're not clear, you can easily get it. So here, minus 15 we do because less 15 done 100 on this is plus seven. Now we doing multiplication 15 into seven, which is one gentle Fife on then 85 plus 707 minus 50. Same way. Actually, you can explain this phenomena. 85 plus seven. If you say so. This is like 100 minus 50. New take It is 85 plus 707 minus 15. That means 100 plus seven is 107 minus 15. It will be right. So I don't we do across subtraction or cross addition. So whatever do that is it is 92. So beyond this, what they say is that when there is the numbers are on, I just say that the base you do 92 double zero minus one judo Fife on were exactly the same step here. So you know why we're doing minus 105 at the end and why you are putting only when we get 92 where you put two zeros so similarly, you can extend this to the higher numbers. Also, it's all same for the higher numbers when we are based as thousands. So it'll come mystery zeroes when base US 10,000 you'll get four zeros on like this, it goes. So that's the whole technique behind this method, how it works. So I hope you have understood it clearly. If you have any questions, feel free to put the questions I will get back to you on one request again, please to practice. Whatever the practice, exercise, arguing, Please do that. That will make sure that you are exported a technique or if some off the concept is not refined. Also, you'll stuck at the point. You'll ask a question, or we will. Cedar tutorial again on the same concept gets refrained on. You will be able to do it flawlessly, so please do practice. There's a key in mathematics. Thank you