I remember, when i was in 6th standard, there was a chapter,"integers", where we were taught negative number multiplication, and i always used to ask why (-)×(-)=(+)....but never got the answer....but today Aman Sir gave the Answer, and that too in such a simple way....12th mein hu, 6saal lag gaye isko jaanne hain😂
U can imagine - as a sign which represents negative of a no. So whenever u multiply a negative and a positive say 7×-1 the -1 will give us the opposite of 7 same goes with negative whenever you multiply it by negative it gives us it's negative .. -4×-1 the opposite of -4 is 4 ..
To avoid this conundrum we use Double Entry method to show profit-loss.At the close of business final balance was losss of $15.Next day the final balance was $15 in profit.Hence the ledger entries will use + and - symbols such that -15$+15$=15$-15$=0.Also actual cash was( -3$)(5$)+(5$)(-3$)=0.Hence the business didn't go bankrupt up till the third ledger entry.Therefore (-)x(-)=(+).Settling total debt of -15$ must be +15$ which must be(-x-) that is (negative value X negative value)= Positive value.
This can easily be understood by timeline. 5*3 means 3 times of 5 which means 15 on right side of time line, -5 *3 means we are doing 3 times of -5 that is -15 but -5 *-3 is we are not only doing 3 times of -5 but also by using - with 3 we are changing direction. That means - of -15 that is right side of 0. Hence +15
The happiness I see among people after truly understanding even this basic thing makes me realise that we all are mathematicians deep inside , we all are same, its just the minutes change in our surrounding we grow up that leads to different tastes, interest, personality etc.
Dear Sir and all those watching this.. Amazing great video first of all. However explanation of this is given in class 6 book of KC Nag. Many of us donno this book name. He is considered a legend in maths from 1930. Please go through..Also you ll get real life significance of this in that book.
the explanation is: negative number is opposite of positive on number line means its direction changes on number line...so if a negative number is multiplied by negative again then the direction of number again changes from left of zero to right of zero
It would be clearer if you spot the numbers on the axis of a graph and then explain how the product of two different sides becomes positive or negative or vice versa.
At first let's assume that we have to give two pens 3 person each then total number of pins we need is 2+ 2 + 2 that is 6 or 2 × 3 ... Cost to take two pens from from each three persons then it will be ( - 2 )+ (- 2 )+ (-2 ) and the answer is minus 6 and minus here represents taking not giving that that is inverse process of something Now if we consider we have to take -2 pens from -3 person That means we have to take 2 pens from - 3 person We can't take from negative in this particular case And for minus we have to reverse the process then it will be to give the pins to 3 people each
I relate integers to the Earth's surface.Negative numbers are like digging the earth and positive numbers are like constructing something on the Earth and zero being the surface. So when, 3 is multiplied with -5 It is like digging the earth thrice with unit five which gives -15. When -3 is multiplied with -5, It's like trying to dig but actually you construct because if it was just +3 you do the action that 5 says but if it -3 do the opposite action of what 5 says. So -5 says to dig 5 units but since we multiply with another negative do the opposite
Kisi seedhe insaan ( +ve ) ko ulta ( -ve ) karoge to vo ulta ( -ve ) ho jaega Par kisi ulte ( -ve ) insaan ko fir se ulta ( -ve ) kardo to vo fir seetha ( +ve ) ho jaega 😁😀🙃🙂🙃🙂😬😬😬
Actually you have to first know what minus is .... Since minus is the mirror image of positive and vice versa ...So if u take the Real line and check What is the negative of positive it'll be obviously negative as mirror image of positive is negative so (-)*(+)=- And then the mirror image of negative is obviously positive I,e (-)*(-)=+ gives us the correct ans ...(where * indicates of ...) Try to understand the hidden concept behind all the things of mathematics,u ll really feel the beauty of maths ...
So but unfortunately we don't have answer to every why question. questions like 1. Why we die? 2. Why life and what is purpose of life? 3. What is life fundamentally? And most important what is consciousness?
1. You die because you are considering yourself body only and body will die as it is nothing but a packet of chemicals 2. Why life? Well because your parents did something Purpose of life? To be better spiritually and more understanding by the end of each day Another purpose is to reduce our flaws and attain salvation 3. A journey which you can make boring(like 99% of people) or you can make it adventurous
And what is consciousness? Well i am not eligible enough to answer this so i recommend you some philosophers like Jiddu krishnamurty, osho and schopenhauer
@@satyammishra7273 thank for your interest in such type of questions, but philosophy already gives it views on this all questions but I still want some checker method to check all this
Say if someone say water boils at 100Φc then we can check that but what after death is such type of questions that we can't It may have two possibilities 1. There is something after death 2 or there is nothing after death But both possibilities we can't tell to this universe people after our death
Not properly explained. So basically what I'm trying to say is that (-) sign indicates opposite direction. So you have to add it in the number line like this - (a) 5×3 = 5+5+5 or 3+3+3+3+3=15=(+) and your answer will be + 15 (b) 5×(-3) So you have to add in number line like this (-3)+(-3)+(-3)+(-3)+(-3) But we know negative side is equal to positive side but opposite in direction so if we take positive of all -3 then answer will be 15 but will be in opposite direction so ans is -15 Similarly, (c) (-3)×(-5) Here if we assume it 3×5 the ans is 15 , now let It is like (-3)×5 = -15 {see (b)} Now again (-3)×(-5) will give opposite of -15 which equals +15 Hope you guys understood it visually
You explained correctly, but in exam if this is asked we will have to prove it instead of making others understand visually, so he is making us prepared for the exam otherwise everyone knows it visually.
Then please do the same for ✓2×(-5). Can you write it in terms of addition? So, The problem with your proof is that you can't generalise it. And hence, it is not even a proof. It is just an interpretation. What he is doing is a proper proof and that's how you are supposed to do proofs in Maths.
We can prove it using number lines as well🤔🤔 Negative number means 180° rotation. If we take 2 negative lines. 1st it rotates to -ve x axis. And when we take another -ve, that rotates another 180°. Which means 360° rotation from +x axis. And there you go. You got that positive line
It is Group (R,+). And every number -(-r ) for r positive denotes the inverse of -r which is r. Actually this man is using associativity of binary operation viz. (-5)3 = (-1)(5.3) = -15 where -1 is the inverse(ordinary additive) of 1. And similar Ring or structure properties.
I hope sir you read my comment , mates this is not right I am not denying the fact that it can be written like this but this does not mean that the LOGIC behind it is like this . This is a way of writing which takes us to the answer . According to me this is like when we multiply two negative numbers the answer becomes positive as when we are multiplying two numbers which are negative we want to get the answer which is positive , we see that when we subtract two negative numbers we move forward in the number line as -1 is the biggest number in it . Here to we have to gain the biggest answer possible which is of-course positive (-2)*(-2) = see here , we are repeatedly adding two negative numbers that means moving to the left makes the number smaller and even smaller , and moving to the right makes the number bigger even bigger , because to the left after 0 we have positive set of numbers . Our motive is to repeatedly add these numbers and gain the maximum answer possible which is positive in this case a negative number which is to be more negative has to be smaller but when a negative number has to be more positive to be bigger ! This means when multiplying two negative numbers means repeatedly adding two number which are morally to be smaller and have to attain the value of being bigger as they're getting added repeatedly they will move towards the right side of the number line and attain the bigger form which is positive in nature . I understand the fact that my idea is not there to be criticised or it is fully right , but in the video the thing shown is of even higher level , it shows how to prove that negative times negative = positive , which means that it fails to explain the basic nature of the idea behind making a number positive when being multiplied . Thanks For Reading I hope you people revert the fault if any :)
THANK YOU SIR हमे यह तो समझ आ गया कि (- * - =+) but जब हम किसी negetive number ko left से right le jate hai to positive क्यों होता है | या जब हम किसी positive number ko left से right या right le jate hai to negative क्यों होता है|
As far as I remember, only M L Aggarwal has answered this question in his book. All other authors just state it as a "law" and move on because this is something never asked in the exams. Most Indian authors write bad books.
Sir why positive number become negative and negative number become positive when we transfer it from left to right or right to left in given equation? Please make a video on this!
After learning this in school in 6th I was stumped but since nobody asked this question I took it as a postulate. (2008) However now in 2022 I'm rediscovering maths with logic :)
Maturity is when you understand that, still the question has not been answered. It basically telling the same thing, using a different approach, that's it .
I believe the core reason for question is to understand why negative multiplied by negative is positive...... Not to prove it..... Sir, please first make them understand one thing that negative is just a way of representing a value with its direction Or negative in the sense it's the direction and i belive it will be much much better if you make the student understand with the number line system and with the raw meaning of multiplication (adding number of times) .... Now hopefully most of them will be satisfactorily understand.... Why -ve *-ve is positive. You can also give an idea of scalar and vector theory to understand.
-5 ×3=-15 hota h aur isko aise bhi likha ja skta h (-5)+(-5)+(-5) mtlb -5 ko 3 baar jodna to in the same way (-5)×(-3) ko kese likha jaega ..reply jarur kijiyega Thanks
Ur way of teaching is god level sir... Ek hi baar me smjh aa jata h mujhe... Calculus se nafrat thi mujhe pr ab pyaar ho rha hai.... Agar read kiya aapne to heart dedo ❤️
Another good explanation for why (-)x(-)=+ It is that when you see a fraction suppose -32/-71 We can write this as (-1)32 / (-1)71 , correct? Now, same numbers can be cancelled out as they are being divided.(-1) gets divided by (-1) and leaves one When 1x32/71 we get 32/71 Which also proves that negative negative = positive How? , you may ask. It is that -32/-71 can be written as -32 x 1/-71 though if you try to make the denominator positive and shift the -1 above you get 1/-1 and you again shift -1 for infinity. To overcome this procedure it can also be interpreted by the way i explained earlier in this comment. I hope you were able to understand.
I thought about this in my mind , it was very simple to understand i dont really understand why people can’t simply just put some mind power and explore mathematics by themselves and not by some formulas which they dont even know how they were derived.
So according to you -1/-1 = 1 You are not just cancelling same number on numerator and denominator i.e, 1/1 *instead you are even cancelling the signs* i.e, -1/-1 =+1 Everyone and even I know the signs can be cancelled in above example and can written as simply 1/1 or even 1 But *understanding why the signs get cancelled is important.*
Let me give my own explanation on *Why negative times negative is positive* Let us consider a example, -7×-7=49 ----eqn(1) Now let's prove it by my own method *-7 can be replaced by -1×7* From eq (1) LHS =(-1×7)×(-1×7) =-1×-1×7×7 =(-1)²×7×7 =7×7. [. (-1)² = 1. ] =49 RHS = LHS and I know you may ask why (-1)² = 1 My answer is ~ *It's just like a paradox*
That's not the way concepts are taught. It's just a proof using some known mathematical rules. Whereas conceptual methods are such that even a non-maths student will be able to understand.
In maths we keep oscillating between zero and infinity. So there has to be equivalence on both sides. The simple way of living peacefully is that keep leaving but never leave believing in yourself. 👍👍👍👍👍
Practically on field it's not postive suppose you give discounts 20% then after 10% in your object and you are shopkeeper -20×-10%= result at the point of shopkeeper he in loss
Mujhe mam ne ek example se bataya tha ki agar koi karj leta hai to wo minus me chala gya fir aur dusri bar karj liya to fir minus means uske pas bahut sare paise ho gye lautane ke layak jisse wo positive ho gya . I know ye thoda ajeeb hai par hum log bhi chhote the 😂 mundi hilate the bhale samajh aaye ya nahi school life is best ❤
I thought it's wrong because in an equation we can multiply or divide any integer except zero. Here, in that way we can prove any integer =any integer, e.g 5 = -10
If you learn trignometric functions, imaginary/complex numbers, complex planes, multiplication of complex numbers, and De Moivre's theorem, you can easily understand, but for those who have not learned them, the explanation will have to be like this video. If you have knowledge about them, you might think: -5=(5)(-1)=(5)(-1+i・0)=5{cos(±π)+i・sin(±π)}, -3=(3)(-1) =(3)(-1+i・0)=3{cos(±π)+i・sin(±π)}, so (-5)×(-3)=5{cos(±π )+i・sin(±π)}×3{cos(±π)+i・sin(±π)}=15{cos(±π)+i・sin(±π)}²=15{cos( ±2π)+i・sin(±2π)}=15(1+i・0)=15(1)=15.
I have a different answer, no offense, which seems more logical than that answer. The negative sign is just a sign to reverse direction. Positive sight describes movement towards positive infinity and negative sign just changes that direction. The basic purpose of a negative sign is just to change direction. If a negative changes the direction once (from positive to negative) then negative again will change that direction again (negative to positive. In summary, negative sign by definition just changes direction and 2 negative signs cancel each other out. So we're left with our default sign, positive sign
Sir ne...distributive law ka apply kia hai....Solve karne ke liya...agar BODMAS use karte toh...LHS pehle se hi...0 ho jata...isliye...aisa nahi kiya... distributive law ka apply kia
multiplication is essentially the addition of a number a particular number of times. Doesn't matter how many times you take 0, you are going to have 0. You can further prove it by real-life examples as that would be more relatable to understand,like taking 0 slices of cakes a 100 times would still mean to have 0 slices
Thats proving this through mathematical equations. Better to understand it intuitively. -5*-3=15 Suppose you have 5 rupees net worth. Then 5 is positive. If you have 3 bank accounts with 5 rupee each, then 5×3 times=15 is your total networth. Now suppose you have 0 savings. Instead you have a deficit of 5 Rupees that you have obtained as a loan. This is your payable. It would be called -5. Suppose you have obtained 3 such loans from friends. So your total deficit or amount payable is -5×3 times = -15. Now taking this example forward, suppose you have 5 Rupee loan (i.e. ‐5), but this time you have instead of 3 such incidence where you are in debt and owe your friends some money, it is the opposite instance where the 3 friends owe you money. This would be denoted as opposite of 3, or (-3). So basically loan (-5)*(-3) = 15. Your total receivables are 15. Your actual networth is in positive, as even though you dont have the cash, but youre not in deficit but instead have receivables of 15 Rupees. In simple terms "negative" is the opposite of positive. To give another example from daily life, enemy is the opposite of friend. If having a friend is positive, and an enemy is negative, theoretically a friend's friend is a friend (+×+=+). A friends enemy is an enemy (+×-=-). An enemy's friend is an enemy (-×+=-) and an enemy's enemy is a friend (-×-=+).
I appreciate it and recommend to CLASS 6TH STUDENTS WHO DEAL WITH -VE INTEGERS FOR THE FIRST TIME AND COULDN'T UNDERSTAND WHAT'S GOING ON???!!?? JUST LIKE ME🙄🙄😃👍♥️
With due respect to the teacher, this is not a good way to explain this concept to kids, it can serve as a mathematical proof. But to develop intuition/feeling a better way is to follow the first principles. Example: Tell them that multiplication is nothing but repeated addition. So, when you do -5 * 3 you are tryign to subtract 5 now once but 3 times - intuition says it should be -15(show on number line). Also, multiplying -5 with 0 means taking our 5 zero times. Now you can explain that -5*-1 is a way to say that you "take out " 5 not once but minus once which means you are taking "out no 5 but minus 5 which is like giving 5 to some one (show on number line)
I remember, when i was in 6th standard, there was a chapter,"integers", where we were taught negative number multiplication, and i always used to ask why (-)×(-)=(+)....but never got the answer....but today Aman Sir gave the Answer, and that too in such a simple way....12th mein hu, 6saal lag gaye isko jaanne hain😂
th-cam.com/video/EbTmlKRIQAU/w-d-xo.html
Oh bro really I am also in class 11 and after 5 years I came to know about this. 😂😂😂
Pata hi nahi chala yaar kaise samaay beetgaya 😕, 6 saal kab hogae
I am in 6 now
Me to 😂😂
I gave this question yesterday to sir on yesterday's batcheet aur sir aapka approach mujhe bohot accha laga
bhai khel ga
th-cam.com/video/lqVEgVea4Dg/w-d-xo.html 😊😊😊
U can imagine - as a sign which represents negative of a no. So whenever u multiply a negative and a positive say 7×-1 the -1 will give us the opposite of 7 same goes with negative whenever you multiply it by negative it gives us it's negative .. -4×-1 the opposite of -4 is 4 ..
To avoid this conundrum we use Double Entry method to show profit-loss.At the close of business final balance was losss of $15.Next day the final balance was $15 in profit.Hence the ledger entries will use + and - symbols such that -15$+15$=15$-15$=0.Also actual cash was( -3$)(5$)+(5$)(-3$)=0.Hence the business didn't go bankrupt up till the third ledger entry.Therefore (-)x(-)=(+).Settling total debt of -15$ must be +15$ which must be(-x-) that is (negative value X negative value)= Positive value.
I never thought of this question but when i taught integers to my junior i explained them through number line jumping and it actually was right😁
Kaise bhai hamey bhi batade jara...mtlb addition subtraction samjh aata h jumping se
Multiply batan pls
@@imdevil8329 he is right ,watch don't memorize video
@@imdevil8329 multiplication is basically repeated addition.
@@uttamraj3786 but bro -5 is added -3 times it doesn't make sense
th-cam.com/video/EbTmlKRIQAU/w-d-xo.html
This can easily be understood by timeline. 5*3 means 3 times of 5 which means 15 on right side of time line, -5 *3 means we are doing 3 times of -5 that is -15 but -5 *-3 is we are not only doing 3 times of -5 but also by using - with 3 we are changing direction. That means - of -15 that is right side of 0. Hence +15
Not time line
It's number line
Consider the number line...
......,-c,-b,-a,0,a,b,c,........
a•b = |a|×|b|×CosA°
= |a|×|b|×Cos0°
=(a×b)
a•(-b)= |a|×|-b|×CosA°
= |a|×|b|×Cos180°
=a×b×(-1)
= -(a×b)
(-a)•(-b)= |-a|×|-b|×CosA°
= |a|×|b|×Cos0°
=a×b×(1)
= (a×b)
😂😂
I thought it with mathematical reasoning,,
If a positive(correct) statement is negative(wrong),, then the sentence is +-=negative(wrong)
Similarly--=+
The happiness I see among people after truly understanding even this basic thing makes me realise that we all are mathematicians deep inside , we all are same, its just the minutes change in our surrounding we grow up that leads to different tastes, interest, personality etc.
Very True
Mahh goshh!! Thanks for the likes ☺️
True
Absolutely
As a medical student,but you won my heart
I must thank Aman Sir for providing us such a great knowledge.
It is not complicated but it is not taught in school
Right
Great explanation sir....
Simple problem and deep concept. Happy to see that people like u are working for maths.
It can be proved by uesing COMPLEX Analysis. convert the number into complex exponent form then do it.
Dear Sir and all those watching this.. Amazing great video first of all. However explanation of this is given in class 6 book of KC Nag. Many of us donno this book name. He is considered a legend in maths from 1930. Please go through..Also you ll get real life significance of this in that book.
This property of ring theory
Algebraic structure (R,+,.)
Additive inverse of ab is a(-b)
a(-b)=-(ab)
Where R is denotes ring
Like real no ,complex no , matrices , and rational no.
But where is why 😮😮😮😮
the explanation is: negative number is opposite of positive on number line means its direction changes on number line...so if a negative number is multiplied by negative again then the direction of number again changes from left of zero to right of zero
Now that's what I call the beauty of maths! Thank you sir. ❤
It would be clearer if you spot the numbers on the axis of a graph and then explain how the product of two different sides becomes positive or negative or vice versa.
At first let's assume that we have to give two pens 3 person each then total number of pins we need is 2+ 2 + 2 that is 6 or 2 × 3 ...
Cost to take two pens from from each three persons then it will be ( - 2 )+ (- 2 )+ (-2 ) and the answer is minus 6 and minus here represents taking not giving that that is inverse process of something
Now if we consider we have to take -2 pens from -3 person
That means we have to take 2 pens from - 3 person
We can't take from negative in this particular case And for minus we have to reverse the process then it will be to give the pins to 3 people each
Btw 2+2+2 is not 2*3 rather it is 3*2 because it means 3 groups of 2...
But there is one more question..
Why we change the sign of a digit when it's transferred from one side of = to other ....?
I was hoping for an intuitive approach. But proving it algebraically is interesting as well.
Not really 🙄
@@anujpal9370 ?
I relate integers to the Earth's surface.Negative numbers are like digging the earth and positive numbers are like constructing something on the Earth and zero being the surface.
So when, 3 is multiplied with -5
It is like digging the earth thrice with unit five which gives -15.
When -3 is multiplied with -5,
It's like trying to dig but actually you construct because if it was just +3 you do the action that 5 says but if it -3 do the opposite action of what 5 says.
So -5 says to dig 5 units but since we multiply with another negative do the opposite
I have a question
Why is any whole/natural number usually written x/1
Like 1/1,2/1,3/1
It's an improper fraction and how do express it in real life
This can be also done by : Let, -ve *-ve= -ve. Cancelling -ve boths sides =>1= -ve which is not possible therefore negative *negative =positive
Mathematical problems always solve by mathematics visualization and imagination. That is the thing would all have to understand.
Kisi seedhe insaan ( +ve ) ko ulta ( -ve ) karoge to vo ulta ( -ve ) ho jaega
Par kisi ulte ( -ve ) insaan ko fir se ulta ( -ve ) kardo to vo fir seetha ( +ve ) ho jaega 😁😀🙃🙂🙃🙂😬😬😬
Thank you sir. Being a student of class 9th it is a pleasure for me to watch your videos
-1 is cos π , which is e raised to the power iπ .... Now -1 × -1 is e raised to the power i2π.... Whish is cos 2π .....that means 1
Sir paheli baar ऐसा कुछ सीखने को मिला आनंद आ गया❤️❤️❤️❤️❤️ 👍👍👍👍👍👍👍👍👍👍👍👍👍
Actually you have to first know what minus is ....
Since minus is the mirror image of positive and vice versa ...So if u take the Real line and check What is the negative of positive it'll be obviously negative as mirror image of positive is negative so (-)*(+)=-
And then the mirror image of negative is obviously positive I,e (-)*(-)=+ gives us the correct ans ...(where * indicates of ...)
Try to understand the hidden concept behind all the things of mathematics,u ll really feel the beauty of maths ...
Nicely explained
So but unfortunately we don't have answer to every why question. questions like
1. Why we die?
2. Why life and what is purpose of life?
3. What is life fundamentally?
And most important what is consciousness?
1. You die because you are considering yourself body only and body will die as it is nothing but a packet of chemicals
2. Why life? Well because your parents did something
Purpose of life? To be better spiritually and more understanding by the end of each day
Another purpose is to reduce our flaws and attain salvation
3. A journey which you can make boring(like 99% of people) or you can make it adventurous
And what is consciousness?
Well i am not eligible enough to answer this so i recommend you some philosophers like Jiddu krishnamurty, osho and schopenhauer
@@satyammishra7273 thank for your interest in such type of questions, but philosophy already gives it views on this all questions but I still want some checker method to check all this
Say if someone say water boils at 100Φc then we can check that but what after death is such type of questions that we can't
It may have two possibilities
1. There is something after death
2 or there is nothing after death
But both possibilities we can't tell to this universe people after our death
@@Nature-rf7jk
Can you make it more clear
I mean what exactly you are saying
बहुत सरल तरीके से समझाया है, और शानदार तरीके से साबित भी कर दिखाया है। अति सराहनीय! धन्यवाद!
Not properly explained.
So basically what I'm trying to say is that (-) sign indicates opposite direction.
So you have to add it in the number line like this -
(a) 5×3 = 5+5+5 or 3+3+3+3+3=15=(+) and your answer will be + 15
(b) 5×(-3)
So you have to add in number line like this (-3)+(-3)+(-3)+(-3)+(-3)
But we know negative side is equal to positive side but opposite in direction so if we take positive of all -3 then answer will be 15 but will be in opposite direction so ans is -15
Similarly,
(c) (-3)×(-5)
Here if we assume it 3×5 the ans is 15 , now let
It is like (-3)×5 = -15 {see (b)}
Now again (-3)×(-5) will give opposite of -15 which equals +15
Hope you guys understood it visually
👌👌👌
Jodd or wot
You explained correctly, but in exam if this is asked we will have to prove it instead of making others understand visually, so he is making us prepared for the exam otherwise everyone knows it visually.
Then please do the same for ✓2×(-5). Can you write it in terms of addition? So, The problem with your proof is that you can't generalise it. And hence, it is not even a proof. It is just an interpretation. What he is doing is a proper proof and that's how you are supposed to do proofs in Maths.
@@ANUJCREATIONS_4518 If you want to learn mathematics you must follow methods. And methods are not imaginary, they are based on actual logic.
We can prove it using number lines as well🤔🤔
Negative number means 180° rotation. If we take 2 negative lines. 1st it rotates to -ve x axis. And when we take another -ve, that rotates another 180°. Which means 360° rotation from +x axis. And there you go. You got that positive line
hydrogen is gas
oxygen is gas
when they meet ,they turn into liquid called water
why?
It is Group (R,+). And every number -(-r ) for r positive denotes the inverse of -r which is r.
Actually this man is using associativity of binary operation viz. (-5)3 = (-1)(5.3) = -15 where -1 is the inverse(ordinary additive) of 1. And similar Ring or structure properties.
Currently in 9th and it's good to understand this concept
I hope sir you read my comment , mates this is not right I am not denying the fact that it can be written like this but this does not mean that the LOGIC behind it is like this . This is a way of writing which takes us to the answer .
According to me this is like when we multiply two negative numbers the answer becomes positive as when we are multiplying two numbers which are negative we want to get the answer which is positive , we see that when we subtract two negative numbers we move forward in the number line as -1 is the biggest number in it .
Here to we have to gain the biggest answer possible which is of-course positive (-2)*(-2) = see here , we are repeatedly adding two negative numbers that means moving to the left makes the number smaller and even smaller , and moving to the right makes the number bigger even bigger , because to the left after 0 we have positive set of numbers . Our motive is to repeatedly add these numbers and gain the maximum answer possible which is positive in this case a negative number which is to be more negative has to be smaller but when a negative number has to be more positive to be bigger !
This means when multiplying two negative numbers means repeatedly adding two number which are morally to be smaller and have to attain the value of being bigger as they're getting added repeatedly they will move towards the right side of the number line and attain the bigger form which is positive in nature .
I understand the fact that my idea is not there to be criticised or it is fully right , but in the video the thing shown is of even higher level , it shows how to prove that negative times negative = positive , which means that it fails to explain the basic nature of the idea behind making a number positive when being multiplied .
Thanks
For Reading I hope you people revert the fault if any :)
Kitna time laga yeh lekhni mai jii
@@lonefaixn9150 why are you seeing time behind it see the effort :)
10-15 mins maybe less or more
SIR ISS CHANNELPE JEE KE SATH SATH ADVANCE LEVEL KI MATHS BHI DAALDENA DHEERE DHEERE 😁🔥✌
BEST CHANNEL FOR MATHS ❤
THANK YOU SIR हमे यह तो समझ आ गया कि
(- * - =+)
but जब हम किसी negetive number ko left से right le jate hai to positive क्यों होता है | या जब हम किसी positive number ko left से right या right le jate hai to negative क्यों होता है|
Actually Bramhagupta had set all the rules about negative number .
But sir this is impressing 👍👍
Multiplication is just form of addition.. using number system line also you can understand.
As far as I remember, only M L Aggarwal has answered this question in his book. All other authors just state it as a "law" and move on because this is something never asked in the exams. Most Indian authors write bad books.
What was his answer
Sir why positive number become negative and negative number become positive when we transfer it from left to right or right to left in given equation? Please make a video on this!
After learning this in school in 6th I was stumped but since nobody asked this question I took it as a postulate. (2008)
However now in 2022 I'm rediscovering maths with logic :)
This teacher is born to make you Love Maths !! Literally 👌👑 TODAY I'VE FOUND A GREAT MATHS TEACHER.🙏👑...
Maturity is when you understand that, still the question has not been answered.
It basically telling the same thing, using a different approach, that's it .
Actually....😥
I believe the core reason for question is to understand why negative multiplied by negative is positive...... Not to prove it.....
Sir, please first make them understand one thing that negative is just a way of representing a value with its direction Or negative in the sense it's the direction and i belive it will be much much better if you make the student understand with the number line system and with the raw meaning of multiplication (adding number of times) .... Now hopefully most of them will be satisfactorily understand....
Why -ve *-ve is positive.
You can also give an idea of scalar and vector theory to understand.
Jee 2025😂😂 Aspirants 🎉🎉❤All the best guys 😅
The distributive property was based on the convention therefore using it doesn't seem the right way...
We can also explain this in terms of chemistry. - attracts += - but - repels - =+ where +=repulsion and -= attraction.
Sir, yeh kabhi socha hi nhi tha, aapko koti koti pranam
True feeling of Maths 👍🏻👍🏻👍🏻
I don't know why it felt I was listening aman dhattarwal for while
Sir please bring more such videos this very helpful and make video on origin of imaginary number
-5 ×3=-15 hota h aur isko aise bhi likha ja skta h
(-5)+(-5)+(-5) mtlb -5 ko 3 baar jodna to in the same way
(-5)×(-3) ko kese likha jaega ..reply jarur kijiyega
Thanks
Sir i tried understanding this on my own in childhood by using number line(ball jumping from number to number in the tables format)
me too bro
@@AmaanibnYasir ji ha vai sahab ji
Ur way of teaching is god level sir... Ek hi baar me smjh aa jata h mujhe... Calculus se nafrat thi mujhe pr ab pyaar ho rha hai.... Agar read kiya aapne to heart dedo ❤️
Sir ne to bhannat bolna hi band kar diye hain😕😕
Another good explanation for why
(-)x(-)=+
It is that when you see a fraction suppose
-32/-71
We can write this as
(-1)32 / (-1)71 , correct?
Now, same numbers can be cancelled out as they are being divided.(-1) gets divided by (-1) and leaves one
When 1x32/71 we get 32/71
Which also proves that negative negative = positive
How? , you may ask.
It is that -32/-71 can be written as -32 x 1/-71 though if you try to make the denominator positive and shift the -1 above you get 1/-1 and you again shift -1 for infinity. To overcome this procedure it can also be interpreted by the way i explained earlier in this comment. I hope you were able to understand.
I thought about this in my mind , it was very simple to understand i dont really understand why people can’t simply just put some mind power and explore mathematics by themselves and not by some formulas which they dont even know how they were derived.
So according to you -1/-1 = 1
You are not just cancelling same number on numerator and denominator i.e, 1/1 *instead you are even cancelling the signs* i.e, -1/-1 =+1
Everyone and even I know the signs can be cancelled in above example and can written as simply 1/1 or even 1
But *understanding why the signs get cancelled is important.*
Let me give my own explanation on
*Why negative times negative is positive*
Let us consider a example,
-7×-7=49 ----eqn(1)
Now let's prove it by my own method
*-7 can be replaced by -1×7*
From eq (1)
LHS
=(-1×7)×(-1×7)
=-1×-1×7×7
=(-1)²×7×7
=7×7. [. (-1)² = 1. ]
=49
RHS = LHS
and I know you may ask why
(-1)² = 1
My answer is ~
*It's just like a paradox*
Sir, you are great , greater and greatest 😍😍
That's not the way concepts are taught. It's just a proof using some known mathematical rules. Whereas conceptual methods are such that even a non-maths student will be able to understand.
Fantastic demonstration ! Well explained ! Thanks !
If you could explain with example what it means to multiple two negative numbers, then we would be more satisfied.
I am thinking the same
How we can practically check this with physical demonstration?
In maths we keep oscillating between zero and infinity. So there has to be equivalence on both sides. The simple way of living peacefully is that keep leaving but never leave believing in yourself. 👍👍👍👍👍
Practically on field it's not postive suppose you give discounts 20% then after 10% in your object and you are shopkeeper -20×-10%= result at the point of shopkeeper he in loss
Wow amazing
Thank you so much Sir 🙏❤️
For explaining this in easy way.
Mujhe mam ne ek example se bataya tha ki agar koi karj leta hai to wo minus me chala gya fir aur dusri bar karj liya to fir minus means uske pas bahut sare paise ho gye lautane ke layak jisse wo positive ho gya .
I know ye thoda ajeeb hai par hum log bhi chhote the 😂 mundi hilate the bhale samajh aaye ya nahi school life is best ❤
I was in very confusion for three days, thank you very much Sir today I know it with the help of you.
this is explanation of how not why.
my question is WHY is it happening?
I thought it's wrong because in an equation we can multiply or divide any integer except zero. Here, in that way we can prove any integer =any integer, e.g 5 = -10
toh phir aap ye bhi bataeye ki "+" ko left se right le jaye toh "_" kiyu hota hai?
Perfect sir 😎👌🏻💯💯
Multiplication as a repeated addition
-3 x -2 means -(-3 + -3)
=-(-6)
=6
AM I WRONG? ❤
Great explanation 🙂🙂🙂
But this is an example... the question is why... what's the reason behind it??
Samajh sakte hai par mahsoos nhi hua
sir we don't need proof in 6th ...but practical proof as we give for positive numbers ...
Sir is very khatarnak
He can prove any thing
Tomorrow he will prove 1=0
Khatarnak hai bhannat sir🤣🤣🤣🤣🔥🔥🔥👍👍👍
Math nhi aata tujhe kya??
It's simple concept of modern algebra...
Wow sir you are amazing 🤩🤩🤩
If you learn trignometric functions, imaginary/complex numbers, complex planes, multiplication of complex numbers, and De Moivre's theorem, you can easily understand, but for those who have not learned them, the explanation will have to be like this video.
If you have knowledge about them, you might think: -5=(5)(-1)=(5)(-1+i・0)=5{cos(±π)+i・sin(±π)}, -3=(3)(-1) =(3)(-1+i・0)=3{cos(±π)+i・sin(±π)}, so (-5)×(-3)=5{cos(±π )+i・sin(±π)}×3{cos(±π)+i・sin(±π)}=15{cos(±π)+i・sin(±π)}²=15{cos( ±2π)+i・sin(±2π)}=15(1+i・0)=15(1)=15.
Explained very well sir👌👌
I have a different answer, no offense, which seems more logical than that answer.
The negative sign is just a sign to reverse direction. Positive sight describes movement towards positive infinity and negative sign just changes that direction. The basic purpose of a negative sign is just to change direction. If a negative changes the direction once (from positive to negative) then negative again will change that direction again (negative to positive.
In summary, negative sign by definition just changes direction and 2 negative signs cancel each other out. So we're left with our default sign, positive sign
Sir mujhe maths se bohot dar lagta tha, par sir aapse maths sikhne ke baad mujhe bohot jyada maths pasand aane lag gaya h sir, thank u very much
I never got doubt abot that .....u asked doubt but proved mathematically ....u equated to value ....
Appreciated,But You can also explain it bit easier way. With Number line and the concept of multiplication in x awis.
How to proof that we can apply distributive law on negative numbers?
Sir Doubt h
BODMAS KE hisab se phele bracket solve hoga na
Phele he simply hoke 0 hoga
Bracket
Wo to tab follow hota h jab bracket simplify nai hota
Yes bro I have the same doubt..
Sir ne...distributive law ka apply kia hai....Solve karne ke liya...agar BODMAS use karte toh...LHS pehle se hi...0 ho jata...isliye...aisa nahi kiya... distributive law ka apply kia
Question :- Equation me side change krne pr numbers or variables ka sign kyu change ho jata hai?
Please iss par v ek video banaiyega.
thank you sir for giving such a awesome explaination but can u please solve it on number line 🙏🏻🙏🏻🙏🏻🙏🏻
You proved it for numbers -5 and -3. How would you prove that your result holds for any number N?
Sir why we get zero when we multiply any number with zero?
multiplication is essentially the addition of a number a particular number of times. Doesn't matter how many times you take 0, you are going to have 0.
You can further prove it by real-life examples as that would be more relatable to understand,like taking 0 slices of cakes a 100 times would still mean to have 0 slices
@@shreyassharma8277 yes sir👍👍🙂
It's called real analysis which is taught in higher educational field that is during 11th or 12th or in future
Best teacher.
Kuchh bhi 🤣
Thats proving this through mathematical equations. Better to understand it intuitively. -5*-3=15
Suppose you have 5 rupees net worth. Then 5 is positive. If you have 3 bank accounts with 5 rupee each, then 5×3 times=15 is your total networth.
Now suppose you have 0 savings. Instead you have a deficit of 5 Rupees that you have obtained as a loan. This is your payable. It would be called -5. Suppose you have obtained 3 such loans from friends. So your total deficit or amount payable is -5×3 times = -15.
Now taking this example forward, suppose you have 5 Rupee loan (i.e. ‐5), but this time you have instead of 3 such incidence where you are in debt and owe your friends some money, it is the opposite instance where the 3 friends owe you money. This would be denoted as opposite of 3, or (-3). So basically loan (-5)*(-3) = 15. Your total receivables are 15. Your actual networth is in positive, as even though you dont have the cash, but youre not in deficit but instead have receivables of 15 Rupees.
In simple terms "negative" is the opposite of positive. To give another example from daily life, enemy is the opposite of friend. If having a friend is positive, and an enemy is negative, theoretically a friend's friend is a friend (+×+=+). A friends enemy is an enemy (+×-=-). An enemy's friend is an enemy (-×+=-) and an enemy's enemy is a friend (-×-=+).
I appreciate it and recommend to CLASS 6TH STUDENTS WHO DEAL WITH -VE INTEGERS FOR THE FIRST TIME AND COULDN'T UNDERSTAND WHAT'S GOING ON???!!?? JUST LIKE ME🙄🙄😃👍♥️
With due respect to the teacher, this is not a good way to explain this concept to kids, it can serve as a mathematical proof. But to develop intuition/feeling a better way is to follow the first principles. Example: Tell them that multiplication is nothing but repeated addition. So, when you do -5 * 3 you are tryign to subtract 5 now once but 3 times - intuition says it should be -15(show on number line). Also, multiplying -5 with 0 means taking our 5 zero times. Now you can explain that -5*-1 is a way to say that you "take out " 5 not once but minus once which means you are taking "out no 5 but minus 5 which is like giving 5 to some one (show on number line)
You earned a sub ❤
sir I thought you would teach this with some scary graph or limits, but it was smart way and very simple thanks a lot