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😂
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.
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 ..
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.
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 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.
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 ❤️
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.
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
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 ...
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
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 .
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 :)
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.
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
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
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 😁😀🙃🙂🙃🙂😬😬😬
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.
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.
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
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. 👍👍👍👍👍
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🙄🙄😃👍♥️
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|
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
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
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 😊😊😊
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.
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 ..
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
As a medical student,but you won my heart
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
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 must thank Aman Sir for providing us such a great knowledge.
It is not complicated but it is not taught in school
Right
It's simple concept of modern algebra...
Sir paheli baar ऐसा कुछ सीखने को मिला आनंद आ गया❤️❤️❤️❤️❤️ 👍👍👍👍👍👍👍👍👍👍👍👍👍
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.
Great explanation sir....
Simple problem and deep concept. Happy to see that people like u are working for maths.
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 ❤️
I thought it with mathematical reasoning,,
If a positive(correct) statement is negative(wrong),, then the sentence is +-=negative(wrong)
Similarly--=+
बहुत सरल तरीके से समझाया है, और शानदार तरीके से साबित भी कर दिखाया है। अति सराहनीय! धन्यवाद!
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 teacher is born to make you Love Maths !! Literally 👌👑 TODAY I'VE FOUND A GREAT MATHS TEACHER.🙏👑...
Currently in 9th and it's good to understand this concept
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.
I was hoping for an intuitive approach. But proving it algebraically is interesting as well.
Not really 🙄
@@anujpal9370 ?
It can be proved by uesing COMPLEX Analysis. convert the number into complex exponent form then do it.
Now that's what I call the beauty of maths! Thank you sir. ❤
Very good method
Keep it up 🙂
Thank you sir. Being a student of class 9th it is a pleasure for me to watch your videos
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
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
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...
SIR ISS CHANNELPE JEE KE SATH SATH ADVANCE LEVEL KI MATHS BHI DAALDENA DHEERE DHEERE 😁🔥✌
BEST CHANNEL FOR MATHS ❤
Sir, yeh kabhi socha hi nhi tha, aapko koti koti pranam
Mathematical problems always solve by mathematics visualization and imagination. That is the thing would all have to understand.
सर आप बहुत बड़े लेवल के अध्यापक है इसलिए..... 🙏🙏🙏🙏
Perfect sir 😎👌🏻💯💯
Good approach to teach basics of integers, which I never think before..............
True feeling of Maths 👍🏻👍🏻👍🏻
Sir aap ossum ho...
Your concept is just too good ..
I will spread your knowledge in my village.
Actually Bramhagupta had set all the rules about negative number .
But sir this is impressing 👍👍
Sir mne iss bare m kabhi socha hi nhii tha but aaj jb pta chala now I am soo surprised😅
You are great sir😊
Aapke liye dil se respect hai sir
Sir, you are great , greater and greatest 😍😍
Amazing proveing sir !! 👍👍
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....😥
After 5-6 years 😅😅 and now I know this thing 😅 thanks sir
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 :)
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.
Fantastic demonstration ! Well explained ! Thanks !
you are amazing sir
lots of love from Himachal ❤
Wow sir you are amazing 🤩🤩🤩
This is how properties of zero are proving other important concepts really amazing....❤❤❤❤.....infinitely
Great explanation 🙂🙂🙂
Very interesting to watch you👍🙏
Sir is very khatarnak
He can prove any thing
Tomorrow he will prove 1=0
Khatarnak hai bhannat sir🤣🤣🤣🤣🔥🔥🔥👍👍👍
Math nhi aata tujhe kya??
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
Best teacher.
Kuchh bhi 🤣
I am very excited when you are teaching 🥰🥰🥰🥰
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
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 😁😀🙃🙂🙃🙂😬😬😬
Wow amazing
Thank you so much Sir 🙏❤️
For explaining this in easy way.
Sir this was really a bhannat explaination
Explained very well sir👌👌
Great discovery by easy explanation.Thank you very much, Sir!
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
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
I never got doubt abot that .....u asked doubt but proved mathematically ....u equated to value ....
Jee 2025😂😂 Aspirants 🎉🎉❤All the best guys 😅
Great sir ji great गजब video था
Sir please bring more such videos this very helpful and make video on origin of imaginary number
I prefer this way
-ve * -ve = +ve. The end..😂😂😂
Faltu ghumna nhi hai..
You earned a sub ❤
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.
But where is why 😮😮😮😮
😂😂😂😂
I don't know why it felt I was listening aman dhattarwal for while
I was in very confusion for three days, thank you very much Sir today I know it with the help of you.
Thanks Sir ❤
hydrogen is gas
oxygen is gas
when they meet ,they turn into liquid called water
why?
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
We can also explain this in terms of chemistry. - attracts += - but - repels - =+ where +=repulsion and -= attraction.
Aap bahut achha padhate h sir jee 🇮🇳🇮🇳🇮🇳🙏🙏🙏🙏🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳
But still, you didn't answer the question "WHY"...
😂
Thank you so much sir for clearing my doubt.
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. 👍👍👍👍👍
Amazing concept Class 11th mei yahi concept samjh mei aaya jake 🌚
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🙄🙄😃👍♥️
That's Gajab 🔥❤️💫
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
You are best teacher of maths
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
I Think now you are become a great mathematician...
Sir ne to bhannat bolna hi band kar diye hain😕😕
Itne saloon ka doubt akhirkar Aaj khatm hua
Great teacher of Mathematics I have ever seen 👍
It can also be prove on number line easily.
thats what he did, but without plotting values on the number line
thank you sir for giving such a awesome explaination but can u please solve it on number line 🙏🏻🙏🏻🙏🏻🙏🏻
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|
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👍👍🙂
Apne mathematically ye samjha diya... Par ek negative ke saath ek aur negative ka multiplication ka significance samjha dijiye
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
This can be also done by : Let, -ve *-ve= -ve. Cancelling -ve boths sides =>1= -ve which is not possible therefore negative *negative =positive
Brilliant teacher....❤🔥
Thank you sir 🙏🏻🙏🏻 for explaining it's concept 😊