Negative × Negative = Positive ( but Why ??😕😏) | Bhannat Maths

[@arghojitsaha3568]

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😂

[@saranshmandal95]

kzbin.info/www/bejne/e5O3np-Bh66Ed7c

[@anonymous10809]

Oh bro really I am also in class 11 and after 5 years I came to know about this. 😂😂😂

[@mohd_sajid-nawaz123.]

Pata hi nahi chala yaar kaise samaay beetgaya 😕, 6 saal kab hogae

[@NaitikSinghA]

I am in 6 now

[@sumeetkage7160]

Me to 😂😂

[@aneekmandal5430]

I gave this question yesterday to sir on yesterday's batcheet aur sir aapka approach mujhe bohot accha laga

[@mannidahiya698]

bhai khel ga

[@chandranichaki9580]

kzbin.info/www/bejne/oqK5dpqMmsZnesk 😊😊😊

[@sanidhyaojha5676]

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😁

[@imdevil8329]

Kaise bhai hamey bhi batade jara...mtlb addition subtraction samjh aata h jumping se Multiply batan pls

[@aayushbhardwaj6735]

@@imdevil8329 he is right ,watch don't memorize video

[@uttamraj3786]

@@imdevil8329 multiplication is basically repeated addition.

[@khushsharma6470]

@@uttamraj3786 but bro -5 is added -3 times it doesn't make sense

[@saranshmandal95]

kzbin.info/www/bejne/e5O3np-Bh66Ed7c

[@royalbeastz8495]

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.

[@AnyaForgerIIT]

Very True

[@royalbeastz8495]

Mahh goshh!! Thanks for the likes ☺️

[@dab6923]

True

[@akshaysekhar4890]

Absolutely

[@harshitgupta7987]

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 ..

[@azharlatif6228]

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.

[@taimooramin5253]

As a medical student,but you won my heart

[@sukhchanbiswas6477]

I must thank Aman Sir for providing us such a great knowledge.

[@sameerkrishnavines706]

It is not complicated but it is not taught in school

[@abishaikh314]

Right

[@omkardeshpande5574]

Great explanation sir.... Simple problem and deep concept. Happy to see that people like u are working for maths.

[@inquisitiveindian36]

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

[@deepansh4961]

Not time line It's number line

[@Ignoubscg2019]

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)

[@lokeshbabukr264]

😂😂

[@j.u.4.n620]

I thought it with mathematical reasoning,, If a positive(correct) statement is negative(wrong),, then the sentence is +-=negative(wrong) Similarly--=+

[@f.fgaming8155]

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

[@munawwerhussain4960]

👌👌👌

[@arjitabhadauria3426]

Jodd or wot

[@shardultripathi1756]

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.

[@mridulsarmah2939]

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.

[@mridulsarmah2939]

@@ANUJCREATIONS_4518 If you want to learn mathematics you must follow methods. And methods are not imaginary, they are based on actual logic.

[@Bhargavi-pz9xf]

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

[@bktprajapat8882]

Sir paheli baar ऐसा कुछ सीखने को मिला आनंद आ गया❤️❤️❤️❤️❤️ 👍👍👍👍👍👍👍👍👍👍👍👍👍

[@ssstriples5105]

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.

[@arghyapramanik9912]

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

[@off-beatgaming4151]

Btw 2+2+2 is not 2*3 rather it is 3*2 because it means 3 groups of 2...

[@Tan-sj6bd]

Now that's what I call the beauty of maths! Thank you sir. ❤

[@prithwiraj1462]

It can be proved by uesing COMPLEX Analysis. convert the number into complex exponent form then do it.

[@rupishere]

Actually Bramhagupta had set all the rules about negative number . But sir this is impressing 👍👍

[@a3xccy379]

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 :)

[@nanigopalbehera7017]

I was hoping for an intuitive approach. But proving it algebraically is interesting as well.

[@anujpal9370]

Not really 🙄

[@nanigopalbehera7017]

@@anujpal9370 ?

[@vivekjaiswal33]

-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

[@siddhant5631]

Mathematical problems always solve by mathematics visualization and imagination. That is the thing would all have to understand.

[@subhamoybanerjee6724]

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.

[@JatinRanjan-v6y]

But where is why 😮😮😮😮

[@somachhukuwa9439]

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!

[@shahbajalam7680]

Thank you sir. Being a student of class 9th it is a pleasure for me to watch your videos

[@BMphysics455]

R/ sir what's the meaning, how can we feel that( -3) x (-5)= 15 Like 3 x 5 = 15 we feel it by repeated addition as 3+3+3+3+3=15

[@SyedSaad-pv5dx]

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 .

[@art_world-.]

Actually....😥

[@mayureshclasses2254]

This property of ring theory Algebraic structure (R,+,.) Additive inverse of ab is a(-b) a(-b)=-(ab)

[@mayureshclasses2254]

Where R is denotes ring Like real no ,complex no , matrices , and rational no.

[@cringetube6778]

Currently in 9th and it's good to understand this concept

[@TheKattarSanatani-108You]

This teacher is born to make you Love Maths !! Literally 👌👑 TODAY I'VE FOUND A GREAT MATHS TEACHER.🙏👑...

[@I_m_soul]

hydrogen is gas oxygen is gas when they meet ,they turn into liquid called water why?

[@shrutin3941]

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

[@Nature-rf7jk]

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?

[@satyammishra7273]

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

[@satyammishra7273]

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

[@Nature-rf7jk]

@@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

[@Nature-rf7jk]

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

[@satyammishra7273]

@@Nature-rf7jk Can you make it more clear I mean what exactly you are saying

[@z.sstudyjunction712]

But there is one more question.. Why we change the sign of a digit when it's transferred from one side of = to other ....?

[@Mir_0919]

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 ...

[@harshitpandey5252]

Nicely explained

[@karansahni6843]

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 ❤️

[@4farhan4]

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.

[@eiyp3]

What was his answer

[@sbacademy6059]

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

[@GursewakSinghOfficial]

SIR ISS CHANNELPE JEE KE SATH SATH ADVANCE LEVEL KI MATHS BHI DAALDENA DHEERE DHEERE 😁🔥✌ BEST CHANNEL FOR MATHS ❤

[@dynamicshiksha7560]

It's simple concept of modern algebra...

[@ABC-wn2id]

Sir please bring more such videos this very helpful and make video on origin of imaginary number

[@jackiechanrarevideos4108]

1. Telling the reason of something 2. Proving something Both are the different things actually. For example, if you ask someone the reason that why we drink water ? But instead of answering your question, if that person shows you other people drinking water and saying that he proved that we drink water. Will that be the correct answer of the question asked in the beginning?? I was started to watch this video in hope to know the Reason of the question but this video contains Proof, NOT THE REASON. Both are different things.

[@Heyreet01]

True

[@arnabsaha6848]

We can also explain this in terms of chemistry. - attracts += - but - repels - =+ where +=repulsion and -= attraction.

[@sam_ir__7461]

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

[@karthikkp2815]

Sir i tried understanding this on my own in childhood by using number line(ball jumping from number to number in the tables format)

[@शनिकर्ण]

me too bro

[@शनिकर्ण]

@@AmaanibnYasir ji ha vai sahab ji

[@AamirHLone]

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.

[@graduate_001]

Jee 2025😂😂 Aspirants 🎉🎉❤All the best guys 😅

[@technicalmaster3200]

This can be also done by : Let, -ve *-ve= -ve. Cancelling -ve boths sides =>1= -ve which is not possible therefore negative *negative =positive

[@pradeepdua3916]

True feeling of Maths 👍🏻👍🏻👍🏻

[@DOOM1947]

Sir aap ossum ho... Your concept is just too good .. I will spread your knowledge in my village.

[@chandanbanua6601]

Wow amazing Thank you so much Sir 🙏❤️ For explaining this in easy way.

[@bharatraval347]

बहुत सरल तरीके से समझाया है, और शानदार तरीके से साबित भी कर दिखाया है। अति सराहनीय! धन्यवाद!

[@shreevatsa_naik]

Sir ne to bhannat bolna hi band kar diye hain😕😕

[@mallarashid4120]

sir we don't need proof in 6th ...but practical proof as we give for positive numbers ...

[@dildaransari1888]

I was in very confusion for three days, thank you very much Sir today I know it with the help of you.

[@ayarottilsandeep545]

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.

[@SHaHMuNeiB4333]

Sir, you are great , greater and greatest 😍😍

[@EREN_YEAGER1548]

Multiplication as a repeated addition -3 x -2 means -(-3 + -3) =-(-6) =6 AM I WRONG? ❤

[@ayushkumthekar3439]

Sir is very khatarnak He can prove any thing Tomorrow he will prove 1=0 Khatarnak hai bhannat sir🤣🤣🤣🤣🔥🔥🔥👍👍👍

[@raghvendrasingh2990]

Math nhi aata tujhe kya??

[@isrolympiad459]

I never got doubt abot that .....u asked doubt but proved mathematically ....u equated to value ....

[@mehuljha4480]

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

[@mayanksinha3939]

Yes bro I have the same doubt..

[@barnalisarma9992]

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

[@sido157]

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 :)

[@lonefaixn9150]

Kitna time laga yeh lekhni mai jii

[@sido157]

@@lonefaixn9150 why are you seeing time behind it see the effort :) 10-15 mins maybe less or more

[@thepsychojoy4597]

Appreciated,But You can also explain it bit easier way. With Number line and the concept of multiplication in x awis.

[@sujoychowdhury8103]

-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

[@Anchit108]

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

[@editprov869]

-a × -b = ab ,but this is wrong Why??this is so because -a × -b = -1(a×b) = -1(ab) = -ab Eg., a = 3 b=4 -3 × -4 = -1(3×4) = -12 We can tell that -a × -b = ab or -ab

[@segayanmx4442]

Fantastic demonstration ! Well explained ! Thanks !

[@rogerd7646]

If you could explain with example what it means to multiple two negative numbers, then we would be more satisfied.

[@mubarakisonline]

I am thinking the same How we can practically check this with physical demonstration?

[@shyamsworldofmusic4378]

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

[@wiseindian8131]

this is explanation of how not why. my question is WHY is it happening?

[@rabrakha608]

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. 👍👍👍👍👍

[@parthgapratimsaha9632]

Sir plz come back to physics wallah....we miss your teaching very much....love from Kolkata sir❤️.

[@TheWhiStLerBoY]

thank you sir for giving such a awesome explaination but can u please solve it on number line 🙏🏻🙏🏻🙏🏻🙏🏻

[@mandeepgrang]

You proved it for numbers -5 and -3. How would you prove that your result holds for any number N?

[@saptarshisahoo5075]

The main reason i don't like this type of videos because these videos try to bring down the essence of mathematics. The correct explanation would be to identify the underlying concrete mathematical structure. Which goes on as: (R,+,*) forms a commutative ring. Rest can be deduced from the axioms of ring. Which he essentially did but without specifying the mathematical tools involved.

[@mukulsharma9010]

Sir I had a question We know that 5x3=15 If I multiply both sides by -1 -1(5x3)=-1(15) But this is not so? How and why?

[@robertlewandowski4466]

Best teacher.

[@himanshumaurya8181]

Kuchh bhi 🤣

[@asimsajjad101]

But still, you didn't answer the question "WHY"...

[@misterproton9839]

Perfect sir 😎👌🏻💯💯

[@boltez6507]

The distributive property was based on the convention therefore using it doesn't seem the right way...

[@arnavverma2461]

Wow sir you are amazing 🤩🤩🤩

[@uttamkumbhakar8599]

Why a positive number change negative number please explain

[@veertejaji36]

Great explanation 🙂🙂🙂

[@dskushwaha]

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.

[@gautamgupta6029]

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🙄🙄😃👍♥️

[@rdx-bhai990]

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|

[@sharadsingh3672]

Sir why we get zero when we multiply any number with zero?

[@shreyassharma8277]

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

[@sujaychatterjee3945]

@@shreyassharma8277 yes sir👍👍🙂

[@kruci6091]

Why does sign change when you change from LHS TO RHS?

[@utkarshdwivedi0076]

Explained very well sir👌👌

[@arossproduction5693]

That Proves the issue, but doesn’t define why..

[@gaurav7582]

Sir i have proved same using geometry, trigonometry and basic algebra

[@angelinageorge2278]

🙂

[@mridulsarmah2939]

Can you show me the proof where you used geometry and trigonometry?

[@chest_no_33]

After 5-6 years 😅😅 and now I know this thing 😅 thanks sir

[@bhaskardwivedi9722]

Samajh sakte hai par mahsoos nhi hua

[@mrboombastic_69420]

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

[@aryanbakshi5977]

Great teacher of Mathematics I have ever seen 👍

[@protonmind3528]

Sir I have a doubt. Why the sign changes when it goes from left to right or vice versa

[@Irrfannn]

You earned a sub ❤

[@targetgovexam0792]

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