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😂
exactly ... all the videos on youtube are explaining this in a stupid way that actually doesn't explain everything .. it turns out these youtubers themselves don't know anything..
Well said! 😂 Shortly, I'm going to write an article on this topic and would love to share with you all the answers to why the multiplication of two negative numbers is positive.
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.
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.
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 ..
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 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
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
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 actually made my own answer for this problem😅. I always thought when we multiply something with -1 we change its direction. Like 5 × -1 = -5 (negative direction) So ofcourse if we want to change direction two times (-1 × -1) we get back to positive direction Hope this helps And also i imagined it before learning physics. So my physics automatically gets better by this thinking
Nahi ..nahi multplication ko bina kisi justification se "reverse direction" se nahi jod sakte. Aap bohot creative ho, maths bhi bhot creative subject compared to any other subject. Lekan maths main unnecessary rules le aa na badi mushkil se sahi mana jaata hai. Cheezen simple se simple rehni chahiye.
@@aadilansari5997 but this was more logical thinking. I am sure it's not proof but if we think multiplication of negative numbers in that way it made a lot easier to imagine negative numbers Edit : Also somtimes proof doesn't help us to think why would that work. Proof is complete logical reasoning of why that work. But we have to use our mind to imagine. Example: We know a^x × a^y = a^(x+y) There is similar identity like that: log x + log y = log xy If we compare it like that we can see why log identy works. But it's proof doesn't help you think like that. Proof : Let N = log x and M = log y so x = 10^N and y = 10^M xy = 10^N × 10^M = 10^(M+N) Taking log both sides log xy = M + N so, log x + log y = log xy
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
Ok, About this I really have one more good proof which uses number line it goes as follows: Imagine yourself at the origin of number line at (0,0) now we all know 2×2=2+2, on no. Line it simply means while going to the positive no. Travel distance of 2 units 2 times Here, now this gives us that : the sign of first digit is positive so we know we will go to right (let +ve no. Be at right side and -ve at your left ).....so while the first digit is positive this means you are facing right and sign of 2nd digit(no. You are multiplying with) decides you move forward or backward......in our example that is 2×2 it gives look to the right and move 2 spaces ahead Now lets consider -2×-2 this means now acc to sign of first digit you are facing -ve numbers(You are looking to left) and sign of 2nd no. Says that move backwards, you are at origin now you are facing -ve and you will move to the opposite distance so you will move backwards 2unuts 2 times sooooooooooo you will get to positive 4 This is the metgod I really like, I dont know whether I was able to explain properly tho😅
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.
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.
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.
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 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 :)
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
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.
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
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
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
A true mathematician will oppose this example and it is not acceptable because you cannt write 0 as (-3+3) because we don't know where that 0 came from it may come from 8-8,6-6 etc but it is proved here because the statement is true that (-5)×(-3)=15
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🙄🙄😃👍♥️
Jab mein 5th me tha aur ye concept hume sikhaya gaya to as usual hum ratt lete hai in formula ko, but me aur mere kuch dost iske piche ka reason puchte the to teacher ko bhi nahi pata hota tha kyu ki vo bhi ratt kar pass hua hai 😂
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. 👍👍👍👍👍
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.
-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
Ramanuzan paradox If S1= 1+2+3+4+5+------------- And S2 = 2+4+6+8+------------ =2 (1+2+3+4+5+------------- ) So can we say S2 = 2 S1 (No, not at all, as S1=S2= infinity) Thus such applications are not true for infinitely increasing series where last number tends to infinity and the sum is infinite, they are only valid for infinitely decreasing series whose last number tends to zero and the infinite series sum has a finite value. Thus ramanuzan paradox is wrong.
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 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
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!
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
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)
