This was the BEST EXPLANATION OUT OF ALL EXPLANATIONS IVE RECEIVED IN SCHOOL AND ON THE INTERNET. I am very good in math and passed because I know the operations…but never could understand why a negative times a negative is a positive is a positive until now! Thank you
For years, I have responded to "Why does negative times negative = positive?" with "it's a debt being cancelled, which is a positive thing for you." To find a video that that so eloquently explains it in concrete concepts with visuals = I love it! I will be showing this video in all my high school courses.
I have a question. We always calculated the -x-=+ in this video as taking away debt but what does it mean for someone who doesn't have debt and only has money. Because sometimes in math there are additions like +4-(-2). In this case for someone who doesn't have debt in the first place and only has money how does -(-2) or -(-a) work here and how does he get richer which means positive? Can you kindly explain?
Im 39 years old and I would avoid using calculations of two negatives because I couldn't understand how to make it work in the real world. After watching this video it makes exact sense as to when to use this type of equation. I went down this rabbit hole because I was learning algebra again and I saw a question that had -1^2 and I assumed the answer was -1 and so I ended up here after a few hours of pondering why two negatives = a positive. Awesome video and I wish they taught this way in shcools tbh.
These are the types of comments that make my day. Thank you for sharing that. And if you have any further questions about anything, then drop me a message at anytime.
Finally, someone answers the WHY a minus times a minus equals a positive! Everyone else is trying to walk a number line this way or that. THANKS SO MUCH!
I'm an English teacher in Japan, and have had my students try to explain these equations, and I have to say that this is the best explanation of neg. X neg. = pos. that I have come across. I still have a couple issues with it because I just see it as somehow ultimately reduced to zero. But then again, my friends call me the ultimate reductionist. haha. Anyway, you are an excellent teacher and your students are very lucky.
The best it could be is 0. In his last example - 2 x -3 = + 6 he then reveals the 6 that was in the bank, if you are just seeing the expression ( what he shows is not an equation) how do you know what was in the bank. I want to see it on a number line.
@@simpleman283 -2 x -3 = 6 is an Equation and not an expression. I'm not sure that I understand your main question, but it sounds like you are doubting how there could be $6 in his bank account at the end. Consider it like this, if you started with $6 in your account, then racked up $6 credit card debt, then your bank account is worth zero. If your dad said he will pay off your cc bill then you are back to $6 again.
@@ramymelhem -2 x -3 = 6 is an equation, agreed. I was talking about - 2 x -3. To me it is just a rule we follow to all stay on the same page, like PEMDAS. They could have made the rule from left to right no matter the operation. Anyone can see -3 + -3 + -3 + -3 + -3 = -3 x 5 = -15 or -5 + -5 + -5 = -5 x 3 = -15. In your explanation you told us to ignore the $6 that was in the bank and look at the expression -2 x -3 then pull it down after we got to 0. In order to evaluate an expression we need all the information, there could have been $6 in the bank or $7. To me subtracting groups is not multiplication. If that is truly subtracting groups then we need a new math symbol such as (G). -(2)G(-3). I know you put a lot of thought and effort into your presentation and I am not trying beat you up in any way but it still is not very clear.
@@simpleman283 I'm honestly not sure if you are trolling with your arguments but I will assume that you mean well. First off, I didn't invent this explanation. I am re-explaining it the way the founder of this entire methodology explained it in his book 1500 years ago. Now allow me to attempt to counter argue your statements. 1. -3 + -3 +-3 + -3 + -3 is not -3 x 5 but rather 5 x -3. It won't impact the answer, but it does make a difference in terms of understanding the literal meaning of the expression. We have 5 groups of -3 in 5 x -3. 2. I suggested to ignore the red tiles (+2 x +3) to draw attention to the blue tiles which represented the credit card statement so that we could derive an expression for it. 3. It's absolutely and utterly irrelevant as to whether we started with $6, $7, or $82.32 in the bank account. What matters is that removing a debt increases your net-worth. That is basic financial literacy. 4. It's not up to you or me to decide whether or not "removing groups" is or isn't considered to be multiplication. Multiplication in its essence refers to deriving "repetitive groups" of any asset, debt, abstract, or non-abstract entity. X=groups plain and simple. You can either 'add' groups or you can 'remove' groups and both would be considered 'multiplication'. There is no need to over-complicate it. Why would you need to start a new math symbol 'G' to represent what an 'x' already does perfectly. How would that change Anything? I feel like the gap in your understanding arises entirely from a mathematical literacy perspective. You understand the difference between an Equation and an expression perfectly fine, but you aren't totally clear as to how multiplication expressions and symbols truly function.... and then you aren't completely sure as to what the positive and negative symbols in front of each number represents. I go through that in the first 3-min of the video. And all that is totally ok because we are all here to learn. Let me know if you have any other questions. I'm happy to help. Let me know if you have any other questions.
🙏🏾🙏🏾🙏🏾 Thank you, this is the 3rd video I've watched on this topic. I was confused with the number line explanations. The day you've related this to money intuitively makes so much sense to me.
Love this so much!! I’m a teacher and I always try to answer the, “why?” and relate it to real for the kids. I was thinking about negative numbers and couldn’t figure out why it works. Thank you for teaching me so I can possibly teach someone else in the future! Take care.
I have a question. We always calculated the -x-=+ in this video as taking away debt but what does it mean for someone who doesn't have debt and only has money. Because sometimes in math there are additions like +4-(-2). In this case for someone who doesn't have debt in the first place and only has money how does -(-2) or -(-a) work here and how does he get richer which means positive? Can you kindly explain?
@Ramy Melhem Naturally,if i have 6$ before I could payoff my debt and remain zero in savings. 👉I have debt of 6$ my friend paid off it now iam free of debt and I have zero amount with me. It's null zero, How is it positive practically? please explain.
First time in my life this ever made sense! I asked this in a high school math class and no one could ever really explain it. I love how you use the words to create a logical argument that mirrors the symbolic math functions.
Thanks so much for sharing this, Chris. I love helping people realize this sort of thing and when it brings clarity then I'm happy. If you are still interested in diving deeper into this topic then I encourage you to read upon a 7th century mathematician named Brahamgupta who invented this entire system to keep track of his money.
I've known since primary school the "rule" for negative x negative and I have watched this and many other videos on this.. but my logic was the answer is the difference between the "starting point" being a negative and how many places it would move in the positive direction. Which would make the new position zero and the difference between that was +6. Is this right? The answer is just the difference between the starting and end point/sum? Rather than literally going from negative nothing to positive something which would mean a movement of +12 which is what I think mixes people? Rewording my clarification, the negative x negative equation is only giving the total movements and not the literal new position or total of "things" or "dollars"..?
I am not in school, and don't really need to know why 2 negatives make a positive. I just WANT to know. And after scouring the internet, this is BY FAR the best explanation.
fabulous!!! My grandson didn't want to just learn the rules.. he wanted to understand it. You are the only one I could find that taught it in real world examples. Thank You!!
I'm 60 years old and about to take my GED math test. This has been the most valuable video ive seen to help me fully comprehend multiplying negative numbers . THANK YOU!
Thanks was awesome...Just started study Astronomy and black holes at University and getting overwhelmed by the maths...That video helped a lot though....any other videos you'd recommend??
Excellent video. This is what makes TH-cam cool. I love learning on YT and I love knowing that someone cared enough to explain this to the world. Thank you so much!
I am compelled to say maths would be demystified and made easy if the world acknowledged that a lot of people who find maths hard are visual learners who do not like cramming maths rules and formulas only but to seek to understand how and why, hence there is a there is a great need to train visual teachers for maths alone as a stand alone speciality of teaching. The Chinese saying that there is no bad student but only a bad teacher is true. You are the best teacher on youtube TBH, please continue to make more math/educational videos.
Wow Precious Dee. I am so honored and humbled at the eloquence of your sentiment. Thank you so much for taking time out of your day to acknowledge my efforts at bringing a more visual aspect to maths education. I've been meaning to revive my channel and you have definitely inspired me to do so in the near future. Thank you.
It makes perfect sense and seems so obvious when it's explained like this! I wonder why so many of us including myself and math teachers couldn't see it until it was demonstrated in this video so thoroughly and eloquently!
I have a question. We always calculated the -x-=+ in this video as taking away debt but what does it mean for someone who doesn't have debt and only has money. Because sometimes in math there are additions like +4-(-2). In this case for someone who doesn't have debt in the first place and only has money how does -(-2) or -(-a) work here and how does he get richer which means positive? Can you kindly explain?
Best video on TH-cam. A dollar saved is a dollar earned. If I borrow $10 (-10), taking away that negative is +10 for me. Thinking that you have an extra $10 is what confuses people. The $10 that was borrowed was something that I never had, so getting back to zero is a plus 10 for me. Thanks for the vid!!!
@Ramy Melhem Naturally,if i have 6$ before I could payoff my debt and remain zero in savings. 👉I have debt of 6$ my friend paid off it now iam free of debt and I have zero amount with me. It's null zero, How is it positive practically? please explain.
Hi Ramy! Very cool video! I do have a question though. If you run this thought experiment in reverse, with the guy having zero dollars in his account (not a debt) and starting with the equation "-2 x -3 =", does this analogy still work? Because you are no longer subtracting debt, because there is no debt to begin with. I guess i'm struggling to understand how something can be made from nothing. Hope this makes sense : )
Hi Liam. Thats such a great question that I will be happy to answer. How can something be made from nothing? Our entire monetary currency system is debt based. I encourage you to research how our debt-based system works, but essentially, money is created out of thin air by central banks on a daily basis and loaned out in a way that is impossible to pay back in full by the population in mass. We are a debt-based society. Thats a bit deeper than you are asking though so let me cut to the chase. Having $0 in your bank account and then presenting that person with a scenario of -2 x -3 would ultimately mean you would be removing 2 groups (-2) of $3 debts (-3). How could you be in debt when ur bank account states $0? Perhaps you bought 2 bags of chips( $3 each) on your credit card. The credit card company wouldve paid that $6 on your behalf which technically means that your net worth is not $0 as ur bank account states, but rather -$6 because you owe the credit card company $6. Paying that debt down means uve increased your valuation by +$6 and now ur back at $0. (-$6 to $0 net worth) is an increase of $6 (in. +$6). I hope that makes sense.
Excellently explained Ramy Melhem Sir! I am one of those people who just took this - x - = + and didn't ask why. Thank you for making me love math even more.This logic will be with me forever now. Respect to you! :)
How does this explanation follow through with a third multiplication. Since three negatives is negative again. Great explanation just not sure how it follows into the next spot.
I like this analogy. It's a great way to remember the rules but it does not explain why the mathematical symbols work the way that they do. I use analogies like this once I feel confident that my students understand the why.
bro i am 13 years old and now i have realised that you are the best for explaning maths this is a basic but main question that everybody has and only few of us know thank you for explaning i have seen and asked many videos for this thanks you have got a new subscriber
After reading god know's how many articles and watching X number of videos and being none the wiser, it finally makes sense! Thank you so much for posting this video and your simple explanation! It has never been explained to me that the first operator is essentially stating whether to add or subtract something and the second whether the thing being added or subtracted is positive or negative...I always thought of it more literally. In school, we were taught to accept that a negative times a negative is positive, but never why.
I'm happy I was able to make a difference in your understanding of negative multiplication. It's viewers like you who I appreciate. 🙏🙏 Let me know if you have any other questions.
Best video so far! Still wrapping my head around it. How would you change the last equation of -2 x -3 to equal zero? while still starting with 2 groups of negative 3? So I am asking (using your example with the bank) If I had 2 groups of negative 3 in the bank, what would I have to multiply to equal zero, instead of having leapt forwars past zero to 6 plus.
You are correct, you end up at zero, BUT you went in the positive direction 6 places. You have zero dollars, but you are 6 dollars richer. That is because when you do get $6 or any other amount, you get to keep it, by not having to pay the old debt. It is not about a real number, it is about which way you went & how much you went.
Awesome video!! Was just wondering how you did this set up. I have tried to get it to look like yours....Any suggestions? Also, which document camera do you use? Thank you!!
Sorry for theate response. I use an overhead camera mounted about a foot above my head on a selfie stick mounted through a shelf. I don't use a document t camera. I have a second camera on my desk for the face shot plus an overhead light to light up my desk. My mic runs through a preamp which I then sync up in post using Adobe premiere. I hope that was helpful. Let me know if you have any questions.
Thank you! I’m helping an awesome 23 year old who never had the chance to go to school but is going for his GED. This helps so much to explain something I realized I never fully understood! Great job; way better than any other explanation I’ve seen!
8 months ago I came hunting the answer to this question. You were very patient with me and helped me, finally get it. I came back to say Thank You again, Merry Christmas Mr. Melhem.
Tq so much brother. But to explain about negetive sign in division. Should we say " divide the debt into two person? Then you will be richer which is positive" ?? Tq for the fast reply
This is a master class of patience and complete lack of ego. The ridicule I felt not understanding this stopped me from trying and me avoid maths education. Things could have been different and will be from now on wards. Thank you
Sorry you had to go through that frustration through all those years. Truly special to hear that I was able to help change that in some capacity. Keep fighting the battle and if you have any questions please let me know.
Ok but in a system if you subtract the debt it will always become 0 right???Is not a set concept like there is -6 and if you do -2 * -3 it will take away the debt.so it will be 0??
If you're subtracting debt then why does -2x-3=-6 and not -4? If I owed my bank 2 dollars and I wanted 4 dollars in my account I would have to give them 6 dollars but what you're saying is I magically get $8?
Melvin Fuentes Hey Melvin Fuentes. Thanks for taking the time to watch this video. Please allow me to clarify. -2 x -3 would mean "remove" 2 groups of $3 "debt". Slow down and think about what that means. Removing 2 piles of $3 debt makes your overall net worth $6 richer (positive)....not 8 and not 4. That would be like saying you will pay back $3 debt today and another $3 debt tomorrow. Ur net worth just went UP (+) 6bucks. When dealing with money, the "solution" to a multiplication problem always, always indicates whether u are getting richer (+) or poorer (-). And removing a debt, as -2 x -3 suggests, always makes u richer (+ answer) in the end. I hope that helps. If not, then let's continue this conversation. I want to make sure that you've totally got this. :)
The best explanation I've ever heard and I worked as a teacher in a middle school. You really managed to say why. I've thought about it in a similar way but applied it to the four quadrants on a graph: So, quadrant I = adding groups of earnings (positive), II = subtracting groups of earnings (negative), III = subtracting groups of debt (positive) and IV = adding groups of debt. In other words, add/substract is on the x axis and earnings/debt is on the y axis. Add all quadrants together and you're back at (0,0) or $0 in your terms - it all balances out. Does that make sense?
Thank you for the compliment. That means a lot to me especially since its coming from a fellow teacher. In regards to the 4 quadrant system, I've never though about it that way. I love it! Thanks for sharing. In the end, both of us are attacking the heart of mathematical linguistics in terms of what the "positive" and "negative" symbols actually mean. Everybody else, it seems, comes up with goofy analogies that work, but don't explain "why".
Ramy Melhem Yeah man, no one was explaining why and just teaching by rote. I was the school's music teacher and my students would come to me for help on their math homework. One kid asked why a negative times a negative equals a positive and I couldn't do it. So I barged into the next math department meeting and asked if anyone could explain why without giving me some weird memorization trick; no one could. I came up the that quadrant thing so I could visually see it. If you plot 2x3 with all the +/- variations, you get four rectangles that are all the same size. Combine them and you get the same rectangle that's 4x bigger, obviously, but it's interesting to see they balance each other out - quadrants I and III are positive and II and IV are negative. Like balancing equations I guess. Anyway, thanks again and keep up the good work - your students are lucky to have you.
Thank you so much for explaining! I never used to understand why two negatives multiplied with each other equaled a positive until I came across this video.
Gold bro! We all just became richer watching this video!
You got pinned.
Yes we all became richer.
I am 48 years old and this is the first time in my life that a - x -=+ made sense to me. Thank you. 🙌
Thank you....ur awesome
I am 49!
And me! Also 48 what happened to high school math in the 80’s????
sanskarimathematics.blogspot.com/2020/12/negative-times-negative-makes-positive.html
I'm 47 and ditto.
This is the best explanation why a negative X negative = positive. Finally a concept I understand! Thank you so much!
Thank you. I'm 48 and that's the first time I understand why it made it a positive. Before I did it because it was what you were supposed to do.
This man is the real MVP. I can never explain this properly, now I can.
Thank you brother. 🙏
This was the BEST EXPLANATION OUT OF ALL EXPLANATIONS IVE RECEIVED IN SCHOOL AND ON THE INTERNET. I am very good in math and passed because I know the operations…but never could understand why a negative times a negative is a positive is a positive until now! Thank you
Thanks so much. I appreciate the lovely sentiment.
As a math teacher this was one of the best visual explanations I have come across. I hope you don't mind if I use it.
Thank you. I'd be happy if you shared it. :)
sanskarimathematics.blogspot.com/2020/12/negative-times-negative-makes-positive.html
sanskarimathematics.blogspot.com/2020/12/negative-times-negative-makes-positive.html
For years, I have responded to "Why does negative times negative = positive?" with "it's a debt being cancelled, which is a positive thing for you." To find a video that that so eloquently explains it in concrete concepts with visuals = I love it! I will be showing this video in all my high school courses.
I have a question. We always calculated the -x-=+ in this video as taking away debt but what does it mean for someone who doesn't have debt and only has money. Because sometimes in math there are additions like +4-(-2). In this case for someone who doesn't have debt in the first place and only has money how does -(-2) or -(-a) work here and how does he get richer which means positive? Can you kindly explain?
@@saarahmuztanazaman7103subtracting debt is adding money to ur card
Im 39 years old and I would avoid using calculations of two negatives because I couldn't understand how to make it work in the real world. After watching this video it makes exact sense as to when to use this type of equation.
I went down this rabbit hole because I was learning algebra again and I saw a question that had -1^2 and I assumed the answer was -1 and so I ended up here after a few hours of pondering why two negatives = a positive. Awesome video and I wish they taught this way in shcools tbh.
These are the types of comments that make my day. Thank you for sharing that. And if you have any further questions about anything, then drop me a message at anytime.
Finally, someone answers the WHY a minus times a minus equals a positive! Everyone else is trying to walk a number line this way or that.
THANKS SO MUCH!
Finally 😊
@@ramymelhem yes, finally!
I'm an English teacher in Japan, and have had my students try to explain these equations, and I have to say that this is the best explanation of neg. X neg. = pos. that I have come across. I still have a couple issues with it because I just see it as somehow ultimately reduced to zero. But then again, my friends call me the ultimate reductionist. haha. Anyway, you are an excellent teacher and your students are very lucky.
Thank you very much. 🙏🙏means a lot. This explanation is the actual reasoning behind the inventor's methodologies.
The best it could be is 0. In his last example - 2 x -3 = + 6 he then reveals the 6 that was in the bank, if you are just seeing the expression ( what he shows is not an equation) how do you know what was in the bank. I want to see it on a number line.
@@simpleman283 -2 x -3 = 6 is an Equation and not an expression. I'm not sure that I understand your main question, but it sounds like you are doubting how there could be $6 in his bank account at the end. Consider it like this, if you started with $6 in your account, then racked up $6 credit card debt, then your bank account is worth zero. If your dad said he will pay off your cc bill then you are back to $6 again.
@@ramymelhem -2 x -3 = 6 is an equation, agreed. I was talking about
- 2 x -3. To me it is just a rule we follow to all stay on the same page, like PEMDAS. They could have made the rule from left to right no matter the operation. Anyone can see -3 + -3 + -3 + -3 + -3 = -3 x 5 = -15 or -5 + -5 + -5 = -5 x 3 = -15. In your explanation you told us to ignore the $6 that was in the bank and look at the expression -2 x -3 then pull it down after we got to 0. In order to evaluate an expression we need all the information, there could have been $6 in the bank or $7. To me subtracting groups is not multiplication. If that is truly subtracting groups then we need a new math symbol such as (G). -(2)G(-3). I know you put a lot of thought and effort into your presentation and I am not trying beat you up in any way but it still is not very clear.
@@simpleman283 I'm honestly not sure if you are trolling with your arguments but I will assume that you mean well. First off, I didn't invent this explanation. I am re-explaining it the way the founder of this entire methodology explained it in his book 1500 years ago. Now allow me to attempt to counter argue your statements.
1. -3 + -3 +-3 + -3 + -3 is not -3 x 5 but rather 5 x -3. It won't impact the answer, but it does make a difference in terms of understanding the literal meaning of the expression. We have 5 groups of -3 in 5 x -3.
2. I suggested to ignore the red tiles (+2 x +3) to draw attention to the blue tiles which represented the credit card statement so that we could derive an expression for it.
3. It's absolutely and utterly irrelevant as to whether we started with $6, $7, or $82.32 in the bank account. What matters is that removing a debt increases your net-worth. That is basic financial literacy.
4. It's not up to you or me to decide whether or not "removing groups" is or isn't considered to be multiplication. Multiplication in its essence refers to deriving "repetitive groups" of any asset, debt, abstract, or non-abstract entity. X=groups plain and simple. You can either 'add' groups or you can 'remove' groups and both would be considered 'multiplication'. There is no need to over-complicate it. Why would you need to start a new math symbol 'G' to represent what an 'x' already does perfectly. How would that change Anything?
I feel like the gap in your understanding arises entirely from a mathematical literacy perspective. You understand the difference between an Equation and an expression perfectly fine, but you aren't totally clear as to how multiplication expressions and symbols truly function.... and then you aren't completely sure as to what the positive and negative symbols in front of each number represents. I go through that in the first 3-min of the video. And all that is totally ok because we are all here to learn.
Let me know if you have any other questions. I'm happy to help.
Let me know if you have any other questions.
That man right there is mowing yards for a bag of chips, a soda, and bus money. Respect.
I'm so old, I get that...
In a nutshell 'negative' is a concept to denote opposite concepts, very simple. Any how your way of explaining is excellent, awesome!!!
🙏🏾🙏🏾🙏🏾 Thank you, this is the 3rd video I've watched on this topic. I was confused with the number line explanations. The day you've related this to money intuitively makes so much sense to me.
At 56, I've been using negative numbers my whole life. Now, for the first time, I understand how they work. Thanks a lot.
Thank you for sharing this. I appreciate you. 🙏
Love this so much!! I’m a teacher and I always try to answer the, “why?” and relate it to real for the kids. I was thinking about negative numbers and couldn’t figure out why it works. Thank you for teaching me so I can possibly teach someone else in the future! Take care.
Thank you, Kristina.
Ramy Melhem You’re welcome! Do you have an Instagram with your videos?
I have a question. We always calculated the -x-=+ in this video as taking away debt but what does it mean for someone who doesn't have debt and only has money. Because sometimes in math there are additions like +4-(-2). In this case for someone who doesn't have debt in the first place and only has money how does -(-2) or -(-a) work here and how does he get richer which means positive? Can you kindly explain?
@@saarahmuztanazaman7103numbers dont have debts
He is lending his money out! yay for getting richer!@@saarahmuztanazaman7103
Man you sure made me finally understand this after years of nobody giving me a good explanation! THANK YOU!
@Ramy Melhem Naturally,if i have 6$ before I could payoff my debt and remain zero in savings.
👉I have debt of 6$ my friend paid off it now iam free of debt and I have zero amount with me.
It's null zero,
How is it positive practically? please explain.
Because the friend paid it "adding" income to the bank account (no such thing as a free lunch)@@mohammadnaseeruddinshad5462
First time in my life this ever made sense! I asked this in a high school math class and no one could ever really explain it. I love how you use the words to create a logical argument that mirrors the symbolic math functions.
Thanks so much for sharing this, Chris. I love helping people realize this sort of thing and when it brings clarity then I'm happy. If you are still interested in diving deeper into this topic then I encourage you to read upon a 7th century mathematician named Brahamgupta who invented this entire system to keep track of his money.
I've known since primary school the "rule" for negative x negative and I have watched this and many other videos on this.. but my logic was the answer is the difference between the "starting point" being a negative and how many places it would move in the positive direction. Which would make the new position zero and the difference between that was +6. Is this right? The answer is just the difference between the starting and end point/sum? Rather than literally going from negative nothing to positive something which would mean a movement of +12 which is what I think mixes people? Rewording my clarification, the negative x negative equation is only giving the total movements and not the literal new position or total of "things" or "dollars"..?
Your logic is spot on
THE BEST EXPLANATION!!!
Thank you so much. You don't know how much peace you gave me by your explanation.
Wow...that makes me so happy to hear. Let me know if you have any further questions about anything else math or science related
I am not in school, and don't really need to know why 2 negatives make a positive. I just WANT to know. And after scouring the internet, this is BY FAR the best explanation.
fabulous!!! My grandson didn't want to just learn the rules.. he wanted to understand it. You are the only one I could find that taught it in real world examples. Thank You!!
Special words indeed. Thank you so much 🙏. I wish you and your grandson the very best.
I am a maths tutor , I have a student always asking "why" so I'm here. Thank you for explaining though its pretty hard for kids to understand.
The why portion of math always requires higher level thinking to understand.
I'm 60 years old and about to take my GED math test.
This has been the most valuable video ive seen to help me fully comprehend multiplying negative numbers . THANK YOU!
You made it so real man
Thanks was awesome...Just started study Astronomy and black holes at University and getting overwhelmed by the maths...That video helped a lot though....any other videos you'd recommend??
Am also curious about division of negative/negative numbers
Excellent video. This is what makes TH-cam cool. I love learning on YT and I love knowing that someone cared enough to explain this to the world. Thank you so much!
I love how you put it. 😍 Absolutely my pleasure.
I am compelled to say maths would be demystified and made easy if the world acknowledged that a lot of people who find maths hard are visual learners who do not like cramming maths rules and formulas only but to seek to understand how and why, hence there is a there is a great need to train visual teachers for maths alone as a stand alone speciality of teaching. The Chinese saying that there is no bad student but only a bad teacher is true. You are the best teacher on youtube TBH, please continue to make more math/educational videos.
Wow Precious Dee. I am so honored and humbled at the eloquence of your sentiment. Thank you so much for taking time out of your day to acknowledge my efforts at bringing a more visual aspect to maths education. I've been meaning to revive my channel and you have definitely inspired me to do so in the near future. Thank you.
Thanks for the awesome lesson!
Thank you Heather. I appreciate it. 🙏
It makes perfect sense and seems so obvious when it's explained like this! I wonder why so many of us including myself and math teachers couldn't see it until it was demonstrated in this video so thoroughly and eloquently!
Thank you very much, sir
I have a question. We always calculated the -x-=+ in this video as taking away debt but what does it mean for someone who doesn't have debt and only has money. Because sometimes in math there are additions like +4-(-2). In this case for someone who doesn't have debt in the first place and only has money how does -(-2) or -(-a) work here and how does he get richer which means positive? Can you kindly explain?
@@saarahmuztanazaman7103numbers dont have debts
Best video on TH-cam. A dollar saved is a dollar earned. If I borrow $10 (-10), taking away that negative is +10 for me. Thinking that you have an extra $10 is what confuses people. The $10 that was borrowed was something that I never had, so getting back to zero is a plus 10 for me. Thanks for the vid!!!
Dibiguous thanks Dibiguous. I appreciate the awesome feedback. All the best my friend.
This is so wonderful! Thank you! Such a difficult concept to explain, but you did such a great job doing it.
Thanks very much
@Ramy Melhem Naturally,if i have 6$ before I could payoff my debt and remain zero in savings.
👉I have debt of 6$ my friend paid off it now iam free of debt and I have zero amount with me.
It's null zero,
How is it positive practically? please explain.
Wow! I was looking for a good youtube video to help me teach one of my students. Great job, this makes so much sense. Great job!
Thanks so much Amy. 🙏
Hi Ramy!
Very cool video! I do have a question though. If you run this thought experiment in reverse, with the guy having zero dollars in his account (not a debt) and starting with the equation "-2 x -3 =", does this analogy still work? Because you are no longer subtracting debt, because there is no debt to begin with. I guess i'm struggling to understand how something can be made from nothing. Hope this makes sense : )
Hi Liam. Thats such a great question that I will be happy to answer.
How can something be made from nothing? Our entire monetary currency system is debt based. I encourage you to research how our debt-based system works, but essentially, money is created out of thin air by central banks on a daily basis and loaned out in a way that is impossible to pay back in full by the population in mass. We are a debt-based society. Thats a bit deeper than you are asking though so let me cut to the chase.
Having $0 in your bank account and then presenting that person with a scenario of -2 x -3 would ultimately mean you would be removing 2 groups (-2) of $3 debts (-3). How could you be in debt when ur bank account states $0? Perhaps you bought 2 bags of chips( $3 each) on your credit card. The credit card company wouldve paid that $6 on your behalf which technically means that your net worth is not $0 as ur bank account states, but rather -$6 because you owe the credit card company $6. Paying that debt down means uve increased your valuation by +$6 and now ur back at $0. (-$6 to $0 net worth) is an increase of $6 (in. +$6).
I hope that makes sense.
@@ramymelhem Thank you ! 😊
The debt analogy really helped, I found imagining the debt as a physical object, like a -1$ coin, helped me see how it worked
Wow, that was amazing. Why tf can't this just be taught in elementary school.
because its boring
sanskarimathematics.blogspot.com/2020/12/negative-times-negative-makes-positive.html
@@TKMKT1516 No, you are just a dumbass.
Last representation was much helpful and intuitive. Great work.
Excellent!!!!! I will use this. Thank you so much.
Sir does this same logic applies when we add or substract an postive and negative intergers?😅
Best math vid I came across in a while. Good job man!
Thank you, Esteban. 🙏
After a lot of research this is the only video which made sense about negative times negative=positive. Best video ever about this topic. Loved it 💖
Thank you so much 🙏
How? He basically said subtracting from a negative is positive....i.e -5-5= 10 he basically proved that
explaining this way is very useful. thanks
but how can we explain it on the number line?
Thank you. I made a separate video for that.
For the past 50 years I never understood this concept until now. Thanks
This is genius!!! Thank you so much! Like you, I was trolling TH-cam, trying to find out WHY? WOW.
Excellently explained Ramy Melhem Sir! I am one of those people who just took this - x - = + and didn't ask why. Thank you for making me love math even more.This logic will be with me forever now. Respect to you! :)
Thank you Bhakti. And If you have any further questions, then please let me know.
How does this explanation follow through with a third multiplication. Since three negatives is negative again. Great explanation just not sure how it follows into the next spot.
It would transform the equation into a 2 step system.
Thanks Mr Melhem. I was struggling to explain the negative concept to my kids and your explanation helped greatly.
Great to hear, Jason. Let me know if you have any other mind-squirming math concepts that you'd like me to take on.
This was perfect. What a great way to explain it. Subscribed for sheer awesomeness.
Thanks for subscribing. I haven't made any content for years now, but comments like this definitely motivate me to want to make a return.
Thank you for this video, it really helped me understand the logic of negative numbers.
this is very well explained, thanks
Thank you so much. 🙏🙏🙏
Love +
Hate -
Love to love = Love
Love to hate = Hate
Hate to love = Hate
Hate to hate = Love
I like this analogy. It's a great way to remember the rules but it does not explain why the mathematical symbols work the way that they do. I use analogies like this once I feel confident that my students understand the why.
If someone smacks you in the face, and then you hit him back that going to make you feel positive.
This is totally brilliant! You’re a superb teacher.
Thank you very much 😊
finally at age of 38 years i understood why it iS like that . all these years i was trying to figure out why it is like that :D THANKS .
It makes me really happy reading these types of stories. Thank you, Mehraj. 🙏
sanskarimathematics.blogspot.com/2020/12/negative-times-negative-makes-positive.html
bro i am 13 years old and now i have realised that you are the best for explaning maths this is a basic but main question that everybody has and only few of us know thank you for explaning i have seen and asked many videos for this thanks you have got a new subscriber
@M.J-lb9zc thank you. You made my day ❤️
After reading god know's how many articles and watching X number of videos and being none the wiser, it finally makes sense! Thank you so much for posting this video and your simple explanation! It has never been explained to me that the first operator is essentially stating whether to add or subtract something and the second whether the thing being added or subtracted is positive or negative...I always thought of it more literally. In school, we were taught to accept that a negative times a negative is positive, but never why.
I'm happy I was able to make a difference in your understanding of negative multiplication. It's viewers like you who I appreciate. 🙏🙏 Let me know if you have any other questions.
Thank you very much for the lession
@@ayushagarwal5362 you're very welcome ❤️
Thank you. Even I understand! With your notation there is no place for confusion.
Алексей Воронцов Thank you
Best video so far! Still wrapping my head around it. How would you change the last equation of -2 x -3 to equal zero? while still starting with 2 groups of negative 3? So I am asking (using your example with the bank) If I had 2 groups of negative 3 in the bank, what would I have to multiply to equal zero, instead of having leapt forwars past zero to 6 plus.
You are correct, you end up at zero, BUT you went in the positive direction 6 places. You have zero dollars, but you are 6 dollars richer. That is because when you do get $6 or any other amount, you get to keep it, by not having to pay the old debt. It is not about a real number, it is about which way you went & how much you went.
Thank you! This makes it very clear. Great video!
Awesome video!! Was just wondering how you did this set up. I have tried to get it to look like yours....Any suggestions? Also, which document camera do you use? Thank you!!
Sorry for theate response. I use an overhead camera mounted about a foot above my head on a selfie stick mounted through a shelf. I don't use a document t camera. I have a second camera on my desk for the face shot plus an overhead light to light up my desk. My mic runs through a preamp which I then sync up in post using Adobe premiere. I hope that was helpful. Let me know if you have any questions.
So that means if I had 2 negative covid tests, then I would have been tested positive?
No. Adding two negatives always equals to another negative. I hope you are in good health.
@@ramymelhem it's just a joke man, don't take it seriously hahahh. Thank you by the way
@@NoName-mn9rw Anytime
Thanks for this video!! Finally why (-)x(-)= +, made sense!! Great video. Keep up the good teaching! 👍🏼
Thank you! I’m helping an awesome 23 year old who never had the chance to go to school but is going for his GED. This helps so much to explain something I realized I never fully understood! Great job; way better than any other explanation I’ve seen!
These are the types of comments that make my day. Thank you so much for sharing. I wish your student the very best and I hope they crush that GED.
Most amazing illustration of negative times negative. Thank you so much.
Thank you very much.
Interesting and memorable way to present this, and great format!
Thanks very much
This is the absolute best explanation I’ve ever heard of this. You sir are an amazing teacher.
Thank you very much. I appreciate you.
Thank you for your effort bro! many people understand what this mystery means. it's like negative times negative = Blessing
8 months ago I came hunting the answer to this question.
You were very patient with me and helped me, finally get it.
I came back to say Thank You again, Merry Christmas Mr. Melhem.
I remember our discussion. Thank you so much man. Have a Merry Christmas to you and your family as well. 🙏
best video to illustrate the idea !!!! BEST, been looking all over the internet for answers
Thank you, Curane!
Good explanations. I'm getting richer in knowledge. Thanks 👍👍👍
Tq so much brother. But to explain about negetive sign in division. Should we say " divide the debt into two person? Then you will be richer which is positive" ?? Tq for the fast reply
The rules for division are a bit different because the division symbol implies a different meaning. I will have to make a separate video on that.
Please do so soon possible. Thank you😊
First time this has ever made sense. About to start teaching 7th grade math and wanted to really understand why the rules work. Thanks!
That's genius 🔥
Luv the way you explained the things step by step with the real life examples, it's the best explanation I've ever received 🙌🏻
Amazing.!.. that is the way to do it. Bet good money kids of all ages would love the style.
Thank you so much 🙏
I was looking for a video for my students and this perfectly explained the concept. Wish I'd been shown this as a kid! Thank you!!
Thank you very much
This is a master class of patience and complete lack of ego.
The ridicule I felt not understanding this stopped me from trying and me avoid maths education.
Things could have been different and will be from now on wards.
Thank you
Sorry you had to go through that frustration through all those years. Truly special to hear that I was able to help change that in some capacity. Keep fighting the battle and if you have any questions please let me know.
@@ramymelhemDear Ramy.
Thank you so much for replying.
People like you are very important in this wonderful world of ours
VERY GOOD...CONGRATS..EXPLAINED VERY WELL
Why does the first sign of a number tell us to subtract or add? Why do we kinda assume it?
That is a great question. It all comes down to convention. It is a system that is designed that way and so we all follow that standard.
Awesome explanation, thank you so much
If we only had teachers like you, math anxiety would not even exist
Loved your explanation! Thanks a lot!
Thank you so much
Very well explained makes sense. Thank you
This is amazing! Finally this makes sense! Thank you
Thanks for the effort and loving teaching from you . Xfrom India
Thank you. ❤ from Canada to the people in India.
Your explanation is awesome. Please explain why negative number divided by negative number is positive.
Well done. Great teacher🎉🎉
Best video explaining this. Thanks
This is the best example of this concept that I have found!
This is best explanation... Thank you so much ...❤❤
I have been waiting for this explanation for the longest time
Ok but in a system if you subtract the debt it will always become 0 right???Is not a set concept like there is -6 and if you do -2 * -3 it will take away the debt.so it will be 0??
Yes and that's a gain of 6 (+6)
Brilliant explanation! Good job!
If you're subtracting debt then why does -2x-3=-6 and not -4? If I owed my bank 2 dollars and I wanted 4 dollars in my account I would have to give them 6 dollars but what you're saying is I magically get $8?
Melvin Fuentes Hey Melvin Fuentes. Thanks for taking the time to watch this video. Please allow me to clarify. -2 x -3 would mean "remove" 2 groups of $3 "debt". Slow down and think about what that means. Removing 2 piles of $3 debt makes your overall net worth $6 richer (positive)....not 8 and not 4. That would be like saying you will pay back $3 debt today and another $3 debt tomorrow. Ur net worth just went UP (+) 6bucks.
When dealing with money, the "solution" to a multiplication problem always, always indicates whether u are getting richer (+) or poorer (-). And removing a debt, as -2 x -3 suggests, always makes u richer (+ answer) in the end.
I hope that helps. If not, then let's continue this conversation. I want to make sure that you've totally got this. :)
The best explanation I've ever heard and I worked as a teacher in a middle school. You really managed to say why. I've thought about it in a similar way but applied it to the four quadrants on a graph:
So, quadrant I = adding groups of earnings (positive), II = subtracting groups of earnings (negative), III = subtracting groups of debt (positive) and IV = adding groups of debt. In other words, add/substract is on the x axis and earnings/debt is on the y axis. Add all quadrants together and you're back at (0,0) or $0 in your terms - it all balances out. Does that make sense?
Thank you for the compliment. That means a lot to me especially since its coming from a fellow teacher. In regards to the 4 quadrant system, I've never though about it that way. I love it! Thanks for sharing. In the end, both of us are attacking the heart of mathematical linguistics in terms of what the "positive" and "negative" symbols actually mean. Everybody else, it seems, comes up with goofy analogies that work, but don't explain "why".
Ramy Melhem Yeah man, no one was explaining why and just teaching by rote. I was the school's music teacher and my students would come to me for help on their math homework. One kid asked why a negative times a negative equals a positive and I couldn't do it. So I barged into the next math department meeting and asked if anyone could explain why without giving me some weird memorization trick; no one could.
I came up the that quadrant thing so I could visually see it. If you plot 2x3 with all the +/- variations, you get four rectangles that are all the same size. Combine them and you get the same rectangle that's 4x bigger, obviously, but it's interesting to see they balance each other out - quadrants I and III are positive and II and IV are negative. Like balancing equations I guess.
Anyway, thanks again and keep up the good work - your students are lucky to have you.
Patrick Cupo
you, sir, are Awesome!
your explanation is magic. thanks. I am going back to school to learn math and drawing.This should help.
Thank you. Let me know of you ever have any math or science questions.
Wow,explained it in a great way
Thank you very much 🙏
Thank you so much for explaining! I never used to understand why two negatives multiplied with each other equaled a positive until I came across this video.
Excellent explanation!! - good job man!
Excellent more of such videos sir 🙏🙏🙏