Current timeTotal duration Google Classroom Facebook Twitter. Video transcript Lets say you are an Ancient Philosopher who was building up mathematics who was building mathematics from the ground up And you already have a reasonable of what a negative number could or should represent and you know how to add and subtract negative numbers But now you are faced with a conundrum What happens when you multiply negative numbers?
Either when you multiply a positive number times a negative number Or when you multiply two negative numbers So, for example You aren't quite sure what should happen if you were to multiply and im just picking two numbers where one is positive and one is negative What would happen if you were to multiply 5 times negative 3 You're not quite sure about this just yet You're also not quite sure what would happen if you multiply two negative numbers.
So lets say negative two times negative 6 This is also unclear to you What you do know, because you are a mathematician, is however you define this or whatever this should be It should hopefully be consistant with all of the other properties of mathematics that you already know And preferably all of the other properties of multiplication That would make you feel comfortable that you are getting this right. That's also consistent with the intuition of adding negative three repeatedly five times, now look above above us slightly higher so you can see ideas of multiplying two negatives, but we can do the exact same product experiment.
We want whatever this answer to be consistent with the rest of mathematics that we know so we can do the same product experiment. What would negative two times six plus negative six to be equal to.
If you add a cold cube add a negative number , the temperature goes down. If you remove a hot cube subtract a positive number , the temperature goes down.
And if you remove a cold cube subtract a negative number , the temperature goes UP! That is, subtracting a negative is the same as adding a positive. Now suppose you have some double cubes and some triple cubes. If you add three double-hot cubes add three-times-positive-two , the temperature goes up by six.
And if you remove two triple-cold cubes subtract two-times-negative-three , you get the same result. Thanks again to you, and to Ben, for your generous patience in working with me. Never too late to learn, good golly! Congrats on making sense of a difficult, abstract idea. There are many. Whatever works. I never stop learning new math, a subject I slept through in high school, avoided in college, then embraced personally and professionally in my thirties.
Perseverance, patience, searching for good models online, and belief in your ability to learn and grow at any age are powerful, helpful attitudes and practices. I am 67 and always pushing my mathematical envelope. Think about this, Michael Paul. It was nice of you to do it. A pleasure and privilege. Feel free to ask for ideas anytime: mikegold umich.
It equals This becomes even more useful when dealing with variables. I did, for years. I believe that it is. Michael Paul, the idea of opposites is interesting. Maybe the number-line is not our friend. This is really working for multiplication for me, without having to turn my mind into a pretzel thinking about hot and cold cubes. But it falls apart with division for me.
I must be missing something. This was the lightbulb for her, the opposite of the opposite is the the thing itself. Thank you for the super helpful article!!! Thank you for clarifying. As a kid, I had just crammed it. And now when my 5th grader asked me why, I was led to your eye opening article.
Skip to content. About Highlights Events Links. Share this: Facebook Twitter More Email. Like this: Like Loading Tagged I'm positive that I hate the slogan 'two negatives make a positive' two negatives make a positive two positives don't make a negative. Published December 14, December 14, Next Post Imagine All the Numbers…. Love your posts and cartoons. Me too! I first came across this in W. Love it Loading Actually I agree. Though, perhaps the opposite of food is no food.
This is definitely a not bad post! Love you comment! I was going to post something very similar. Well said. I read some of this out loud to my family and we all loved it. Keep it up! Subtraction is just the addition of negative numbers. This post is not not very good. Also, we agree that a pair of chips of opposite colors one red, one black represents 0. How would you use chips to represent a debt of 25 units? The simplest way would be to place 25 red chips in the circle, representing Now, how do you show a payment of 5 chips?
We might think of the second action as someone you paying off part of a debt. Why do 2 negatives equal a positive? Does two negatives make a positive in grammar? How do you calculate negative numbers? Do you distribute the negative?
What does distribute the negative mean? Why do you distribute the negative sign? How do you distribute variables? What does a negative sign look like? What are plus and minus signs called? Previous Article Do people die because of Black Friday? Next Article What was the artist trying to convey to the observer? Back To Top.
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