Why “Negative x Negative” Should Not Be Taught At School Anymore

I heard it and learned it before. But it was only a few years ago that I was able to wonder greatly: Why does a negative number multiplied by another negative number result in a positive number? I asked a lot of math experts within my social circle and they all came up with the same answer: “Because the rules say so.”

But I came up with a follow-up question: Why do the rules say so? What are the real-world applications of such a rule? When I insisted on such a question, I got this statement from a Math veteran: “I've been teaching algebra for more than 20 years, don't you dare question that rule that has been around long before you were born!”

The one who said it was right in some ways, who do I think I am if I begin to question such a solid mathematical rule? “A negative times a negative is positive, it is just like that by definition, stop asking and just get over it!” All my friends tell me that. But here's the problem: I SIMPLY CAN'T GET OVER IT.

Why can't I let it go? Because I believe that the entire mathematical system- all the formulas, equations, expressions, or any number for that matter, are invented because: they are meant to represent real-world objects, and real-world situations.

Even though Math belongs to the bracket that I call “My Weakest Spot” category in terms of mental undertakings, I firmly believe that if a mathematical discipline can't be applied in reality, then it shouldn't be pursued, let alone be taught at all. Math, I believe is a system built to solve problems, not cause any.

Before I asked a few friends and acquaintances about what they think, I gave them the statement enclosed in brackets. They all agreed. Unfortunately, they are just as baffled as I am as to how negative times negative can be applied in reality.

It is quite understandable that the concept of negative numbers is established because it is meant to represent debts, deficits, lack(s), or anything that someone should fill out for or replace once he is capable of doing so. I told them, I don't really think that such a question can ever be applied in reality.

Picture this situation:

Pedro has a debt of three pesos. (-3)

Later, he added two pesos (-2) to his debt.

This would mean that he has now a debt of five pesos. (-5)

Mathematically, it can be stated as: (-3) + (-2) = -5

The rules of algebra dictate that “negative plus negative, is equal to negative” so there's nothing wrong with the example above.

Here are the basic rules of Algebra multiplications, in case you want to be refreshed:

Now here's the tricky scenario:

Juan has a debt of three pesos. ( -3 )

Later, he doubled it ( -3) * (-2 )

According to Algebra, this would result into positive 6. ( -3 )* ( -2) = 6

Now let's ask: how can that be? If we are going to bring these situations into reality, it should actually make Pedro a debtor of five pesos (-5) and Juan, a debtor of six pesos. (-6) But instead, Juan would actually have his debt vanished, while Pedro would still be liable to pay five pesos.

And to make it even trickier, Juan would actually have an income of six pesos. Why? BECAUSE HE DOUBLED HIS DEBT!” Is this fair, or even sensible? If we are going to apply that in reality, Pedro would have this intense outburst of injustice.

I'm not saying the rules of this kind of math are wrong. My question is, why do they invent such a set of rules, if it can't even be applied in reality?

Let’s take a look at it from a different perspective. Let’s say negative is equal to a “lie” while positive is equal to a “truth.” We would then have a statement that goes like this:

“3 lies”, multiplied by “2 lies”, is equal to “6 truths” – Really? How? Why?

Another baffling example would be this:

Let’s say negative is represented by a black paint, while positive is a white paint. We can then say that…

“3 pails of black paint” multiplied by “2 pails of black paint” is equal to “6 pails of white paint” – Oh come on… can that be real?

If there is no real-world application to the concept of negative times negative, then it shouldn't be taught anymore, in my opinion. I'm not saying the entire subject of Algebra should be stopped though, for we can tell that it's a very important field of discipline. I'm just referring to the concept of multiplying negative numbers.

We should also include the concept of dividing negative numbers as well, for they basically work the same.

If you're a math expert, or if you have an opinion about this, please explain your point in the comment box. Perhaps, you can make me sleep better in the next nights.

Thanks.