In math why and how do two negatives make a positive number?

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why is -12 x-12=144???

Answer 1

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In mathematics, when you multiply two negative numbers, you will always get a positive number. Also, when you divide a negative number by a negative number, you will always get a positive number. There are ways to prove this "formally," using axioms and rules of inference, but I'll give you an intuitive explanation, which is in some ways better (it is what a mathematician would usually start with, before "formalizing" his proof).

Consider x and y, two positive real numbers. We want to show that (-x) times (-y) is equal to xy:

[xy + x(-y)] + (-x)(-y) = xy + [x(-y) + (-x)(-y)] (this is just the distributive law)

Consider the first half of the equation:
[xy + x(-y)] + (-x)(-y) = x(y - y) + (-x)(-y)
= 0 + (-x)(-y)
= (-x)(-y)

Now consider the second half of the equation:

xy + [x(-y) + (-x)(-y)] = xy + [(x - x)(-y)]
= xy + [0(-y)]
= xy

But the two sides of the equation are the equal. So, if x and y are any two positive numbers, (-x)(-y) = xy.

As for division, consider x and y, two positive numbers. We know that for any positive number x, x/x = 1. It follows that (-x)/(-x) =1 as well. We already have the special case of a negative number divided by itself being equal to the positive number 1. Would this also be the case for (-x)/(-y), where x and y are two different positive numbers? Suppose not. Suppose that (-x)/(-y) = (-z), where z is some positive real number. Then:

{(-y) times [(-x)/(-y)]} = [(-y) times (-z)]
But [(-y) times (-x)/(-y)] is simply equal to (-x). So (-x) = (-y)(-z).

But (-y)(-z) = yz, which we know is positive. (-x) is negative, a contradition.

So (-x)/(-y) has to be a positive number. There is no way for it to be negative.

Answer 2

while multiplying two negative no. results into a positive no.
Ex (-1)*(-2)=2

Answer 3

You have to delve into the topic of real analysis to know this, using elementary concepts and axioms. The proof starts by proving that (-1) (-1) = 1, and that's all I'm going to say on the matter.

Answer 4

This is because they "cancel" or "distribute" out each other.


I'll show you some word examples.


She is not not my sister.

You may think I have extremely bad grammar, but this statement is somewhat true. Two negatives make a positive.
It says shes not my sister, but, when theres another negative, it is exactly the opposite of what you said before, meaning she is my sister.

Or, not that isn't my dog.

This one is more tricky. You noticed how they were split apart, right? but, since it was still describing the dog, it does "cancel" out each other.


Now maybe it would be good to use some math examples.

we all know that -3*2= -6

and we know that -2*3=-6.

But we still don't understand why that happens now, do we?

This is because of the concept of intergers.

We know that 2*3=6...by common sense of multiplication. But by definitions of intergers, which are all whole numbers and their opposites, making the opposite of two multiplied by three equal to the opposite of six.


But we also know that -2*-3=6

But why does it do it?
Up until college+ levels, there are only theories.

But, since we are taking the opposite of both numbers, we must make the product, the opposite of the expected product.

Catch my drift?

Answer 5

they only make a positive when ur multiplying them not adding and they just do its a rule of math.lol.

Answer 6

lets say you have 2 numbers, -2 and -4
subtract -4 from -2,you will get
-2--4 so the answer is a positive 2.

Answer 7

In math two numbers with same sign will always have a product that is positive, so two negative numbers when multiplied will gave a product that is positive number

Answer 8

In two situations three negative numbers make a positive number
1. Divide a -Ve no. with a -ve no.
2. Multiply a -ve no. with a -ve no.
3. Substarct a -ve no. which is lower than from the no. substracted.
like(-2 - (-3) = 1)

In all other cases the result would be a negative no.

Answer 9

This stems from how we define negative numbers.

Negative numbers are "additive inverses."

For example, -5 is the number so that 5 + (-5) = 0.

So what's great is that -1 times a number gives you its additive inverse (this comes from the distributive law). This is extremely important. So:

What is the additive inverse of 7?

-1 × 7 = -7

So the question is: what is the product of two negative numbers? Why is it positive? Well, let's choose 3 and 5 for no particular reason. What is this product?

(-3) × (-5) = ?

Well, we know for a fact that -1 × 3 = -3 and same for 5, so we can rearrange this mess:

(-3) × (-5) = (-1)×(-1)× 3 × 5 = (-1)×(-1) × 15

So the question is really: why is this 15?

Well, here's the reason. You're multiplying by -1 twice. If you multiply by -1 once, you get the additive inverse (-15 in this case). If you multiply by -1 again, you want the additive inverse OF the additive inverse. But we know that:

15 + (-15) = 0

Which means that the additive inverse of -15 is 15 itself. This is why (-1)×(-1)=1, and why any two negative numbers multiply to give a positive one.

Answer 10

These are the four conditions when multiplying numbers together.

- * - = +
-* + = -
+ * - = -
+* + =+

Hope this helps. The reason why is because they are math rules and because it makes sense.