why minus into minus is equal to plus?

Question

In mathematics why minus multiplied by minus is equal to plus?

Answer 1

A short mathematical explanation:

Assume you have two negative numbers u,v. Then there exists two numbers positive number a and b such that u=-a and v=-b. Therefore v+b=0, and u(v+b)=0.

By the distributive law:
u(v+b)=uv+ub=uv+(-a)b=uv-ab=0. Thus uv=ab, and the product of two negative numbers is the product of two positive numbers.

Why does this make sense in the real world?

Assume that you owe 5 people 5 dollars. We can consider owing to be a negative number of having, so you have -5 dollars for 5 people or -25 dollars total.

But if it was only 4 people, you would only have -20 dollars, for 3 it would be -15, for 2 it would be -10, for 1 it would be -5 and for 0 it would be 0. So, each time you remove a person, you add 5 dollars. When you have -1 people that you have -5 dollars for (you can also say you have -1 people that you owe 5 dollars to, or there is 1 person that owes you five dollars) you continue to add 5 dollars. Now you have -1*-5=5, so two negatives multiplied together to make a positive.

Answer 2

If one thinks of multiplication as grouping, then we have made a positive group by taking away a negative number twelve times.

A Mathematical Explanation

If we can agree that a negative number is just a positive number multiplied by -1, then we can always write the product of two negative numbers this way:

(-a)(-b) = (-1)(a)(-1)(b) = (-1)(-1)ab
For example,

-2 * -3 = (-1)(2)(-1)(3)

= (-1)(-1)(2)(3)

= (-1)(-1) * 6
So the real question is,

(-1)(-1) = ?
and the answer is that the following convention has been adopted:

(-1)(-1) = +1
This convention has been adopted for the simple reason that any other convention would cause something to break.

For example, if we adopted the convention that (-1)(-1) = -1, the distributive property of multiplication wouldn't work for negative numbers:

(-1)(1 + -1) = (-1)(1) + (-1)(-1)

(-1)(0) = -1 + -1

0 = -2
As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth."

Since everything except +1 can be excluded as impossible, it follows that, however improbable it seems, (-1)(-1) = +1.

Answer 3

In mathematics, it is a rule (I think) that when a number is to be subracted to a negative number, the negative number becomes positive, because two negatives make a positive. It's also like having double negatives in English. If the two are used consecutively, or within a sentence, the two would cancel each other out and become a positive.

Answer 4

Well i guess a simple example is better because this question is a about logic. Let say we have 1 man and 1 woman, A and B, and they own each other money.

Let say A owns B 24 dollars, and B owns A 12 dollars.

To A,

Debt of A to B = -24 , Debt of B to A = -12
Total debt = Debt of A to B - Debt of B to A
= -24 - (-12)

But the logic is i own her 24 and she own me 12, so after discounting those she own me, i still own her 12.

Therefore, Total debt = -24 - (-12) = -24 + 12 = -12
Thus came the rule which is just logic.

Answer 5

let's say -2 times -3. the first number is being added the second number of times in multiplication. so adding NEGATIVE 2 NEGATIVE 3 TIMES, you would get 6. Because 2 +2+2= 6 But it is negative and negative so they cancel each other out to be positive.

Answer 6

I'll explain :
Take 1 minus and put it horizontally, take another minus and put it vertically, now overlap both of them, the result is ++++