Why Product of two negative numbers is a Positive?

To make something negative is to reverse its polarity. If you reverse the polarity of something positive, it becomes negative. But, if you reverse the polarity of something that is negative, it becomes positive. However, I did locate the following explanation on Drexel University's Math Forum website. I believe what it's saying is that it's "just because". Sometimes, that's the only answer there is for some things. But, anyway, here it is: 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.

Hi See -1 * -1 = 1 but one short something and one short something..here you are meaning about addition where absolutely you will get -2 not 1.

That is an easy one! Jerzgirl gives you a wonderfully detailed response so I will try something simpler. I was thinking of how in the English language two negatives make a positive (example: "I am not going to not answer this question" means "I am going to answer this question") and I ran across this fun site which explains just what I think you want to know in two different but equally effective ways: http://www.mathsisfun.com/multiplying-negatives.html Enjoy!

I probably won't add anything to the other attempts at explaining this, but here goes... When you multiply a number by 1, the answer is the number itself. But if you multiply a number by -1, the answer is the number itself but with the opposite sign. Take the number 2. 1 x -2 = -2 and so -1 x -2 = -(-2) = 2. I'll try to illustrate this with a real-world example, which I think is what you're after. Imagine you have $1. You put it in a bank account and the bank say, right, you've lent us this dollar, and for this privilege we'll double it for you at the end of the week. You are owed $2 (=2 x $1). The next week you need to take out your money as you need to pay a bill. As the bill is for $2, you need to take out your $1 and borrow another $1. So your balance is now $-1. The bank says right, as you've now taken our $1, we're going to want it back, and you're going to have to pay us back $2 by the end of the week. (Fair's fair!) You owe the bank $2 (=2 x $-1 = $-2). Now let's pretend that the bank changed their mind at the last minute. They have a sudden change of heart and decide to implement a bit of a strange policy for a bank! As you've been a loyal customer (for over a week now ), they will compensate you for any debt that you have with them! They'll pay you 2 times whatever you owe them. They will reverse the direction of the payment. Your debt to them is $1. So you currently have $-1. As part of their previous policy you'd have to pay them 2 times this: (2 x $-1). However, the new policy means that they will pay you 2 times this, so in effect you will pay: (-2 x $-1). This equates to them paying you $2. So -2 x -1 = 2. I'm not sure that this explains it in the way that you're after but it hopefully shows this concept of negative multiplication in a more tangible way.

I think you can demonstrate it this way: We know that +2 x -3 = -6 because it's like saying (-3) + (-3) = -6 But if -2 x -3 = -6 that would mean that +2 = -2 and this is not true

It is because we are when multiplying it means we are adding the multiplicand according to the number of its multiplier. We can easily understand it from positive numbers and we are using the same concept in negative numbers but of course in reverse format.

Because when you add two negatives, you are moving left down the number line. Like when it's below zero and it gets even colder the temperature goes down. But when you multiply it must be positive because you are not counting the number of negatives. Like if you had -5(6) you have 6 groups of neg 5. So its a shortcut for repeat adding -5 -5 -5 -5 -5 -5 =-30. But neg by neg is actually counting forward. -(-5) -(-5) - (-5) -(-5) -(-5) -(-5)=30.

It's a rule.When multiply a negative number with a negative number the result should be positive.

Multiplication is nothing but addition of the same number n many times. If you start adding a negative number in reverse order you get the product of a negative and positive numbers. Similarly if you start adding it according to negation it becomes a positive number. Hope I made myself clear. I am not so good at explaining things.