why does (-1)x(-1)= +1?

Answer 1

because who ever made up the math skills or what ever had to make it hard for everyone else.

Answer 2

By definition -1 is the unique number a such that 1 + a = 0.
Using this, we know that
1 + (-1) = 0
(1+(-1))^2 = 0
Using the distributed law:
(1+(-1))(1+(-1))
1*1 + 1*(-1) + (-1)*1 + (-1)*(-1) = 0
Since 1 * a = a for all a, this simplifies to:
1 + (-1) + (-1) + (-1)*(-1) = 0
since 1 + (-1) = 0. this becomes
(-1) + (-1)*(-1) = 0
And since 1 + (-1) = 0, we can rewrite this as
(-1) + (-1)*(-1) = (-1) + 1
cancelling gives us
(-1)*(-1) = 1.
So (-1)*(-1) = 1

Answer 3

suppose it is not (-1)*(-1)=2 for the sake of argument.

(-1)+1=0 right, fundamental properties of numbers.

(-1)(-1+1)=(-1)*0 multiply both sides by (-1)

(-1)*(-1)+(-1)*1=0 by the distributive property.

2+(-1)=1 which of course does not equal 0

so if (-1)*(-1)= anything other than +1 then we can prove all numbers are equal. And we would have a really boring number system.

Answer 4

Mathematicians invented the term negative to mean opposite (meaning that if you have 3, what can you add to it to get 0? -3) So if you have -1*(-1) Its the same as [opposite 1*(-1)]. Since 1 times any number is that number, 1*(-1)=(-1), So we have [opposite (-1)] or [opposite opposite 1]. The opposite of an opposite is the origional. Therefore -1*(-1)=+1

Answer 5

I have a friend who is great in literature and philosophy, but nil at maths, and he finished school many years ago so he forgot it all. Just yesterday I explained exactly this question to him in this simple way: "Minus means an OPPOSITE direction. -1x-1=+1 means that if you turn BACK twice, you'll be facing FORWARD again." He got it just fine.

I think this explanation is not simplistic, it is perfectly valid. Minus and plus are two opposite sides of the real line. Multiplying by -1 means flipping everything.

Btw, not everyone beleives that... some say that "Educators are lying bastards. -1 x -1= +1 is WRONG, it is academic stupidity and is evil. The educated stupid should acknowledge the natural antipodes of +1 x +1 = +1and -1 x -1 = -1 exist as plus and minus values of opposite creation - depicted by opposite sexes and opposite hemispheres. Entity is death worship - for it cancels opposites." :)

See http://www.timecube.com/

Answer 6

Break it down into 2 equations.

-1 * -1 = +1

- * - = +

1 * 1 = 1

Another example.

-2 * -3 = +6
- * - = +
2 * 3 = 6

Answer 7

As many other people have posted, the product of two negative numbers is a positive number, but it can be difficult to understand why. Here's an example I like to use to illustrate the idea:

Imagine that you're in a hot air balloon, and you've got the burner going, so that you're climbing higher into the air. Let's say that every second, you climb another three inches. Let's also say that we'll measure climbing higher as a "positive distance," and sinking lower as a "negative distance." (Draw a picture if it'll help.)

Question One: ten seconds from now, where will you be compared to where you are now?
Answer: Ten seconds in the future, times climbing 3 inches per second, makes 30 inches higher. (+10) x (+3) = +30.

Question Two: ten seconds ago, where were you compared to where you are now?
Answer: Ten seconds in the *past*, times climbing 3 inches per second, means you were then 30 inches lower than you are now. (-10) x (+3) = -30.

Now, let's change the situation. Let's say that, instead of having the burner going, you're slowly letting hot air out of the balloon, so that you're *dropping* 3 inches every second.

Question Three: ten seconds from now, where will you be compared to where you are now?
Answer: Ten seconds in the future, times dropping 3 inches per second, means you will be 30 inches lower than you are now. (+10) x (-3) = -30.

**Question Four**: ten seconds ago, where were you compared to where you are now?
Answer: Ten second in the *past*, times dropping 3 inches per second, means you were 30 inches higher than you are now!
(-10) x (-3) = +30.

So there's a real-life scenario where multiplying two negatives gives a positive result.

Honestly, it can sometimes seem like the "rules" you're taught in your math classes are needlessly complicated and designed to give you migraines. In fact, they're not even "rules" at all. They're more like behaviors. The people who studied math over the years observed that numbers have certain properties and behave in certain ways in the real world, just like someone like Jane Goodall observes gorillas living in the wild. You're taught these properties and behaviors so that you can solve number problems in the real world when they come up -- and they do, eventually, come up. :)

Hope that helps!

[Edited to add: By the way, another person mentioned that, in speaking, two negatives makes a positive. In fact, that's not true in all languages, just in English. In the (I think) 1700's, a lot of English-language "geniuses" like Samuel Johnson -- we call that "grammatical prescriptivists now" -- decided on many of the rules of English grammar and published them in books. The notion that one should never utter a double-negative like "There isn't nobody here", and that doing so created the contrasting positive, was a rule created from scratch, but modeled on... you guessed it... multiplying negative numbers!]

Answer 8

because of the Facter of 0. Read Zero By Charles Siefe

Answer 9

For the same reason a double negative equals a positive. If you were to say, for example, that you didn't not do something...then you're saying that you did do it. Same principle.

Answer 10

It is a fundamental rule of mathematics when - sign is multiplied by - sign the product is positive.

Answer 11

!~ coz two negetive makes a positive ~! oh...wait ...you have to read this joke coz it really relates to this..
(in Math class)
Student: Sir, may i come in ?
Teacher: No
Student: can i come in now ?
Teacher: No
(Then the student comes in..)
Teacher: Why did you come in? i Said "no" !!?!
Student: Sir, didn't you alwayz say two negetives make a positive !!!!
ha! ha! ... i just had to ryte it !! (^_^) have fun !!