Best Answer

There are many intuitive explanations that show it works. For example, you can look at debt as a negative number or you can use the number line to see why negative times negative is a positive. None of these is really a proof. In fact, since any negative number is really the same positive number multiplied by -1, i.e. -5=5x-1 when we really need to ask only why is -1x-1=1. One good, but often not satisfying, answer is that if we use any other convention, then it won't work. The fact is, it is a convention.

For the mathematical purist, here is a nice proof that two negatives multiplied together equal a positive

Let a and b be any two real numbers. Consider the number n defined by

n = ab + (-a)(b) + (-a)(-b).

We can write

n= ab + (-a)[ (b) + (-b) ] if we just actor out -a

= ab + (-a)(0)

= ab + 0

= ab.

Also,

n = [ a + (-a) ]b + (-a)(-b) if we factor out b

= 0 * b + (-a)(-b)

= 0 + (-a)(-b)

= (-a)(-b).

So we have

n = ab

and

n = (-a)(-b)

Hence, by the transitivity of equality, we have

ab = (-a)(-b) and the proof is complete.

Q: Why does a negative times a negative always equal a positive?

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A negative times a negative always equals a positive, no matter what the numbers are.

No. A positive times a negative is always negative. A negative times a negative is always a positive.

when you have a negative times a negative it will equal a positive but when you have a negative times a positive it will equal a negative no matter what!

because you are dividing with same signs

positive times negative equals negative. positive times positive equals positive. negative times negative equals positive

Related questions

-10 x -5 = +50A negative times a negative will always equal a positive number.A negative times a positive will always equal a negative number.A positive times a positive will always equal a positive number.- x - = +- x + = -+ x + = +

Yes

A negative times a negative always equals a positive, no matter what the numbers are.

No. A positive times a negative is always negative. A negative times a negative is always a positive.

it equals positive one. one squared is always one. if they're both negative, negative times negative is always positive.

when you have a negative times a negative it will equal a positive but when you have a negative times a positive it will equal a negative no matter what!

-12A negative times a positive is always a negative.A negative times a negative is always positive.

A positive number times a positive number will always get you a positive number A negative number times a negative number will always get you a positive number (same signs will get you a positive number) but A positive number times a negative number will always get you a negative number or A negative number times a positive number will always get you a negative number (different signs will get you a negative number)

no. it is still negative.

a negative times a positive is a negative. plz recomend me.

a positive a negative times a negative also equals a positive

A negative times a positive is always a negative.