why does a negative number multiplied with a negative number results in a positive number?

Answer 1

Think of the negative sign as representing the opposite side of zero from your current location. The negative of a positive is a negative, but the negative of a negative is a positive. Or, in a different approach, multiplication by a positive is repeated addition while multiplication by a negative is repeated subtraction.

Answer 2

Imagine, for a moment, that you're in a hot-air balloon. You have the flame going, so your balloon is rising. Let's say that you're rising at a nice steady climb: 2 feet every second. Let's also say that we'll consider up to be a "positive" direction, and down to be a "negative" direction.

Question 1: compared to where you are now, where will you be in 5 seconds?
Answer: you multiply the number of seconds by the speed. (5 seconds from now)(2 feet higher every second) = 10 feet higher. 5 x 2 = 10 -- a positive result.

Question 2: compared to where you are now, where were you 5 seconds ago?
Answer 2: let's think of time in the past as a "negative time" direction. (5 seconds ago)(2 feet higher every second) = 10 feet lower. (-5) x 2 = -10.

Now, let's change the situation. The flame isn't on, and in fact there's a small hole in the balloon, so you're slowly dropping -- 2 feet every second.

Question 3: compared to where you are now, where will you be in 5 seconds?
Answer 3: (5 seconds from now)(2 feet lower every second) = 10 feet lower. 5 x (-2) = -10 -- a negative result.

Question 4, and here's where we answer your question: compared to where you are now, where were you 5 seconds ago?
Answer 4: (5 seconds ago)(2 feet lower every second) = 10 feet higher!! (-5) x (-2) = +10. A negative times a negative came out to be a positive!

So the answer is: a negative times a negative is a positive because, in the real world, that's the way numbers work. :)

Hope that helps!

Answer 3

Think of the negative sign as representing the opposite side of zero from your current location. The negative of a positive is a negative, but the negative of a negative is a positive. Or, in a different approach, multiplication by a positive is repeated addition while multiplication by a negative is repeated subtraction.

Answer 4

If you think of it on a number line, it helps. On a number line, the negative means to move to the left. But a negative reverses the move to the left and makes it move to the right. A move to the right is in the positive direction.
http://simple.wikipedia.org/wiki/Number

Answer 5

Why is −1 times −1 equal to 1?

Why is −1 multiplied by −1 equal to 1? More generally, why is a negative times a negative a positive? There are two ways to answer this question. The first is intuitive and conceptual; the second is formal and algebraic.
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Intuitive explanation

There are many ways to conceptualise multiplication. Let's confine ourselves to positive numbers, for the moment.

Now, multiplication is basically repeated addition. To multiply 5 by 3, we can imagine a straight stick 5 metres long in front of us. We lay it out flat 3 times in the same direction, with the back tip of the stick placed where the front tip was on the previous time. After we lay it down 3 times, the front tip will lie exactly 5 × 3 = 15 metres from the back tip where we originally placed it.

What would it mean to lay down a stick "negatively many times"? One answer is to say that it would result in a displacement where, if we were to lay it down 3 times immediately after, we would return to where we started. Imagine performing this. It is the same action as multiplying by a positive number except we are pointing in the opposite direction. If we were going east to multiply by a positive, we go west to multiply by a negative.

This is fine, but it only covers a stick of "positive length". How do we multiply using this type of stick? If we assume that multiplication should not depend on order, then 5 × −3 = −3 × 5 = − 15. Now, stand at a point. Laying out a stick of length 5, minus 3 times, sends us 15 metres west (using the east/west above). However, this is the same result as if we had pointed west originally and laid a stick of 5 metres down 3 times. In other words, to multiply using a stick of negative length, we should point ourselves in the opposite direction before laying down the stick.

Now, we can see why −1 × −1 = 1. We point east originally. Our stick has length −1, so we turn ourselves to point west. Then, we lay the stick down negative one times, i.e. we point ourselves back again in the east direction and lay the stick down. This is the same as if we had simply dropped the stick in front of us pointing east without moving ourselves at all.
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Algebraic explanation

The algebraic explanation is essentially a formalisation of the above intuitive explanation. Start with the equation

0 = 0\cdot 0 = (1+(-1))\cdot (1+(-1))

The first equality follows from the fact that "anything times zero is zero". The second follows from the definition of −1 as additive inverse of 1: it is precisely that number that when added to 1 gives 0. Now, using the distributive law, we see that

0 = (1\cdot 1) + ((-1)\cdot 1) + (1\cdot (-1)) + ((-1)\cdot (-1)) = -1 + ((-1)\cdot (-1))

The second equality follows from the fact that 1 is a multiplicative identity and simple addition. But now we add 1 to both sides of this last equation to see that

−1 × −1 = 1.

The above argument holds in any ring. It has a flavour common to some of the basic results in abstract algebra.

For the detailed explaination please go to...

Answer 6

it is so because multiplication of two negative no. gives positive no. in result. Example:- -2*-5=10

Answer 7

because a negative number will change the sign of any number it is multiplied against....

hence, a negative number will change a positive number to negative and...

a negative number will change a negative number to positive....

Answer 8

I know it's not a mathematical reason, but I always like the saying, "Two wrongs don't make a right, but they make you feel good." So from that I always know that 2 negatives in multiplication or division will make a positive. :)

Answer 9

THINK OF IT AS MAKE BELIEVE MATH.
WE PRETEND 2 boxes of no apples plus two more boxes of no apples is four boxes of no apples. OR -2 x -2 = +4 WE Still have no apples, BUT we do have 4 BOXES ["somethings"]. It's a RULE so later in math we can call the
"somethings" "X" or "A" or a Greek letter like Phi or Beta or Kappa.
BESIDES: +2 x +2 = +4 and +2 x -2 = -4 [SO MINUS 2 X Minus 2 HAS TO
be "SOMETHING" ! It's just a neat math "tool" like a wrench to fix something

Answer 10

negative sign signifies reverse or opposite,when a negative value is multiplied with another negative value, it means reverse of reverse or opposite of opposite which is positive.if you are moving backward in a car,what is backward of backward,it is forward.