Why does multiplying 2 negative numbers equal a positive?
Each number has an “additive inverse” associated to it (a sort of “opposite” number), which when added to the original number gives zero. The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.
What is a negative times by a negative?
Rule 3: A negative number times a negative number, equals a positive number. Two negatives make a positive, so a negative number times a negative number makes a positive number. If you look at it on the number line, walking backwards while facing in the negative direction, you move in the positive direction.
How do you prove negative times negative is a positive?
Using the fact multiplication is commutative, a negative times a positive is also negative. Similarly, we can prove that a negative times a negative is a positive. Since we know that −ab is negative, and the sum of these two terms is 0, therefore (−a) × (−b) is positive.
What happens when you subtract a negative from a negative?
Rule 3: Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, – (-4) becomes +4, and then you add the numbers. This would read “negative two minus negative 4”.
Why negative minus negative equals positive?
Rule 3: Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. So we’re changing the two negative signs into a positive, so the equation now becomes -2 + 4.
Why is negative negative positive?
Explanation: We know that negative times anything means that it will change the sign. Ideally, the second negative should change the sign of our original number (which is also negative). So, our original negative sign is changed into a positive sign when a negative is multiplied to it.