Additive Inverse

Definition:

In mathematics, the additive inverse of a number is what we add to a number to create the sum of zero. 

So in other words, we can say that the additive inverse of x is -x, which is equal and opposite in sign to it.

                   – 3  +  3  =  0

Number  Additive Inverse

                   2  +  -2  =  0

Number  Additive Inverse

For example, the additive inverse of the positive number 4 is -4, which is equal and opposite in sign to it and their sum, 4 + (-4) = 0, the additive inverse of -0.5 is o.5, because -0.5 + 0.5 = 0.

The additive inverse of 3 is -3. The additive inverse of -5 is 5. The additive inverse of y is -y. 

The sum of a number and its additive inverse is 0.

Note: Zero is the additive inverse of itself or additive inverse of 0 is 0.

The additive inverse of p is another number q, then the sum of p + q equals zero.

The additive inverse of p is equal and opposite in sign to it so, p = -q.

Additive inverse of a negative number

Additive inverse of a negative number is equal and opposite in sign to it. It means that the additive inverse of a negative number is positive.

For example, if m = – 6, then its additive inverse is n = 6. We can verify that the sum of m +n equals to zero, so when m = -6 and n = 6, we have – 6 + 6 = 0.

                 Graphical Representation

We can also see the additive inverse visually. First we consider the real number line. 

The number line usually drawn horizontally, with zero in the middle, the negative numbers to its left side and the positive numbers on the right side. 

We place the point x and its additive inverse or -x, we know that the point 0 is the midpoint between x and its additive inverse -x.

A number and its additive inverse are equidistant from the zero.

Two numbers with opposite sign fall on either side of zero on the number line at equal distance. 

For example, when x = 3, its additive inverse is -3 are equidistant from the zero.