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Quantitative Aptitude > Arithmetic Aptitude > Additive Inverse Property | Calculator and Graphical Representation
Arithmetic Aptitude

Additive Inverse Property | Calculator and Graphical Representation

Additive Inverse

It states that additive inverse of a number is basically what we add to number for creating the sum of a zero. In other words, we can say that the additive inverse of a variable X is any other number, y until the sum of X+Y is equal to zero.

The additive inverse of the variable X is equal and also opposite in sign to it therefore, Y = -X or vice versa. Example: the additive inverse of negative number 5 is -5. That’s because when we add 5 and -5 then, as a result, we get the answer = 0.

Additive Inverse Calculator

What about this inverse when it comes to a negative number? Using the same approach as earlier, if the variable X is a negative number.

Then the additive inverse of X will be equal and opposite in sign to it. This means that this inverse of a negative number will be positive.

For instance, if the variable X is equal to -12, then the additive inverse of the variable X will be Y = 12. We can check that the sum of X+Y is equal to zero. When X = -12 and Y = 12, than it results in -12 + 12 = 0.

We should note that the additive inverse of 0 is 0. Because zero is the only real number, that is equal to its own additive inverse. It is also the one and only number for which the equation X = -X becomes true.

additive inverse

Graphical Representation of Additive Inverse

We might also think of the additive inverse visually. Let us consider the real number line. The real number line that we have to draw horizontally, with 0 near the middle.

It has negative numbers to its left and the positive ones on the right side. Two number having opposite signs fall on either side of 0 at equal distance on the number line.

Once we locate the point corresponding to a number X on the number line. Then we are aware that the additive inverse, or the variable -X, will with respect to 0 on the opposite side of the number line.

In fact, point 0 is the middle point between the variable X and its additive inverse -X. For example, when X = 5, then the additive inverse of X will be -5. It is very clear to see that point 0 is the middle point of the segment between -5 and 5.

Common Example

For any number we can calculate it by multiplying it with -1: that results in –n = -1 X n. example of rings of the numbers are integers, real numbers, rational numbers, and complex numbers.

Relation to Subtraction

It is related closely to the subtraction. This can be seen as an addition to the opposite:

a – b = a + (-b).

Conversely, it is also said to be a subtraction from zero.

-a = 0 – a.

Hence, unary minus sign notation is seen as a shorthand for subtraction with (0) symbol omitted. In correct typography, there should be no space present after unary (-).

Some Other Properties

In addition to the identities mentioned above, negation has algebraic properties that are as follows:

−(−a) = a, it is an operation of evolution

−(a + b) = (−a) + (−b)

a − (−b) = a + b

(−a) × b = a × (−b) = −(a × b)

(−a) × (−b) = a × b

Notably, (−a)2 = a2

Solved Question For You

Ques. If ‘a’ is a real number, then a−1 is said to be:

(A). Inverse of a.
(B). Identity of a.
(C). Transpose of a.
(D). Determinant of a.

Ans. (A). Inverse of a.

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