Understanding the Additive Inverse: Exploring the Concept and Properties in Mathematics

additive inverse

In mathematics, the additive inverse or the opposite of a number refers to a number that, when added to the original number, gives a sum of zero

In mathematics, the additive inverse or the opposite of a number refers to a number that, when added to the original number, gives a sum of zero. It represents the opposite direction or reversal of a number on a number line.

To find the additive inverse of a number, simply change the sign of the number. For example:

– The additive inverse of 5 is -5. (5 + (-5) = 0)
– The additive inverse of -12 is 12. (-12 + 12 = 0)
– The additive inverse of 0 is 0 itself. (0 + 0 = 0)

Properties of Additive Inverse:
1. For any number a, the sum of a and its additive inverse is always zero.
a + (-a) = 0

2. The additive inverse of the additive inverse of a number is the number itself.
-(-a) = a

3. The additive inverse is unique for each number.
For example, if the additive inverse of a number a is -b, then the additive inverse of -b is a.

The concept of additive inverse is used in various mathematical operations, such as subtraction, finding the difference between two numbers, solving linear equations, and in abstract algebra where studying number systems like integers, rational numbers, and real numbers involves understanding the properties of additive inverses.

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