Understanding the Additive Inverse in Mathematics: Definition, Examples, and Applications

additive inverse

In mathematics, the additive inverse of a number is a value that, when added to the original number, results in the sum being zero

In mathematics, the additive inverse of a number is a value that, when added to the original number, results in the sum being zero. In other words, for any real number “a,” the additive inverse, denoted as “-a,” is the number that satisfies the equation a + (-a) = 0.

For example, let’s consider the number 5. The additive inverse of 5 is -5. If we add 5 and -5 together, we get 5 + (-5) = 0. This means that -5 is the additive inverse of 5.

Similarly, the additive inverse of -2 is 2. If we add -2 and 2 together, we get -2 + 2 = 0. This shows that 2 is the additive inverse of -2.

In general, for any real number “a,” its additive inverse “-a” can be found by changing the sign of “a.” If “a” is positive, then “-a” will be negative, and if “a” is negative, then “-a” will be positive.

It is worth noting that zero is its own additive inverse, as adding zero to any number does not change its value. For example, 0 + 0 = 0, so 0 is the additive inverse of itself.

The concept of additive inverse is fundamental in mathematics and is used in various areas such as solving equations, simplifying expressions, and understanding number systems.

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