To determine the additive inverse of [tex]\(\frac{1}{2}\)[/tex], we need to find the number that, when added to [tex]\(\frac{1}{2}\)[/tex], yields zero.
The concept of an additive inverse is straightforward: for any given number [tex]\(x\)[/tex], its additive inverse is [tex]\(-x\)[/tex]. When you add [tex]\(x\)[/tex] and [tex]\(-x\)[/tex], the sum is always zero.
Following this rule, let's identify the additive inverse step by step for [tex]\(\frac{1}{2}\)[/tex]:
1. Definition Identification:
- The number we start with is [tex]\(\frac{1}{2}\)[/tex].
- We want to find a number that, when added to [tex]\(\frac{1}{2}\)[/tex], equals zero.
2. Expression of the Condition:
- Let the additive inverse be denoted as [tex]\(y\)[/tex].
- We need to solve the equation [tex]\(\frac{1}{2} + y = 0\)[/tex].
3. Solving the Equation:
- To isolate [tex]\(y\)[/tex], subtract [tex]\(\frac{1}{2}\)[/tex] from both sides of the equation:
[tex]\[
y = 0 - \frac{1}{2}
\][/tex]
- Simplify the right-hand side:
[tex]\[
y = -\frac{1}{2}
\][/tex]
Therefore, the additive inverse of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(-\frac{1}{2}\)[/tex].
When expressed as a decimal, [tex]\(-\frac{1}{2}\)[/tex] equals [tex]\(-0.5\)[/tex].
Thus, the additive inverse of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(-0.5\)[/tex].
