To determine the additive inverse of [tex]\(\frac{1}{2}\)[/tex], we need to understand the concept of an additive inverse. The additive inverse of a number is a value that, when added to the original number, results in zero.
Let's denote the original number as [tex]\(a\)[/tex]. The additive inverse of [tex]\(a\)[/tex] is the number [tex]\(b\)[/tex] such that:
[tex]\[ a + b = 0 \][/tex]
Given [tex]\(a = \frac{1}{2}\)[/tex], we need to find [tex]\(b\)[/tex] that satisfies:
[tex]\[ \frac{1}{2} + b = 0 \][/tex]
To isolate [tex]\(b\)[/tex], subtract [tex]\(\frac{1}{2}\)[/tex] from both sides:
[tex]\[ b = 0 - \frac{1}{2} \][/tex]
[tex]\[ b = -\frac{1}{2} \][/tex]
Therefore, the additive inverse of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(-\frac{1}{2}\)[/tex].
Let's review the provided options to identify which [tex]\(-\frac{1}{2}\)[/tex] corresponds to:
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(2\)[/tex]
- [tex]\(-2\)[/tex]
None of the given options directly represent [tex]\(-\frac{1}{2}\)[/tex].
Therefore, the additive inverse of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(-\frac{1}{2}\)[/tex]. Since negative [tex]\(\frac{1}{2}\)[/tex] isn't listed among the multiple choice options you provided, it implies the correct choice should have been included as:
- [tex]\(-\frac{1}{2}\)[/tex]
The correct additive inverse is:
[tex]\[-0.5\][/tex]
But none of the listed choices matches this exactly.
