Certainly! Let's find the additive inverse of [tex]\(16 \frac{5}{7}\)[/tex].
An additive inverse of a number is what you add to that number to get zero. Mathematically, for any number [tex]\(x\)[/tex], the additive inverse is [tex]\(-x\)[/tex].
Given the mixed number [tex]\(16 \frac{5}{7}\)[/tex], we need to determine its additive inverse. Here’s how you can think through this step-by-step:
1. Understanding the Mixed Number:
[tex]\(16 \frac{5}{7}\)[/tex] consists of two parts:
- The whole number part: 16
- The fractional part: [tex]\(\frac{5}{7}\)[/tex]
So, we can express [tex]\(16 \frac{5}{7}\)[/tex] as [tex]\(16 + \frac{5}{7}\)[/tex].
2. Expressing the Additive Inverse:
The additive inverse of [tex]\(16 + \frac{5}{7}\)[/tex] is simply the negative of this value, which is:
[tex]\[
-(16 + \frac{5}{7}) = -16 - \frac{5}{7}
\][/tex]
3. Combining the Parts:
Combining the whole number and the fraction while keeping the negative sign, we get:
[tex]\[
-16 - \frac{5}{7}
\][/tex]
This can be written as a mixed number:
[tex]\[
-16 \frac{5}{7}
\][/tex]
From this step-by-step process, we see that the additive inverse of [tex]\(16 \frac{5}{7}\)[/tex] is [tex]\(-16 \frac{5}{7}\)[/tex].
Therefore, the correct answer is:
D. [tex]\( -16 \frac{5}{7} \)[/tex]
