Alright, let's break this down step by step.
1. Understanding Additive Inverses:
- Two numbers are additive inverses if their sum is zero. In other words, if you add a number to its additive inverse, the result should be zero.
2. Identifying the Values:
- The given number is [tex]\(\frac{5}{8}\)[/tex].
- Let's denote its additive inverse as [tex]\(m\)[/tex]. For the number [tex]\(\frac{5}{8}\)[/tex], its additive inverse will be a number that, when added to [tex]\(\frac{5}{8}\)[/tex], gives us zero.
- According to our mathematical expectation, the number that adds to [tex]\(\frac{5}{8}\)[/tex] to yield zero would be [tex]\(-\frac{5}{8}\)[/tex].
3. Placing These Numbers on the Number Line:
- [tex]\(\frac{5}{8}\)[/tex]: This is a positive number, so it will be to the right of zero on the number line.
- [tex]\(m\)[/tex] ([tex]\(-\frac{5}{8}\)[/tex]): This is a negative number, so it will be to the left of zero on the number line.
4. Sum of the Numbers:
- The sum of [tex]\(\frac{5}{8}\)[/tex] and [tex]\(-\frac{5}{8}\)[/tex] is zero. This means the point labeled "Sum" will be at zero on the number line.
Now, on a number line, here is how we can place the values:
- [tex]\(\frac{5}{8}\)[/tex] will be placed to the right of zero.
- [tex]\(m\)[/tex] or [tex]\(-\frac{5}{8}\)[/tex] will be placed to the left of zero, at an equal distance from zero as [tex]\(\frac{5}{8}\)[/tex].
- The label "Sum" will be placed at zero, as the sum of [tex]\(\frac{5}{8}\)[/tex] and [tex]\(-\frac{5}{8}\)[/tex] is zero.
Positions on the number line:
```
Left of zero -------------------- Zero -------------------- Right of zero
m 0 5/8
(-5/8) (5/8)
```
Step-by-step placement:
- [tex]\(m = -\frac{5}{8}\)[/tex] at -0.625 on the number line (left side of zero).
- [tex]\(\frac{5}{8} = 0.625\)[/tex] at 0.625 on the number line (right side of zero).
- Sum at 0 on the number line.
So, the final placements are:
- [tex]\(\frac{5}{8}\)[/tex] should be dragged to 0.625.
- [tex]\(m\)[/tex] should be dragged to -0.625.
- "Sum" should be dragged to 0.
