The number [tex]$m$[/tex] and [tex]$\frac{5}{8}$[/tex] are additive inverses.

Drag and drop [tex][tex]$\frac{5}{8}$[/tex][/tex] and [tex]$m$[/tex] to their correct positions on the number line.

Drag and drop the label "Sum" to the sum of [tex]$\frac{5}{8}$[/tex] and [tex][tex]$m$[/tex][/tex].

[tex]$\frac{5}{8}$[/tex]
[tex]m[/tex]
Sum



Answer :

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.