Sure, let's work through the solution step-by-step.
### Step 1: Identify the number [tex]\( m \)[/tex]
The number [tex]\( m \)[/tex] is given as the additive inverse of [tex]\(\frac{5}{8}\)[/tex]. The additive inverse of a number is the number that, when added to the original number, results in zero. So, [tex]\( m = -\frac{5}{8} \)[/tex].
### Step 2: Place [tex]\(\frac{5}{8}\)[/tex] and [tex]\( m \)[/tex] on the number line
- [tex]\(\frac{5}{8}\)[/tex] is a positive number slightly less than 1.
- [tex]\( m \)[/tex] or [tex]\(-\frac{5}{8}\)[/tex] is a negative number slightly more than -1.
### Step 3: Determine the sum of [tex]\(\frac{5}{8}\)[/tex] and [tex]\( m \)[/tex]
The sum of [tex]\(\frac{5}{8}\)[/tex] and [tex]\( m \)[/tex] (which is [tex]\( -\frac{5}{8} \)[/tex]) should be:
[tex]\[ \frac{5}{8} + \left(-\frac{5}{8}\right) = 0 \][/tex]
### Step 4: Place the sum on the number line
The sum of these two numbers is 0.
### Summary:
1. [tex]\(\frac{5}{8}\)[/tex] is placed at [tex]\(0.625\)[/tex] on the number line.
2. [tex]\( m \)[/tex] or [tex]\(-\frac{5}{8}\)[/tex] is placed at [tex]\(-0.625\)[/tex] on the number line.
3. The label "Sum" is placed at [tex]\(0\)[/tex] on the number line.
Here's how it looks on the number line:
- [tex]\(\frac{5}{8}\)[/tex] at [tex]\( 0.625 \)[/tex]
- [tex]\( m \)[/tex] (or [tex]\(-\frac{5}{8}\)[/tex]) at [tex]\( -0.625 \)[/tex]
- "Sum" at [tex]\( 0 \)[/tex]
