To determine which expression models the situation described as "the difference of a number and 8," let's break down the phrase step-by-step.
1. Identifying the Number:
The phrase mentions "a number," which we will represent by [tex]\( n \)[/tex].
2. Understanding the Operation:
The word "difference" in mathematics refers to subtraction.
3. Order of Terms:
In a subtraction operation, the order of terms is crucial. The phrase says "the difference [of a number] and 8." This means we start with the number [tex]\( n \)[/tex] and then subtract 8 from it.
Based on these steps, the expression that shows the difference of a number [tex]\( n \)[/tex] and 8 is [tex]\( n - 8 \)[/tex].
Now, let's match this with the given options to find the correct one:
- [tex]\( n - 8 \)[/tex]
- [tex]\(\frac{8}{n}\)[/tex]
- [tex]\(\frac{n}{8}\)[/tex]
- [tex]\(8 - n\)[/tex]
The correct expression that models the situation is:
[tex]\[ n - 8 \][/tex]
Therefore, the correct answer is [tex]\( n - 8 \)[/tex], which corresponds to the first option provided.
