Certainly! Let's break down the phrase "one-fourth of a number."
Elaina wrote variable expressions to represent this phrase.
To understand what "one-fourth of a number" means, let's first figure out the mathematical representation of one-fourth:
- One-fourth can be written as [tex]\(\frac{1}{4}\)[/tex].
Now, we need to attach this to the concept of "a number," which we can represent using a variable, such as [tex]\(n\)[/tex].
There are two common ways to express one-fourth of a number in variable form:
1. Multiplying the number [tex]\(n\)[/tex] by one-fourth:
- This can be written as [tex]\(\frac{1}{4} \times n\)[/tex].
- Simplifying this, we can write it as [tex]\(\frac{1}{4n}\)[/tex] or [tex]\(\frac{1}{4} \cdot n\)[/tex].
2. Dividing the number [tex]\(n\)[/tex] by 4:
- This can be written as [tex]\(n \div 4\)[/tex].
- In fraction form, this is written as [tex]\(\frac{n}{4}\)[/tex].
So, the correct variable expressions Elaina could have written are:
- [tex]\(\frac{1}{4} n\)[/tex]
- [tex]\(\frac{n}{4}\)[/tex]
Now, let's check the other options:
3. Inverting the one-fourth relationship by writing [tex]\(\frac{4}{n}\)[/tex]:
- This expression represents "four divided by a number," which is not equivalent to one-fourth of a number.
4. Dividing 4 by the number [tex]\(n\)[/tex]:
- Writing it as [tex]\(4 \div n\)[/tex] represents "four divided by a number," which, again, is not one-fourth of a number.
Given this analysis, the only correct expressions Elaina could have written are:
- [tex]\(\frac{1}{4} n\)[/tex]
- [tex]\(\frac{n}{4}\)[/tex]
Thus, the correct answers are:
[tex]\[
\frac{1}{4} n \quad \text{and} \quad \frac{n}{4}
\][/tex]
