To understand which variable expressions correctly represent the phrase "one-fourth of a number," let's break down the phrase mathematically.
The key phrase here is "one-fourth of a number," which can be understood as taking the number [tex]\( n \)[/tex] and dividing it by 4. Alternatively, this can be seen as multiplying the number [tex]\( n \)[/tex] by [tex]\( \frac{1}{4} \)[/tex].
Now let's analyze each given option:
1. [tex]\( 4 \div n \)[/tex]: This expression means dividing 4 by the number [tex]\( n \)[/tex]. This does not represent "one-fourth of a number." Instead, it represents the reciprocal of the number divided by 4.
2. [tex]\( \frac{n}{4} \)[/tex]: This expression means taking the number [tex]\( n \)[/tex] and dividing it by 4. This directly represents "one-fourth of a number."
3. [tex]\( \frac{4}{n} \)[/tex]: This expression means dividing 4 by the number [tex]\( n \)[/tex]. Similar to the first option, this represents the reciprocal of the number divided into 4 parts, not "one-fourth of a number."
4. [tex]\( \frac{1}{4} n \)[/tex]: This expression means multiplying the number [tex]\( n \)[/tex] by [tex]\( \frac{1}{4} \)[/tex]. This is another correct way to represent "one-fourth of a number."
Therefore, the correct variable expressions that Elaina could have written to represent "one-fourth of a number" are:
- [tex]\( \frac{n}{4} \)[/tex]
- [tex]\( \frac{1}{4} n \)[/tex]
These options correctly encapsulate the mathematical meaning of taking one-fourth of a given number [tex]\( n \)[/tex].
