To find the number of pencils per student, you first calculate the total number of pencils available and then divide that total by the number of students.
The teacher has 6 boxes of pencils, and if each box contains \( x \) pencils, the total number of pencils can be expressed as \( 6x \).
To determine how many pencils each student will receive, you divide the total number of pencils by the number of students:
\[ \text{Pencils per student} = \frac{6x}{30} \]
This simplifies to:
\[ \text{Pencils per student} = \frac{6}{30}x = \frac{1}{5}x \]
None of the options you provided directly represent this simplified fraction. However, the expression that would represent the total number of pencils divided by the number of students is \( \frac{6x}{30} \).
So, the closest correct option based on your choices is:
\( \frac{6x}{30} \) which represents the total number of pencils per student.
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