To find the relationship between the number of students and the number of tables in fraction form, we start with the information given in the problem.
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We know that 8 students can sit around 1 table. This gives us the ratio: \[ \frac{8 \text{ students}}{1 \text{ table}} \]
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We also know that 48 students can sit around 6 tables. This gives us the ratio: \[ \frac{48 \text{ students}}{6 \text{ tables}} \]
Now, let's simplify the second fraction: \[ \frac{48 \text{ students}}{6 \text{ tables}} = \frac{48}{6} = 8 \] This means that 8 students can also sit around 1 table, confirming our first ratio.
From both ratios, we see that the number of students is consistently 8 for each table.
Therefore, the relationship can be expressed as: \[ \frac{8 \text{ students}}{1 \text{ table}} \]
The proportion between the number of students and the number of tables without reducing it to the lowest terms is: \[ \frac{8}{1} \]
Thus, the final answer is: \[ \frac{8}{1} \]