To find the relationship between the number of students and the number of tables, we can represent the relationship as a fraction where the numerator is the number of students and the denominator is the number of tables.
From the information given:
- One table has 8 students.
- Six tables have 45 students.
We can write the proportions separately for one table and six tables:
-
For one table: \[ \text{Fraction for one table} = \frac{8 \text{ students}}{1 \text{ table}} = \frac{8}{1} \]
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For six tables: \[ \text{Fraction for six tables} = \frac{45 \text{ students}}{6 \text{ tables}} = \frac{45}{6} \]
Now we can represent the relationship between the number of students (S) and the number of tables (T) in fraction form based on one table: \[ \frac{S}{T} = \frac{8}{1} \]
And based on six tables: \[ \frac{S}{T} = \frac{45}{6} \]
Thus, the ratios that represent the students to tables are:
- For one table: \(\frac{8}{1}\)
- For six tables: \(\frac{45}{6}\)
In summary, the relationship can be represented as:
- \(\frac{8}{1} \) for one table, and \(\frac{45}{6} \) for six tables, both showing the number of students per each case without reducing it to the lowest terms.
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