To find a rational number with a denominator of 7 that lies between 7 and 8, we start by expressing the two whole numbers as fractions with a denominator of 7.
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Convert 7 to a fraction with a denominator of 7:
\[ 7 = \frac{7 \times 7}{7} = \frac{49}{7} \]
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Convert 8 to a fraction with a denominator of 7:
\[ 8 = \frac{8 \times 7}{7} = \frac{56}{7} \]
Now, we are looking for a rational number \(\frac{n}{7}\) such that:
\[ \frac{49}{7} < \frac{n}{7} < \frac{56}{7} \]
This can be simplified to:
\[ 49 < n < 56 \]
The integers \(n\) that satisfy this inequality are 50, 51, 52, 53, 54, and 55. We can choose any of these integers.
For example, if we select \(n = 52\), the corresponding rational number is:
\[ \frac{52}{7} \]
This is a rational number with a denominator of 7 that is between 7 and 8. Other options include:
- \(\frac{50}{7}\)
- \(\frac{51}{7}\)
- \(\frac{53}{7}\)
- \(\frac{54}{7}\)
- \(\frac{55}{7}\)
Any of these would also be valid answers. However, as requested, one possible answer is:
\[ \frac{52}{7} \]