To determine whether \( 517 \frac{5}{1} 7 \) is a rational number between \( 5 \frac{1}{4} \), we first need to interpret the given expressions correctly.
However, the way the numbers are presented seems unconventional. Let's simplify it for clarity:
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Understanding the numbers:
- If \( 517 \frac{5}{1} 7 \) is interpreted as \( 517 \) (which appears to be a whole number) followed by another number, it could mean \( 517.57 \).
- If we interpret \( 5 \frac{1}{4} \) as \( 5.25 \).
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Rational numbers:
- A rational number is defined as any number that can be expressed as the quotient of two integers. Both \( 517.57 \) and \( 5.25 \) are rational numbers.
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Finding the range:
- We want to see if \( 517.57 \) is indeed between \( 5.25 \) and \( 514 \).
As \( 517.57 \) is significantly greater than both \( 514 \) and \( 5.25 \):
Therefore, the statement is False.
So, the final answer is: False.