To determine which fraction has the greatest value, we can compare the given fractions:
- \(\frac{5}{6}\)
- \(\frac{1}{6}\)
- \(-\frac{1}{6}\)
- \(-\frac{5}{6}\)
Here’s how we can evaluate them:
- \(\frac{5}{6}\) is a positive fraction that is very close to 1, so it is quite large.
- \(\frac{1}{6}\) is also a positive fraction, but it is much smaller than \(\frac{5}{6}\).
- \(-\frac{1}{6}\) is a negative fraction.
- \(-\frac{5}{6}\) is also a negative fraction and is less than \(-\frac{1}{6}\).
Since \(\frac{5}{6}\) is the only positive fraction and is greater than both \(\frac{1}{6}\) and the negative fractions, it is clear that \(\frac{5}{6}\) has the greatest value among the given options.
Thus, the fraction with the greatest value is:
\(\frac{5}{6}\)
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