To determine which fraction has the greatest value among the given fractions, let's list them out clearly for comparison:
1. [tex]\(\frac{5}{6}\)[/tex]
2. [tex]\(\frac{1}{6}\)[/tex]
3. [tex]\(-\frac{1}{6}\)[/tex]
4. [tex]\(-\frac{5}{6}\)[/tex]
First, note that the fractions with the negative signs ([tex]\(-\frac{1}{6}\)[/tex] and [tex]\(-\frac{5}{6}\)[/tex]) are less than zero, so they cannot be the greatest value. Therefore, we can focus on the positive fractions:
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{1}{6}\)[/tex]
Now, compare the two positive fractions. We can observe that [tex]\(\frac{5}{6}\)[/tex] is greater than [tex]\(\frac{1}{6}\)[/tex]. This is because:
- [tex]\(\frac{5}{6}\)[/tex] represents five parts out of six, which is a larger fraction of the whole compared to [tex]\(\frac{1}{6}\)[/tex], which represents only one part out of six.
Thus, the fraction [tex]\(\frac{5}{6}\)[/tex] has the greatest value among the given fractions.
Therefore, the greatest value is:
[tex]\[ \frac{5}{6} \][/tex]
which equals approximately [tex]\(0.8333333333333334\)[/tex].
