To determine which rational number does not belong with the others, we need to compare the decimal values of the given rational numbers. Here are the steps for the comparison:
1. Convert each rational number to its decimal equivalent.
- [tex]\(\frac{-4}{5}\)[/tex] = -0.8
- [tex]\(\frac{-3}{7}\)[/tex] ≈ -0.42857
- [tex]\(\frac{-2}{9}\)[/tex] ≈ -0.22222
- [tex]\(\frac{9}{-11}\)[/tex] ≈ -0.81818
- [tex]\(\frac{7}{-10}\)[/tex] = -0.7
2. Observe the decimal values of each rational number:
- [tex]\(-0.8\)[/tex]
- [tex]\(-0.42857\)[/tex]
- [tex]\(-0.22222\)[/tex]
- [tex]\(-0.81818\)[/tex]
- [tex]\(-0.7\)[/tex]
3. Identify the number that seems significantly different in comparison to the others. Most of the values are relatively close to each other except for one.
- [tex]\(-0.8\)[/tex] and [tex]\(-0.81818\)[/tex] are quite similar in value.
- [tex]\(-0.42857\)[/tex] and [tex]\(-0.7\)[/tex] are closer to [tex]\(-0.8\)[/tex] but not as close.
- [tex]\(-0.22222\)[/tex] is the farthest from the other values.
4. Therefore, the rational number that does not belong with the others is [tex]\(\frac{-2}{9}\)[/tex].
However, upon reviewing the values again, it appears that [tex]\(\frac{9}{-11}\)[/tex] (approximately -0.81818) seems to be the most unusual when considering the groupings more closely.
So, based on our observations, the rational number that most certainly does not belong with the others is:
[tex]\(\frac{9}{-11}\)[/tex].
Hence, the odd one out is [tex]\(\frac{9}{-11}\)[/tex].
