To order the numbers from least to greatest, we first need to convert all numbers into decimal or common fractions for easier comparison. Here are the numbers given:
- \(1\) (or \(1.0\))
- \(-\frac{2}{3}\) (approximately \(-0.6667\))
- \(-\frac{11}{6}\) (approximately \(-1.8333\))
- \(-\frac{1}{6}\) (approximately \(-0.1667\))
Now let's arrange these numbers in order:
- The largest negative is \(-\frac{1}{6}\) (which is \(-0.1667\)).
- Next is \(-\frac{2}{3}\) (which is \(-0.6667\)).
- Next is \(-\frac{11}{6}\) (which is \(-1.8333\)).
- Finally \(1\) is the last one.
So, the order from least to greatest is: \(-\frac{11}{6}, -\frac{2}{3}, -\frac{1}{6}, 1\).
Now, let's assess the sets you provided to see which is ordered from least to greatest:
- One-half, negative two-thirds, negative one-sixth, Negative 1 and one-sixth
- One-half, negative one-sixth, negative two-thirds, negative 1 and one-sixth
- Negative one-sixth, negative 1 and one-sixth, negative two-thirds, one-half
- Negative 1 and one-sixth, negative two-thirds, negative one-sixth, one-half
We convert these expressions to decimals for clarity:
- \(1/2 = 0.5\)
- \(-2/3 \approx -0.6667\)
- \(-1/6 \approx -0.1667\)
- \(-1\) (or \(-1.0\))
- \(1/6 \approx 0.1667\)
Now, let's check each option:
- One-half (0.5), Negative two-thirds (-0.6667), Negative one-sixth (-0.1667), Negative 1 and one-sixth (-1 + 1/6 = -0.8333) - NOT in order.
- One-half (0.5), Negative one-sixth (-0.1667), Negative two-thirds (-0.6667), Negative 1 and one-sixth (-0.8333) - NOT in order.
- Negative one-sixth (-0.1667), Negative 1 and one-sixth (-0.8333), Negative two-thirds (-0.6667), One-half (0.5) - NOT in order.
- Negative 1 and one-sixth (-0.8333), Negative two-thirds (-0.6667), Negative one-sixth (-0.1667), One-half (0.5) - is in order.
Thus, the fourth option is the only one that is ordered from least to greatest:
Negative 1 and one-sixth, Negative two-thirds, Negative one-sixth, One-half.
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