Question

Order from least to greatest: 1
2
, −2
3
, −11
6
, −1
6
.


A number line going from negative 1 to 0.

Which of the following sets 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

Answers

Answered by GPT-4o mini
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. \(1\) (or \(1.0\))
2. \(-\frac{2}{3}\) (approximately \(-0.6667\))
3. \(-\frac{11}{6}\) (approximately \(-1.8333\))
4. \(-\frac{1}{6}\) (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:

1. One-half, negative two-thirds, negative one-sixth, Negative 1 and one-sixth
2. One-half, negative one-sixth, negative two-thirds, negative 1 and one-sixth
3. Negative one-sixth, negative 1 and one-sixth, negative two-thirds, one-half
4. 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:

1. **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.
2. **One-half (0.5), Negative one-sixth (-0.1667), Negative two-thirds (-0.6667), Negative 1 and one-sixth (-0.8333)** - NOT in order.
3. **Negative one-sixth (-0.1667), Negative 1 and one-sixth (-0.8333), Negative two-thirds (-0.6667), One-half (0.5)** - NOT in order.
4. **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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