Which set of rational numbers are ordered from least to greatest?

Question

A number line going from negative 3 to positive 3 in increments of 1.
Negative 2 and StartFraction 5 Over 6 EndFraction, negative two-thirds, 1 and StartFraction 1 Over 6 EndFraction, 1 and StartFraction 5 Over 6 EndFraction
1 and StartFraction 5 Over 6 EndFraction, 1 and StartFraction 1 Over 6 EndFraction, negative two-thirds, negative 2 and StartFraction 5 Over 6 EndFraction
Negative two-thirds, 1 and one-sixth, 1 and StartFraction 5 Over 6 EndFraction, negative 2 and StartFraction 5 Over 6 EndFraction
Negative 2 and StartFraction 5 Over 6 EndFraction, 1 and StartFraction 5 Over 6 EndFraction, 1 and one-sixth, negative two-thirds

Answer 1

To order the numbers from least to greatest, we first need to convert all the numbers to a comparable form (either decimals or improper fractions).

The numbers are:

1. -2 and \( \frac{5}{6} \) = -2.8333 (approx)
2. -2/3 = -0.6667 (approx)
3. 1 and \( \frac{1}{6} \) = 1.1667 (approx)
4. 1 and \( \frac{5}{6} \) = 1.8333 (approx)

Now we can order them from least to greatest based on their decimal values:

• -2 and \( \frac{5}{6} \) = -2.8333
• -2/3 = -0.6667
• 1 and \( \frac{1}{6} \) = 1.1667
• 1 and \( \frac{5}{6} \) = 1.8333

Therefore, the correct ordering from least to greatest is:

• Negative 2 and \( \frac{5}{6} \)
• Negative two-thirds
• 1 and \( \frac{1}{6} \)
• 1 and \( \frac{5}{6} \)

This corresponds to: Negative 2 and \( \frac{5}{6} \), negative two-thirds, 1 and \( \frac{1}{6} \), 1 and \( \frac{5}{6} \)

So, the answer is: Negative 2 and \( \frac{5}{6} \), negative two-thirds, 1 and \( \frac{1}{6} \), 1 and \( \frac{5}{6} \).