To determine which set of rational numbers are ordered from least to greatest, we need to compare the four given rational numbers:
- [tex]\( -2 \frac{5}{6} \)[/tex]
- [tex]\( -\frac{2}{3} \)[/tex]
- [tex]\( 1 \frac{1}{6} \)[/tex]
- [tex]\( 1 \frac{5}{6} \)[/tex]
### Step 1: Convert Mixed Fractions to Improper Fractions or Decimals
- [tex]\( -2 \frac{5}{6} \)[/tex] can be written as [tex]\( -2 - \frac{5}{6} = -2.8333 \)[/tex].
- [tex]\( -\frac{2}{3} \)[/tex] can be written as a decimal as [tex]\( -0.6667 \)[/tex].
- [tex]\( 1 \frac{1}{6} \)[/tex] can be written as [tex]\( 1 + \frac{1}{6} = 1.1667 \)[/tex].
- [tex]\( 1 \frac{5}{6} \)[/tex] can be written as [tex]\( 1 + \frac{5}{6} = 1.8333 \)[/tex].
### Step 2: Arrange the Numbers from Least to Greatest:
Using the decimal values we calculated:
- [tex]\( -2.8333 \)[/tex] (which corresponds to [tex]\( -2 \frac{5}{6} \)[/tex])
- [tex]\( -0.6667 \)[/tex] (which corresponds to [tex]\( -\frac{2}{3} \)[/tex])
- [tex]\( 1.1667 \)[/tex] (which corresponds to [tex]\( 1 \frac{1}{6} \)[/tex])
- [tex]\( 1.8333 \)[/tex] (which corresponds to [tex]\( 1 \frac{5}{6} \)[/tex])
So, the order from least to greatest is:
1. [tex]\( -2 \frac{5}{6} \)[/tex]
2. [tex]\( -\frac{2}{3} \)[/tex]
3. [tex]\( 1 \frac{1}{6} \)[/tex]
4. [tex]\( 1 \frac{5}{6} \)[/tex]
### Conclusion:
The correct ordered set of rational numbers from least to greatest is given by:
[tex]\[ -2 \frac{5}{6}, -\frac{2}{3}, 1 \frac{1}{6}, 1 \frac{5}{6} \][/tex]
Thus, the correct answer is:
[tex]\[ 1. \ -2 \frac{5}{6}, -\frac{2}{3}, 1 \frac{1}{6}, 1 \frac{5}{6} \][/tex]
