Answered

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

A. [tex]-2 \frac{5}{6},-\frac{2}{3}, 1 \frac{1}{6}, 1 \frac{5}{6}[/tex]

B. [tex]1 \frac{5}{6}, 1 \frac{1}{6},-\frac{2}{3},-2 \frac{5}{6}[/tex]

C. [tex]-\frac{2}{3}, 1 \frac{1}{6}, 1 \frac{5}{6},-2 \frac{5}{6}[/tex]

D. [tex]-2 \frac{5}{6}, 1 \frac{5}{6}, 1 \frac{1}{6},-\frac{2}{3}[/tex]



Answer :

GinnyAnswer
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]

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