Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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]

Sagot :

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]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.