To determine which set of fractions is ordered from least to greatest, let's examine each choice and compare the fractions.
We start with the given fractions: [tex]\(\frac{7}{8}, \frac{5}{11}, \frac{2}{3}\)[/tex].
To compare the fractions, let's convert each one to its decimal equivalent:
1. [tex]\(\frac{7}{8}\)[/tex]:
- Decimal: [tex]\( \frac{7}{8} = 0.875 \)[/tex]
2. [tex]\(\frac{5}{11}\)[/tex]:
- Decimal: [tex]\( \frac{5}{11} \approx 0.4545 \)[/tex]
3. [tex]\(\frac{2}{3}\)[/tex]:
- Decimal: [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
Now, we need to order these decimal values from least to greatest:
- [tex]\(0.4545\)[/tex]
- [tex]\(0.6667\)[/tex]
- [tex]\(0.875\)[/tex]
So, the fractions in ascending order are:
[tex]\[
\frac{5}{11}, \frac{2}{3}, \frac{7}{8}
\][/tex]
Now, let's review the choices given:
A) [tex]$\frac{7}{8}, \frac{5}{11}, \frac{2}{3}$[/tex]
B) [tex]$\frac{5}{11}, \frac{7}{8}, \frac{2}{3}$[/tex]
C) [tex]$\frac{2}{3}, \frac{5}{11}, \frac{7}{8}$[/tex]
D) [tex]$\frac{5}{11}, \frac{2}{3}, \frac{7}{8}$[/tex]
Among these choices, the correct order from smallest to largest is in:
D) [tex]$\frac{5}{11}, \frac{2}{3}, \frac{7}{8}$[/tex]
Thus, the answer is:
D
