To determine the correct ordering of the fractions from greatest to least, we first need to convert each fraction to its decimal equivalent for easier comparison. Let's break down each fraction:
1. [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[ \frac{2}{3} \approx 0.6667 \][/tex]
2. [tex]\(\frac{3}{8}\)[/tex]:
[tex]\[ \frac{3}{8} = 0.375 \][/tex]
3. [tex]\(\frac{5}{12}\)[/tex]:
[tex]\[ \frac{5}{12} \approx 0.4167 \][/tex]
Now, let's compare these decimal values to find the order from greatest to least:
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex] is the greatest.
- [tex]\(\frac{5}{12} \approx 0.4167\)[/tex] is less than [tex]\(\frac{2}{3}\)[/tex] but greater than [tex]\(\frac{3}{8}\)[/tex].
- [tex]\(\frac{3}{8} = 0.375\)[/tex] is the least.
Thus, the correct order from greatest to least is:
[tex]\[ \frac{2}{3}, \frac{5}{12}, \frac{3}{8} \][/tex]
Looking at the given options:
A: [tex]\(\frac{2}{3}, \frac{3}{8}, \frac{5}{12}\)[/tex]
B: [tex]\(\frac{5}{12}, \frac{3}{8}, \frac{2}{3}\)[/tex]
C: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex]
D: [tex]\(\frac{3}{8}, \frac{2}{3}, \frac{5}{12}\)[/tex]
Option C matches the order we found:
[tex]\[
\boxed{3}
\][/tex]
