To solve the problem of ordering the fractions [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{3}{8}\)[/tex], [tex]\(\frac{3}{4}\)[/tex], and [tex]\(\frac{1}{8}\)[/tex] from greatest to smallest, let's follow these steps:
1. Compare the values of the fractions:
- [tex]\(\frac{2}{3}\)[/tex] converts to approximately [tex]\(0.6666666666666666\)[/tex].
- [tex]\(\frac{3}{8}\)[/tex] converts to [tex]\(0.375\)[/tex].
- [tex]\(\frac{3}{4}\)[/tex] converts to [tex]\(0.75\)[/tex].
- [tex]\(\frac{1}{8}\)[/tex] converts to [tex]\(0.125\)[/tex].
2. Arrange these decimal equivalents in descending order:
- The largest value is [tex]\(0.75\)[/tex] which corresponds to [tex]\(\frac{3}{4}\)[/tex].
- The next largest value is [tex]\(0.6666666666666666\)[/tex] which corresponds to [tex]\(\frac{2}{3}\)[/tex].
- The next largest value is [tex]\(0.375\)[/tex] which corresponds to [tex]\(\frac{3}{8}\)[/tex].
- The smallest value is [tex]\(0.125\)[/tex] which corresponds to [tex]\(\frac{1}{8}\)[/tex].
Putting it all together, the fractions ordered from greatest to smallest are:
[tex]$
\frac{3}{4}, \frac{2}{3}, \frac{3}{8}, \frac{1}{8}.
$[/tex]
Since none of the provided options matches this correct ordering, it's evident that none of the given answers is correct.
