Sure, let's order the given fractions from greatest to least.
We are given the fractions:
[tex]\[
\frac{11}{12}, \frac{7}{10}, \frac{5}{6}
\][/tex]
### Step-by-Step Solution:
1. List the fractions:
- [tex]\(\frac{11}{12}\)[/tex]
- [tex]\(\frac{7}{10}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
2. Convert each fraction to a decimal to easily compare them:
- [tex]\(\frac{11}{12} \approx 0.9167\)[/tex]
- [tex]\(\frac{7}{10} = 0.7\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
3. Compare the decimal values:
- [tex]\(0.9167\)[/tex] (which represents [tex]\(\frac{11}{12}\)[/tex])
- [tex]\(0.8333\)[/tex] (which represents [tex]\(\frac{5}{6}\)[/tex])
- [tex]\(0.7\)[/tex] (which represents [tex]\(\frac{7}{10}\)[/tex])
4. Order them from greatest to least:
- The greatest decimal value is [tex]\(0.9167\)[/tex] or [tex]\(\frac{11}{12}\)[/tex]
- The next greatest decimal value is [tex]\(0.8333\)[/tex] or [tex]\(\frac{5}{6}\)[/tex]
- The smallest decimal value is [tex]\(0.7\)[/tex] or [tex]\(\frac{7}{10}\)[/tex]
Thus, the fractions in decreasing order are:
[tex]\[
\frac{11}{12}, \frac{5}{6}, \frac{7}{10}
\][/tex]
### Verify the Answer Choices
- Option A: [tex]\(\frac{11}{12}, \frac{7}{10}, \frac{5}{6}\)[/tex] — This is not correct as [tex]\(\frac{7}{10}\)[/tex] is not greater than [tex]\(\frac{5}{6}\)[/tex].
- Option B: [tex]\(\frac{5}{6}, \frac{11}{12}, \frac{7}{10}\)[/tex] — This is not correct as [tex]\(\frac{11}{12}\)[/tex] is greater than [tex]\(\frac{5}{6}\)[/tex].
- Option C: [tex]\(\frac{11}{12}, \frac{5}{6}, \frac{7}{10}\)[/tex] — This matches our order from greatest to least.
- Option D: [tex]\(\frac{5}{6}, \frac{7}{10}, \frac{11}{12}\)[/tex] — This is not correct as [tex]\(\frac{11}{12}\)[/tex] should be first.
### Conclusion
The correct answer is Option C: [tex]\(\frac{11}{12}, \frac{5}{6}, \frac{7}{10}\)[/tex].
