To arrange the given rational numbers [tex]\(\frac{-2}{7}\)[/tex], [tex]\(\frac{5}{7}\)[/tex], [tex]\(\frac{24}{35}\)[/tex], and [tex]\(\frac{11}{-21}\)[/tex] in descending order, follow these steps:
1. Convert the fractions to decimal form:
- [tex]\(\frac{-2}{7} \approx -0.2857142857142857\)[/tex]
- [tex]\(\frac{5}{7} \approx 0.7142857142857143\)[/tex]
- [tex]\(\frac{24}{35} \approx 0.6857142857142857\)[/tex]
- [tex]\(\frac{11}{-21} = -\frac{11}{21} \approx -0.5238095238095238\)[/tex]
2. Compare the decimal values to determine their order from largest to smallest:
- The values are [tex]\(0.7142857142857143\)[/tex], [tex]\(0.6857142857142857\)[/tex], [tex]\(-0.2857142857142857\)[/tex], and [tex]\(-0.5238095238095238\)[/tex].
3. Arrange the decimal values in descending order:
- The largest value is [tex]\(0.7142857142857143\)[/tex].
- The next largest value is [tex]\(0.6857142857142857\)[/tex].
- The next is [tex]\(-0.2857142857142857\)[/tex].
- The smallest value is [tex]\(-0.5238095238095238\)[/tex].
4. Match the arranged decimal values back to their original fractions:
- [tex]\(0.7142857142857143\)[/tex] corresponds to [tex]\(\frac{5}{7}\)[/tex].
- [tex]\(0.6857142857142857\)[/tex] corresponds to [tex]\(\frac{24}{35}\)[/tex].
- [tex]\(-0.2857142857142857\)[/tex] corresponds to [tex]\(\frac{-2}{7}\)[/tex].
- [tex]\(-0.5238095238095238\)[/tex] corresponds to [tex]\(\frac{11}{-21}\)[/tex] or [tex]\(-\frac{11}{21}\)[/tex].
Therefore, the rational numbers arranged in descending order are:
[tex]\[
\frac{5}{7}, \frac{24}{35}, \frac{-2}{7}, \frac{11}{-21}
\][/tex]
