Sure, let's arrange the given fractions in descending order.
1. Convert the fractions to decimal form to make comparison easier:
- [tex]\(\frac{-1}{10} = -0.1\)[/tex]
- [tex]\(\frac{8}{-15} = -\frac{8}{15} = -0.533\)[/tex] (approx)
- [tex]\(\frac{19}{30} = 0.633\)[/tex] (approx)
- [tex]\(\frac{-2}{-5} = \frac{2}{5} = 0.4\)[/tex]
2. List the decimal representations:
- [tex]\(-0.1\)[/tex]
- [tex]\(-0.533\)[/tex] (approx)
- [tex]\(0.633\)[/tex] (approx)
- [tex]\(0.4\)[/tex]
3. Arrange these decimals in descending order:
- The largest value is [tex]\(0.633\)[/tex], or [tex]\(\frac{19}{30}\)[/tex]
- The next largest value is [tex]\(0.4\)[/tex], or [tex]\(\frac{2}{5}\)[/tex]
- Then comes [tex]\(-0.1\)[/tex], or [tex]\(\frac{-1}{10}\)[/tex]
- Finally, the smallest value is [tex]\(-0.533\)[/tex], or [tex]\(\frac{8}{-15}\)[/tex]
4. Write the fractions in descending order:
- [tex]\(\frac{19}{30}\)[/tex]
- [tex]\(\frac{2}{5}\)[/tex]
- [tex]\(\frac{-1}{10}\)[/tex]
- [tex]\(\frac{8}{-15}\)[/tex]
Therefore, the fractions arranged in descending order are:
[tex]\[
\frac{19}{30}, \frac{2}{5}, \frac{-1}{10}, \frac{8}{-15}
\][/tex]
