First, let's start by identifying the given rational numbers and converting them to decimal form, which will make it easier to compare their values.
The given rational numbers are:
1. [tex]\( \frac{2}{-3} \)[/tex]
2. [tex]\( \frac{-4}{9} \)[/tex]
3. [tex]\( \frac{-5}{12} \)[/tex]
4. [tex]\( \frac{7}{-18} \)[/tex]
Now, let's convert each of these to their decimal equivalents:
1. [tex]\( \frac{2}{-3} = -0.6666666666666666 \)[/tex]
2. [tex]\( \frac{-4}{9} = -0.4444444444444444 \)[/tex]
3. [tex]\( \frac{-5}{12} = -0.4166666666666667 \)[/tex]
4. [tex]\( \frac{7}{-18} = -0.3888888888888889 \)[/tex]
Next, we need to arrange these decimal values in descending order:
- [tex]\(-0.3888888888888889\)[/tex]
- [tex]\(-0.4166666666666667\)[/tex]
- [tex]\(-0.4444444444444444\)[/tex]
- [tex]\(-0.6666666666666666\)[/tex]
Rewriting these in their original fractional forms gives us the following order:
1. [tex]\( \frac{7}{-18} \)[/tex] (which is [tex]\(-0.3888888888888889\)[/tex] in decimal form)
2. [tex]\( \frac{-5}{12} \)[/tex] (which is [tex]\(-0.4166666666666667\)[/tex] in decimal form)
3. [tex]\( \frac{-4}{9} \)[/tex] (which is [tex]\(-0.4444444444444444\)[/tex] in decimal form)
4. [tex]\( \frac{2}{-3} \)[/tex] (which is [tex]\(-0.6666666666666666\)[/tex] in decimal form)
Therefore, the rational numbers ordered in descending order are:
[tex]\[ \frac{7}{-18}, \frac{-5}{12}, \frac{-4}{9}, \frac{2}{-3} \][/tex]
