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. \(\( \frac{2}{-3} \)\)
2. \(\( \frac{-4}{9} \)\)
3. \(\( \frac{-5}{12} \)\)
4. \(\( \frac{7}{-18} \)\)
Now, let's convert each of these to their decimal equivalents:
1. \(\( \frac{2}{-3} = -0.6666666666666666 \)\)
2. \(\( \frac{-4}{9} = -0.4444444444444444 \)\)
3. \(\( \frac{-5}{12} = -0.4166666666666667 \)\)
4. \(\( \frac{7}{-18} = -0.3888888888888889 \)\)
Next, we need to arrange these decimal values in descending order:
- \(\(-0.3888888888888889\)\)
- \(\(-0.4166666666666667\)\)
- \(\(-0.4444444444444444\)\)
- \(\(-0.6666666666666666\)\)
Rewriting these in their original fractional forms gives us the following order:
1. \(\( \frac{7}{-18} \)\) (which is \(\(-0.3888888888888889\)\) in decimal form)
2. \(\( \frac{-5}{12} \)\) (which is \(\(-0.4166666666666667\)\) in decimal form)
3. \(\( \frac{-4}{9} \)\) (which is \(\(-0.4444444444444444\)\) in decimal form)
4. \(\( \frac{2}{-3} \)\) (which is \(\(-0.6666666666666666\)\) in decimal form)
Therefore, the rational numbers ordered in descending order are:
\(\[ \frac{7}{-18}, \frac{-5}{12}, \frac{-4}{9}, \frac{2}{-3} \]\)
