Numbers `(-11)/(20), (7)/(-15), (17)/(-30)` and `(-3)/(10)` are written in descending order as

Options

A. `(17)/(-30) gt (-11)/(20) gt (-3)/(10) gt (7)/(-15)`
B. `(-3)/(10) gt (7)/(-15) gt (-11)/(20) gt (17)/(-30)`
C. `(-3)/(10) gt (-11)/(20) gt (7)/(-15) gt (17)/(-30)`
D. `(-11)/(20) gt (17)/(-30) gt (-3)/(10) gt (7)/(-15)`

Answer

To arrange the numbers \(-\frac{11}{20}\), \(\frac{7}{-15}\), \(\frac{17}{-30}\), and \(-\frac{3}{10}\) in descending order, we will first convert each fraction into its decimal form.

### Step 1: Convert each fraction to decimal form

1. **Convert \(-\frac{11}{20}\)**:
\[ -\frac{11}{20} = -0.55 \]

2. **Convert \(\frac{7}{-15}\)**:
\[ \frac{7}{-15} = -\frac{7}{15} \approx -0.4667 \]

3. **Convert \(\frac{17}{-30}\)**:
\[ \frac{17}{-30} = -\frac{17}{30} \approx -0.5667 \]

4. **Convert \(-\frac{3}{10}\)**:
\[ -\frac{3}{10} = -0.3 \]

### Step 2: List the decimal values

Now we have the following decimal values:
- \(-\frac{11}{20} \approx -0.55\)
- \(-\frac{7}{15} \approx -0.4667\)
- \(-\frac{17}{30} \approx -0.5667\)
- \(-\frac{3}{10} \approx -0.3\)

### Step 3: Arrange the decimal values in descending order

To arrange these values in descending order, we compare them:
- The largest value (least negative) is \(-0.3\) (from \(-\frac{3}{10}\)).
- The next largest is \(-0.4667\) (from \(-\frac{7}{15}\)).
- The next is \(-0.55\) (from \(-\frac{11}{20}\)).
- The smallest value (most negative) is \(-0.5667\) (from \(-\frac{17}{30}\)).

Thus, the descending order is:
\[ -\frac{3}{10} > -\frac{7}{15} > -\frac{11}{20} > -\frac{17}{30} \]

### Final Answer

The numbers in descending order are:
\[ -\frac{3}{10}, -\frac{7}{15}, -\frac{11}{20}, -\frac{17}{30} \]