Numbers and `(-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 them into a common denominator so that we can easily compare their values.

### Step 1: Identify the common denominator
The denominators are 20, 15, 30, and 10. The least common multiple (LCM) of these numbers is 60.

### Step 2: Convert each fraction to have the common denominator of 60
1. For \(-\frac{11}{20}\):
\[ -\frac{11}{20} = -\frac{11 \times 3}{20 \times 3} = -\frac{33}{60} \]

2. For \(\frac{7}{-15}\):
\[ \frac{7}{-15} = -\frac{7 \times 4}{15 \times 4} = -\frac{28}{60} \]

3. For \(-\frac{17}{30}\):
\[ -\frac{17}{30} = -\frac{17 \times 2}{30 \times 2} = -\frac{34}{60} \]

4. For \(-\frac{3}{10}\):
\[ -\frac{3}{10} = -\frac{3 \times 6}{10 \times 6} = -\frac{18}{60} \]

### Step 3: List the converted fractions
Now we have:
- \(-\frac{33}{60}\)
- \(-\frac{28}{60}\)
- \(-\frac{34}{60}\)
- \(-\frac{18}{60}\)

### Step 4: Compare the fractions
Since all fractions have the same denominator, we can compare the numerators:
- \(-33\)
- \(-28\)
- \(-34\)
- \(-18\)

### Step 5: Order the fractions based on the numerators
The order from greatest to least (considering that more negative means smaller) is:
1. \(-\frac{18}{60}\) (greatest)
2. \(-\frac{28}{60}\)
3. \(-\frac{33}{60}\)
4. \(-\frac{34}{60}\) (least)

### Step 6: Write the final answer in descending order
Thus, the numbers in descending order are:
\[ -\frac{3}{10}, -\frac{7}{15}, -\frac{11}{20}, -\frac{17}{30} \]