Arrange the following rational number in descending order:
`frac(-2)(5),frac(7)(-10),frac(-11)(15),frac(19)(-30)`

Options

A. `frac(-2)(5)gtfrac(-11)(15)gtfrac(7)(-10)gtfrac(19)(-30)`
B. `frac(-11)(15)gtfrac(19)(-30)gtfrac(7)(-10)gtfrac(-2)(5)`
C. `frac(-2)(5)gtfrac(19)(-30)gtfrac(7)(-10)gtfrac(-11)(15)`
D. none of these

Answer

To arrange the given rational numbers in descending order, we will follow these steps:

### Step 1: Identify the Rational Numbers
The rational numbers we need to arrange are:
1. \(-\frac{2}{5}\)
2. \(\frac{7}{-10}\) (which is the same as \(-\frac{7}{10}\))
3. \(-\frac{11}{15}\)
4. \(\frac{19}{-30}\) (which is the same as \(-\frac{19}{30}\))

### Step 2: Find a Common Denominator
To compare these fractions, we need to convert them to have a common denominator. The least common multiple (LCM) of the denominators \(5, 10, 15, 30\) is \(30\).

### Step 3: Convert Each Fraction
Now we will convert each fraction to have the denominator \(30\):

1. \(-\frac{2}{5}\):
\[ -\frac{2}{5} = -\frac{2 \times 6}{5 \times 6} = -\frac{12}{30} \]

2. \(-\frac{7}{10}\):
\[ -\frac{7}{10} = -\frac{7 \times 3}{10 \times 3} = -\frac{21}{30} \]

3. \(-\frac{11}{15}\):
\[ -\frac{11}{15} = -\frac{11 \times 2}{15 \times 2} = -\frac{22}{30} \]

4. \(-\frac{19}{30}\):
\[ -\frac{19}{30} \text{ (already has the denominator 30)} \]

### Step 4: Compare the Numerators
Now we have:
1. \(-\frac{12}{30}\)
2. \(-\frac{21}{30}\)
3. \(-\frac{22}{30}\)
4. \(-\frac{19}{30}\)

To compare these fractions, we look at the numerators:
- \(-12\)
- \(-21\)
- \(-22\)
- \(-19\)

### Step 5: Arrange in Descending Order
Since all the fractions have the same negative denominator, the fraction with the least negative numerator is the largest. Thus, we arrange them as follows:
1. \(-\frac{12}{30}\) (largest)
2. \(-\frac{19}{30}\)
3. \(-\frac{21}{30}\)
4. \(-\frac{22}{30}\) (smallest)

### Final Answer
In descending order, the rational numbers are:
\[ -\frac{2}{5}, -\frac{19}{30}, -\frac{7}{10}, -\frac{11}{15} \]