`(-2)/3, 5/2, (-1)/6` in descending order can be arranged as :

Options

A. `5/2, (-1)/6, (-2)/3`
B. `(-2)/(3), 5/2, (-1)/6`
C. `(-1)/6, 5/2, (-2)/3`
D. `5/2, (-2)/3, (-1)/6`

Answer

To arrange the numbers \(-\frac{2}{3}, \frac{5}{2}, -\frac{1}{6}\) in descending order, we will follow these steps:

### Step 1: Convert the fractions to decimal form
- \(-\frac{2}{3} = -0.6667\) (approximately)
- \(\frac{5}{2} = 2.5\)
- \(-\frac{1}{6} = -0.1667\) (approximately)

### Step 2: Identify the largest number
From the decimal values:
- \(2.5\) (which is \(\frac{5}{2}\)) is the largest.

### Step 3: Compare the negative numbers
Now we will compare the negative numbers:
- \(-0.6667\) (which is \(-\frac{2}{3}\))
- \(-0.1667\) (which is \(-\frac{1}{6}\))

Since \(-0.1667\) is greater than \(-0.6667\), we can conclude:
- The next largest number is \(-\frac{1}{6}\).
- The smallest number is \(-\frac{2}{3}\).

### Step 4: Write the numbers in descending order
Putting it all together, the numbers in descending order are:
\[ \frac{5}{2}, -\frac{1}{6}, -\frac{2}{3} \]

### Final Answer:
The descending order is: \(\frac{5}{2}, -\frac{1}{6}, -\frac{2}{3}\).

---