Arrange `(5)/(8), -(3)/(16),-(1)/(4)` and `(17)/(32)` in the descending order of their magnitudes. Also, find the sum of the lowest and the largest of these rational numbers. Express the result obtained as a decimal fraction correct to two decimal places.

Answer

To solve the problem of arranging the rational numbers \( \frac{5}{8}, -\frac{3}{16}, -\frac{1}{4}, \) and \( \frac{17}{32} \) in descending order of their magnitudes and finding the sum of the lowest and largest of these numbers, we can follow these steps:

### Step 1: Identify the Rational Numbers
The given rational numbers are:
1. \( \frac{5}{8} \)
2. \( -\frac{3}{16} \)
3. \( -\frac{1}{4} \)
4. \( \frac{17}{32} \)

### Step 2: Find the LCM of the Denominators
The denominators are 8, 16, 4, and 32. We need to find the least common multiple (LCM) of these numbers.

- The LCM of 8, 16, 4, and 32 is 32.

### Step 3: Convert Each Rational Number to Have a Common Denominator
Now we will convert each fraction to have a denominator of 32.

1. \( \frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32} \)
2. \( -\frac{3}{16} = -\frac{3 \times 2}{16 \times 2} = -\frac{6}{32} \)
3. \( -\frac{1}{4} = -\frac{1 \times 8}{4 \times 8} = -\frac{8}{32} \)
4. \( \frac{17}{32} \) remains \( \frac{17}{32} \)

### Step 4: List the Converted Fractions
Now we have:
1. \( \frac{20}{32} \)
2. \( -\frac{6}{32} \)
3. \( -\frac{8}{32} \)
4. \( \frac{17}{32} \)

### Step 5: Arrange in Descending Order of Magnitude
Now we can arrange these fractions based on their numerators:
- \( \frac{20}{32} \) (largest)
- \( \frac{17}{32} \)
- \( -\frac{6}{32} \)
- \( -\frac{8}{32} \) (smallest)

Thus, the descending order is:
1. \( \frac{20}{32} \) (or \( \frac{5}{8} \))
2. \( \frac{17}{32} \)
3. \( -\frac{6}{32} \) (or \( -\frac{3}{16} \))
4. \( -\frac{8}{32} \) (or \( -\frac{1}{4} \))

### Step 6: Identify the Largest and Smallest Rational Numbers
- The largest rational number is \( \frac{5}{8} \).
- The smallest rational number is \( -\frac{1}{4} \).

### Step 7: Calculate the Sum of the Largest and Smallest Rational Numbers
Now we will find the sum of these two numbers:
\[ \frac{5}{8} + \left(-\frac{1}{4}\right) = \frac{5}{8} - \frac{1}{4} \]
To perform this operation, we need a common denominator:
- The denominator for \( \frac{1}{4} \) can be converted to 8:
\[ -\frac{1}{4} = -\frac{2}{8} \]
Now we can add:
\[ \frac{5}{8} - \frac{2}{8} = \frac{3}{8} \]

### Step 8: Convert the Result to Decimal
Now, we convert \( \frac{3}{8} \) to a decimal:
\[ \frac{3}{8} = 0.375 \]
Rounding to two decimal places gives us:
\[ 0.38 \]

### Final Answer
The rational numbers arranged in descending order are:
1. \( \frac{5}{8} \)
2. \( \frac{17}{32} \)
3. \( -\frac{3}{16} \)
4. \( -\frac{1}{4} \)

The sum of the largest and smallest rational numbers is:
\[ 0.38 \]