Solve: -4/16 - (-3/8) + 2/8 + (-1/4) | Mixed Fraction Operations

To solve the problem, we will follow these steps:

• Simplify each fraction where possible.
• Find a common denominator for all fractions.
• Convert each fraction to have this common denominator.
• Perform the required operations: subtraction and addition.

Let's begin solving the problem:

Step 1: Simplify each fraction.
- $-\frac{4}{16}$ simplifies to $-\frac{1}{4}$ since both numerator and denominator can be divided by 4.
- The fractions $-(-\frac{3}{8})$, $\frac{2}{8}$, and $-\frac{1}{4}$ are already in their simplest forms.

Step 2: Find the common denominator.
The denominators are 4 and 8. The least common denominator (LCD) is 8.

Step 3: Convert each fraction to an equivalent fraction with this common denominator:
- $-\frac{1}{4}$ becomes $-\frac{2}{8}$ because $\frac{1}{4} \times \frac{2}{2} = \frac{2}{8}$.
- $-(-\frac{3}{8})$ simplifies to $\frac{3}{8}$ (due to subtracting a negative, which makes it positive).
- $\frac{2}{8}$ remains unchanged, as it already has the common denominator.
- $-\frac{1}{4}$ becomes $-\frac{2}{8}$ for the same reason as above.

Step 4: Perform the operations:
$-\frac{2}{8} + \frac{3}{8} + \frac{2}{8} - \frac{2}{8}$.

Adding and subtracting these fractions with a common denominator:
- Combine them as $(-2 + 3 + 2 - 2)/8 = 1/8$.

Therefore, the solution to the problem is $\frac{1}{8}$.