The expression in the image is:

$1 \left( -\frac{1}{2} \right)^2 - 1 \left( -\frac{4}{2} \right) - 1$

Let's solve this step by step.

Step 1: Simplify each part of the expression.

1. First term:
   $1 \left( -\frac{1}{2} \right)^2 = 1 \times \frac{1}{4} = \frac{1}{4}$

2. Second term:
   $-1 \left( -\frac{4}{2} \right) = -1 \times -2 = 2$

3. Third term:
   $-1 = -1$

Step 2: Combine all terms.

$\frac{1}{4} + 2 - 1$

Step 3: Perform the arithmetic.

$\frac{1}{4} + 2 - 1 = \frac{1}{4} + 1 = \frac{1 + 4}{4} = \frac{5}{4}$

So, the final answer is:

$\boxed{\frac{5}{4}}$

Would you like more details or have any other questions?

Here are 5 questions that expand on this concept:

1. What is the general process for simplifying expressions with fractions and exponents?
2. How do negative signs affect the outcome when working with fractions?
3. How can you simplify similar algebraic expressions more efficiently?
4. What happens if the exponent is odd in a similar problem?
5. How can you convert a fraction into a decimal for a final answer?

Tip: Always carefully handle negative signs and exponents, especially when working with fractions, to avoid small errors that may affect the result.