Let's break down and solve the expression:

\[
(0.5 + 52) + \left( 2 \times \frac{1}{4} \times 25\% \right)
\]

### Step 1: Simplify the first part.
\[
0.5 + 52 = 52.5
\]

### Step 2: Simplify the second part.
- 25% is equivalent to \(\frac{25}{100} = 0.25\)
\[
2 \times \frac{1}{4} \times 0.25
\]
- Start by multiplying:
\[
2 \times \frac{1}{4} = \frac{2}{4} = 0.5
\]
\[
0.5 \times 0.25 = 0.125
\]

### Step 3: Add the results together.
\[
52.5 + 0.125 = 52.625
\]

Thus, the value of the expression is:
\[
\boxed{52.625}
\]

Would you like more details on any step?

### Related Questions:
1. How do you simplify expressions involving fractions and percentages?
2. What are the properties of addition and multiplication used here?
3. How can percentages be converted to decimals?
4. How do parentheses affect the order of operations in expressions?
5. How would the result change if we increased the percentage in the second part?

### Tip:
When working with percentages in calculations, always convert them to their decimal form (e.g., \(25\% = 0.25\)) for easier computation.

This guide shows how to solve the arithmetic expression (0.5 + 52) + (2 x ¼ x 25%) step-by-step. It covers key concepts in percentages, fractions, multiplication, and addition, making it suitable for Grades 6-8 students. Learn how to break down and simplify complex expressions using basic math principles.

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