To simplify the expression \( a \frac{1}{2} \left( a \frac{1}{2} - 2 \right) \), we can follow these steps:

### Step 1: Express the fractions as products
Rewrite the terms that involve fractions:
\[
a \frac{1}{2} = \frac{a}{2}
\]
So the expression becomes:
\[
\frac{a}{2} \left( \frac{a}{2} - 2 \right)
\]

### Step 2: Distribute \(\frac{a}{2}\) into the parentheses
Use the distributive property to expand the expression:
\[
\frac{a}{2} \cdot \frac{a}{2} - \frac{a}{2} \cdot 2
\]

### Step 3: Multiply each term
1. \(\frac{a}{2} \cdot \frac{a}{2} = \frac{a^2}{4}\)
2. \(\frac{a}{2} \cdot 2 = \frac{2a}{2} = a\)

### Step 4: Combine the terms
The expression simplifies to:
\[
\frac{a^2}{4} - a
\]

So, the simplified form of the expression is:
\[
\frac{a^2}{4} - a
\]

Would you like a more detailed explanation, or do you have any questions?

Here are five related questions you might find helpful:
1. How do you simplify expressions with mixed fractions and variables?
2. What is the distributive property, and how is it used in algebraic expressions?
3. How can you factor quadratic expressions like \(\frac{a^2}{4} - a\)?
4. How do you handle operations involving fractions and algebraic variables?
5. What strategies help in solving equations with variables and fractions?

**Tip**: Always check if you can factor your final expression further or simplify it more.

Learn how to simplify the algebraic expression a 1/2 (a 1/2 - 2) using the distributive property and operations with fractions. This problem covers key algebraic concepts and is suitable for students in Grades 7-9.

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