Let's simplify the expression step by step:

Given expression:

$4 + \frac{1}{2} - (3 - 2) + 3$

Step 1: Simplify inside the parentheses

$3 - 2 = 1$

Substitute this back: $4 + \frac{1}{2} - 1 + 3$

Step 2: Combine terms sequentially

1. Start with $4 + \frac{1}{2}$: $4 + \frac{1}{2} = 4.5$
2. Subtract $1$: $4.5 - 1 = 3.5$
3. Add $3$: $3.5 + 3 = 6.5$

Final Answer:

$6.5$

Let me know if you would like further details or clarifications! 😊

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Here are 5 related questions for further exploration:

1. How do you simplify expressions with fractions and decimals mixed together?
2. What is the difference between using parentheses and brackets in math?
3. How would the solution change if the fraction were negative?
4. What is the importance of following the order of operations in solving expressions?
5. Can this expression be rewritten as a fraction instead of a decimal?

Tip: Always remember to solve parentheses and simplify step by step according to the order of operations (PEMDAS).