Step-by-Step Evaluation of the Expression: -3/4 + 5 - 2 ÷ 4 - 2 + 1/2

To evaluate the expression -3/4 + 5 - 2 ÷ 4 - 2 + 1/2, we will follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

1. Evaluate Division:
   Start with the division part of the expression, which is -2 ÷ 4:
   -2 ÷ 4 = -1/2.
   Now we can rewrite the expression:

2. -3/4 + 5 - 1/2 - 2 + 1/2

3. Combine like terms:
   Before proceeding, notice we have two fractions to combine, and we need to convert everything to a common denominator.
4. Convert whole numbers to fractions:
   5 can be written as 5/1 and -2 can be written as -2/1. Thus, rewrite the expression as:
   -3/4 + 5/1 - 1/2 - 2/1 + 1/2
5. Finding a common denominator:
   The common denominator for 4, 1, and 2 is 4. So we convert all fractions:
   5/1 = 20/4
   -2/1 = -8/4
   -1/2 = -2/4
   1/2 = 2/4
6. Rewrite the expression:

-3/4 + 20/4 - 2/4 - 8/4 + 2/4

7. Combine all fractions:

= (-3 + 20 - 2 - 8 + 2) / 4

8. Calculating the numerator:
   -3 + 20 = 17
   17 - 2 = 15
   15 - 8 = 7
   7 + 2 = 9

So, the final expression is:

9/4

9. Convert to a mixed number (if necessary):
   9/4 can be expressed as a mixed number. Dividing 9 by 4 gives 2 with a remainder of 1, thus:
   9/4 = 2 ¹/₄

Final Answer:
The evaluated expression is 9/4 or as a mixed number 2 1/4.