Evaluating the Expression: -1/2 + (-6 ÷ -3 - 1/4 + 5)

To evaluate the expression -1/2 + (-6 ÷ -3 - 1/4 + 5), we will follow these steps:

1. Evaluate the division:
   -6 ÷ -3 = 2 (since a negative divided by a negative is positive)
2. Substitute the result back into the expression:
   Now the expression looks like this: -1/2 + (2 - 1/4 + 5)
3. Combine the integer values:
   The integers 2 and 5 combine to give 7:
   -1/2 + (7 - 1/4)
4. Get a common denominator to combine 7 and -1/4:
   The common denominator for 4 and 1 (the denominator of 7 when expressed as a fraction) is 4:
   7 = 28/4 (because 7 * 4 = 28)
   Now we can combine: 28/4 - 1/4 = 27/4
5. Now combine this with -1/2:
   Convert -1/2 to have a common denominator of 4:
   -1/2 = -2/4
   Therefore, we now have:
   -2/4 + 27/4
6. Combine the fractions:
   (-2 + 27)/4 = 25/4

The final result is: 25/4, which can also be expressed as a mixed number: 6 1/4.

Final Answer: 25/4 or 6 1/4