Step-by-Step Evaluation of the Arithmetic Expression

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

1. Identify the expression: We have 5 - 4 ÷ (1/4) + 1/2.
2. Perform division first: In the expression, perform the division 4 ÷ (1/4). Dividing by a fraction is equivalent to multiplying by its reciprocal:

4 ÷ (1/4) = 4 × (4/1) = 4 × 4 = 16

3. Substitute back into the expression: Now, replace 4 ÷ (1/4) with 16:

5 - 16 + 1/2

4. Perform the subtraction: Now, calculate 5 - 16:

5 - 16 = -11

5. Add the fraction: Now, the expression is -11 + 1/2. To add these, we can express -11 as a fraction:

-11 = -11/1 = -22/2

6. Add the fractions: Now we can add -22/2 + 1/2:

-22/2 + 1/2 = (-22 + 1)/2 = -21/2

7. Final result: The final result is:

-21/2

8. As a mixed number, this can be expressed as:

-10 1/2

So, the evaluated expression is -21/2 or as a mixed number, -10 1/2.