To evaluate the expression -\frac{3}{4} + \frac{5}{-2} \div 4 - 2 + \frac{1}{2}, we’ll break it down into manageable steps.
Step 1: Simplify Division
First, we need to handle the division in the expression:
\frac{5}{-2} \div 4
To divide by a fraction, we multiply by the reciprocal:
\frac{5}{-2} \div 4 = \frac{5}{-2} \times \frac{1}{4} = \frac{5 \times 1}{-2 \times 4} = \frac{5}{-8}
Now, the expression looks like this:
-\frac{3}{4} + \frac{5}{-8} - 2 + \frac{1}{2}
Step 2: Find a Common Denominator
Next, we need a common denominator to combine the fractions. The denominators are 4, 8, and 2. The least common multiple (LCM) of these numbers is 8. Let's convert each fraction:
-\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8}-2 = -2\times \frac{8}{8} = -\frac{16}{8}\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
So now we have:
-\frac{6}{8} + \frac{5}{-8} - \frac{16}{8} + \frac{4}{8}
Step 3: Combine the Fractions
Now that all fractions are over a common denominator, we can combine them:
- Combine the numerators:
-6 + 5 - 16 + 4
Calculating the numerators:
-6 + 5 = -1-1 - 16 = -17-17 + 4 = -13
So, we have:
\frac{-13}{8}
Final Result
The final answer can be expressed as a mixed number:
-\frac{13}{8} = -1 \frac{5}{8}
Thus, the evaluated expression is:
-1 \frac{5}{8} or \frac{-13}{8}