−1/2(8×1/4÷2+5−(6−∣−6∣) −7)

Let's break down and simplify the expression step by step.

The given expression is:

\[
-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - (6 - | -6 |) - 7 \right)
\]

### Step 1: Simplify absolute value \( | -6 | \)

The absolute value of \(-6\) is 6.

So, the expression becomes:

\[
-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - (6 - 6) - 7 \right)
\]

### Step 2: Simplify the inner subtraction

\[
6 - 6 = 0
\]

Now the expression is:

\[
-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - 0 - 7 \right)
\]

Which simplifies to:

\[
-\frac{1}{2} \left( 8 \times \frac{1}{4} \div 2 + 5 - 7 \right)
\]

### Step 3: Perform the multiplication and division

First, compute \( 8 \times \frac{1}{4} = 2 \).

Next, divide 2 by 2:

\[
2 \div 2 = 1
\]

Now the expression is:

\[
-\frac{1}{2} \left( 1 + 5 - 7 \right)
\]

### Step 4: Simplify the addition and subtraction

\[
1 + 5 = 6
\]
\[
6 - 7 = -1
\]

Now the expression becomes:

\[
-\frac{1}{2} \times (-1)
\]

### Step 5: Multiply

\[
-\frac{1}{2} \times (-1) = \frac{1}{2}
\]

### Final Answer:

\[
\frac{1}{2}
\]

Would you like more details or have any questions? Here are some related problems for practice:

1. Simplify: \( -\frac{1}{3} (9 \times \frac{2}{3} - 4 + | -8 | - 2) \)
2. Solve: \( -\frac{1}{4}(12 \div 3 \times 5 - (4 - | -2 |) + 6) \)
3. Evaluate: \( \frac{1}{5}(10 - (8 - | -7 |) \div 2 + 3) \)
4. Simplify: \( -\frac{2}{3} (6 \times \frac{3}{2} - 9 + 5 - | -4 |) \)
5. Solve: \( \frac{1}{4}(16 \div 2 - (10 - | -9 |) + 7) \)

**Tip:** Always handle absolute values and parentheses first when simplifying complex expressions.

−1/2(8×1/4÷2+5−(6−∣−6∣)−7)

Learn how to simplify the complex arithmetic expression −1/2(8×1/4÷2+5−(6−∣−6∣)−7). This step-by-step solution covers key concepts such as absolute value and order of operations, suitable for students in Grades 6-8.

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