https://file.aiquickdraw.com/mathbot/file/17268011582994fdlcxui.jpg

Let's work through the problems from the image step by step. The exercises involve absolute values and basic arithmetic operations. I'll solve a few of these, and you can let me know if you'd like the rest solved in detail.

### 1) 
\[
|56 - 15| \times 8 + \frac{|14|}{2} = ?
\]
- \( |56 - 15| = |41| = 41 \)
- \( \frac{|14|}{2} = \frac{14}{2} = 7 \)
- \( 41 \times 8 = 328 \)
- \( 328 + 7 = 335 \)

Answer: \( 335 \)

### 2)
\[
\frac{|8|}{4} \times |4 - 1| = ?
\]
- \( \frac{|8|}{4} = \frac{8}{4} = 2 \)
- \( |4 - 1| = |3| = 3 \)
- \( 2 \times 3 = 6 \)

Answer: \( 6 \)

### 3)
\[
| -8 | \times \frac{1 + 2}{|4|} \times |7| = ?
\]
- \( | -8 | = 8 \)
- \( \frac{1 + 2}{|4|} = \frac{3}{4} \)
- \( |7| = 7 \)
- \( 8 \times \frac{3}{4} \times 7 = 8 \times 5.25 = 42 \)

Answer: \( 42 \)

### 4)
\[
\frac{| -7 \times 4 |}{2} \times \frac{|10|}{| -5 |} = ?
\]
- \( | -7 \times 4 | = | -28 | = 28 \)
- \( \frac{| -28 |}{2} = \frac{28}{2} = 14 \)
- \( \frac{|10|}{| -5 |} = \frac{10}{5} = 2 \)
- \( 14 \times 2 = 28 \)

Answer: \( 28 \)

Would you like me to continue solving the rest, or would you prefer to solve some on your own and get help when needed?

### 5 Related Questions:
1. How do absolute values affect the outcome of equations?
2. How can you simplify complex expressions with fractions and absolute values?
3. What are some key strategies for solving multi-step arithmetic problems?
4. How do you handle negative numbers when calculating absolute values?
5. How do you apply the order of operations (PEMDAS) in these types of problems?

### Tip:
Always handle the absolute value first, then move on to basic arithmetic operations according to the order of operations (PEMDAS).

Evaluate the absolute value expressions involving arithmetic operations from the given worksheet.

Work through step-by-step solutions for evaluating absolute value expressions, involving addition, subtraction, multiplication, and division. This is suitable for students in Grades 6-8 and covers key mathematical concepts like absolute values and order of operations.

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