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).