Let's solve the given problems one by one based on the image.

1. $150 - 100 \div (-2) =$

We need to follow the order of operations (PEMDAS/BODMAS):

• First, perform division: $100 \div (-2) = -50$
• Then, subtract: $150 - (-50) = 150 + 50 = 200$

Answer: $200$

2. $-25 \times (-4) + (-35) =$

• First, perform multiplication: $-25 \times (-4) = 100$
• Then, add $100 + (-35) = 100 - 35 = 65$

Answer: $65$

3. $-124 \times (500 \div 50) =$

• First, perform division inside parentheses: $500 \div 50 = 10$
• Then, multiply: $-124 \times 10 = -1240$

Answer: $-1240$

4. $250 + (-8) \times 25 =$

• First, perform multiplication: $(-8) \times 25 = -200$
• Then, add: $250 + (-200) = 250 - 200 = 50$

Answer: $50$

5. $750 - (-2) \times (-250) + (-50) =$

• First, multiply $(-2) \times (-250) = 500$
• Then, calculate the expression: $750 - 500 + (-50) = 750 - 500 - 50 = 200$

Answer: $200$

Let me know if you'd like more details on any of these solutions!

Here are five related questions:

1. How do we prioritize operations in complex expressions?
2. Why does subtracting a negative number result in addition?
3. How does the distributive property work in algebraic expressions?
4. What is the difference between positive and negative multiplication?
5. How can parentheses change the result of an expression?

Tip: Always solve expressions inside parentheses first and pay attention to signs when multiplying or dividing negative numbers.