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The image shows a math problem where you are asked to compare pairs of expressions in **Part A** and determine which is greater, smaller, or equal without evaluating them. Additionally, in **Part B**, you are asked to choose one pair from **Part A** and explain how you determined which is greater.

Here’s how you can approach this:

### Part A:
You're supposed to compare the following pairs using \(>, =, <\):

1. \(108 - (81 + 3)\) vs. \(108 - 81 + 3\)
2. \((7 + 28) \times (152 + 302)\) vs. \((152 + 302) \times 28\)
3. \(588 \times 65\) vs. \((500 + 8) \times (5 + 60)\)
4. \(1,006 \div 67\) vs. \((762 + 1,006) \div 67\)

### Strategy for Comparison Without Evaluation:
1. **Expression 1:**
   - \(108 - (81 + 3)\) is different from \(108 - 81 + 3\) due to parentheses. In the first, you subtract the sum \(81 + 3\), while in the second, you subtract 81, then add 3.

2. **Expression 2:**
   - \((7 + 28) \times (152 + 302)\) can be rearranged, but you're comparing two different multiplication orders. Both expressions are equivalent because multiplication is commutative.

3. **Expression 3:**
   - \(588 \times 65\) and \((500 + 8) \times (5 + 60)\) may seem different, but the second expression breaks down the numbers into simpler factors. By distributive property, these could be equal but simplified differently.

4. **Expression 4:**
   - \(1,006 \div 67\) vs. \((762 + 1,006) \div 67\). In this case, you're comparing a simple division with a larger sum divided by 67, which makes the second expression larger.

### Part B:
For **Part B**, you'd choose one of the pairs and explain your reasoning, such as how parentheses or the order of operations affect the outcome without computing exact values.

Would you like to work through one specific comparison more thoroughly? Let me know if you want further details!

Here are some relative questions for you to consider:
1. How do parentheses affect the outcome of an expression?
2. Why is multiplication commutative, and how does that affect expression comparison?
3. How does the distributive property simplify complex multiplication?
4. What happens when you divide a larger sum versus a smaller number?
5. How can estimation help in comparing expressions without fully evaluating them?

**Tip**: Always apply the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) carefully to avoid mistakes.

Compare the expressions in Part A and Part B without evaluating.

This problem explores how to compare expressions using the order of operations (PEMDAS) and properties like commutative and distributive properties. Students are challenged to compare pairs of expressions without directly calculating them. Suitable for middle school students (Grades 6-8).

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