Here’s the breakdown and solution for the worksheet:

Section A: Find the value of each expression

1. (8 - 3) × 2

   • Step 1: Simplify inside the parentheses: $8 - 3 = 5$.
   • Step 2: Multiply: $5 \times 2 = 10$.
   • Answer: 10

2. 10 - (5 + 2)

   • Step 1: Simplify inside the parentheses: $5 + 2 = 7$.
   • Step 2: Subtract: $10 - 7 = 3$.
   • Answer: 3

3. (2 + 3) × (4 + 5)

   • Step 1: Simplify both sets of parentheses: $2 + 3 = 5$ and $4 + 5 = 9$.
   • Step 2: Multiply: $5 \times 9 = 45$.
   • Answer: 45

4. (9 × 3) + (9 × 2)

   • Step 1: Multiply inside both sets of parentheses: $9 \times 3 = 27$ and $9 \times 2 = 18$.
   • Step 2: Add: $27 + 18 = 45$.
   • Answer: 45

5. [9 × (6 - 3)] × 2

   • Step 1: Simplify inside the parentheses: $6 - 3 = 3$.
   • Step 2: Multiply inside the brackets: $9 \times 3 = 27$.
   • Step 3: Multiply by 2: $27 \times 2 = 54$.
   • Answer: 54

Section B: Find the value of each expression if $a = 2$ and $b = 3$

1. 8 - (3 × 2)

   • Step 1: Multiply: $3 \times 2 = 6$.
   • Step 2: Subtract: $8 - 6 = 2$.
   • Answer: 2

2. 2 + 3 × 4 + 5

   • Step 1: Follow the order of operations (PEMDAS). Multiply first: $3 \times 4 = 12$.
   • Step 2: Add: $2 + 12 + 5 = 19$.
   • Answer: 19

3. 10 - 5 + 2

   • Step 1: Follow left-to-right for addition/subtraction: $10 - 5 = 5$.
   • Step 2: Add: $5 + 2 = 7$.
   • Answer: 7

4. [9 × (6 - 3)] × 2

   • This is the same as Section A, Question 5.
   • Answer: 54

5. (6 + 6) × 4

   • Step 1: Simplify inside the parentheses: $6 + 6 = 12$.
   • Step 2: Multiply: $12 \times 4 = 48$.
   • Answer: 48

Let me know if you'd like further explanation on any step or section.

Follow-up Questions:

1. What is the importance of parentheses in evaluating mathematical expressions?
2. How does the order of operations (PEMDAS) affect the solution to a problem?
3. Can you solve for variables in expressions involving unknowns using these rules?
4. What happens if parentheses are omitted in an expression?
5. How can the distributive property simplify expressions like $(9 \times 3) + (9 \times 2)$?

Tip: Always simplify parentheses first and remember PEMDAS to avoid calculation errors!