Let's solve each expression step by step using the
order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
---
Problem 1:
Expression:
$$
3 + [(9 \div 3) \cdot 2] + [(2 \cdot 6) \div 3]
$$
Step-by-step:
1. Evaluate inside parentheses:
- $9 \div 3 = 3$
- $2 \cdot 6 = 12$
2. Now substitute:
$$
3 + [3 \cdot 2] + [12 \div 3]
$$
3. Perform multiplication and division:
- $3 \cdot 2 = 6$
- $12 \div 3 = 4$
4. Now:
$$
3 + 6 + 4 = 13
$$
✔ Answer: 13
---
Problem 2:
Expression:
$$
[(3 + 9) \div (3 \cdot 2)] + [(2 \cdot 6) \div 3]
$$
Step-by-step:
1. Inside parentheses:
- $3 + 9 = 12$
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$
2. Substitute:
$$
[12 \div 6] + [12 \div 3]
$$
3. Perform divisions:
- $12 \div 6 = 2$
- $12 \div 3 = 4$
4. Add:
$$
2 + 4 = 6
$$
✔ Answer: 6
---
Problem 3:
Expression:
$$
(3 + 9) \div [(3 \cdot 2 + 2 \cdot 6) \div 3]
$$
Step-by-step:
1. Numerator: $3 + 9 = 12$
2. Denominator: $(3 \cdot 2 + 2 \cdot 6) \div 3$
- First, do multiplications:
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$
- Then addition: $6 + 12 = 18$
- Then divide: $18 \div 3 = 6$
3. So now:
$$
12 \div 6 = 2
$$
✔ Answer: 2
---
Problem 4:
Expression:
$$
(3 + 9 \div 3 \cdot 2) + (2 \cdot 6 \div 3)
$$
Important: No parentheses around $9 \div 3 \cdot 2$, so follow
left-to-right for same precedence (division and multiplication).
Step-by-step:
1. First part: $3 + 9 \div 3 \cdot 2$
- $9 \div 3 = 3$
- $3 \cdot 2 = 6$
- $3 + 6 = 9$
2. Second part: $2 \cdot 6 \div 3$
- $2 \cdot 6 = 12$
- $12 \div 3 = 4$
3. Add both parts:
$$
9 + 4 = 13
$$
✔ Answer: 13
---
Problem 5:
Expression:
$$
[(3 + 9) \div 3 \cdot 2 + 2] \cdot (6 \div 3)
$$
Step-by-step:
1. Start with innermost:
- $3 + 9 = 12$
2. So expression becomes:
$$
[12 \div 3 \cdot 2 + 2] \cdot (6 \div 3)
$$
3. Work inside the first bracket:
- $12 \div 3 = 4$
- $4 \cdot 2 = 8$
- $8 + 2 = 10$
4. Second part: $6 \div 3 = 2$
5. Now:
$$
10 \cdot 2 = 20
$$
✔ Answer: 20
---
Problem 6:
Expression:
$$
[(3 + 9 \div 3) \cdot 2] + (2 \cdot 6 \div 3)
$$
Step-by-step:
1. Inside first bracket: $3 + 9 \div 3$
- $9 \div 3 = 3$
- $3 + 3 = 6$
2. Multiply by 2: $6 \cdot 2 = 12$
3. Second part: $2 \cdot 6 \div 3$
- $2 \cdot 6 = 12$
- $12 \div 3 = 4$
4. Add:
$$
12 + 4 = 16
$$
✔ Answer: 16
---
✔ Final Answers:
| Expression | Answer |
|----------|--------|
| $3 + [(9 \div 3) \cdot 2] + [(2 \cdot 6) \div 3]$ |
13 |
| $[(3 + 9) \div (3 \cdot 2)] + [(2 \cdot 6) \div 3]$ |
6 |
| $(3 + 9) \div [(3 \cdot 2 + 2 \cdot 6) \div 3]$ |
2 |
| $(3 + 9 \div 3 \cdot 2) + (2 \cdot 6 \div 3)$ |
13 |
| $[(3 + 9) \div 3 \cdot 2 + 2] \cdot (6 \div 3)$ |
20 |
| $[(3 + 9 \div 3) \cdot 2] + (2 \cdot 6 \div 3)$ |
16 |
Let me know if you'd like a visual breakdown or explanation of any specific one!
Parent Tip: Review the logic above to help your child master the concept of order of operations with parentheses worksheet.
