Order of Operations Practice Worksheet with six problems for solving complex expressions.

Let's solve each expression in the Order of Operations Practice grid step by step using the PEMDAS rule:

- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

We'll go through each cell one by one.

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Top Left:

$$
3 + [(9 ÷ 3) \cdot 2] + [(2 \cdot 6) ÷ 3]
$$

1. Inside parentheses:
- $9 ÷ 3 = 3$
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$
- $12 ÷ 3 = 4$

2. Now substitute:
$$
3 + 6 + 4 = 13
$$

✔ Answer: 13

---

Top Right:

$$
[(3 + 9) ÷ (3 \cdot 2)] + [(2 \cdot 6) ÷ 3]
$$

1. Parentheses:
- $3 + 9 = 12$
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$

2. Division:
- $12 ÷ 6 = 2$
- $12 ÷ 3 = 4$

3. Add:
$$
2 + 4 = 6
$$

✔ Answer: 6

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Middle Left:

$$
(3 + 9) ÷ [(3 \cdot 2 + 2 \cdot 6) ÷ 3]
$$

1. Numerator: $3 + 9 = 12$

2. Denominator:
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$
- $6 + 12 = 18$
- $18 ÷ 3 = 6$

3. Divide:
$$
12 ÷ 6 = 2
$$

✔ Answer: 2

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Middle Right:

$$
(3 + 9 ÷ 3 \cdot 2) + (2 \cdot 6 ÷ 3)
$$

Note: No parentheses around $9 ÷ 3 \cdot 2$, so follow left-to-right for multiplication/division.

1. First part: $3 + 9 ÷ 3 \cdot 2$
- $9 ÷ 3 = 3$
- $3 \cdot 2 = 6$
- $3 + 6 = 9$

2. Second part: $2 \cdot 6 ÷ 3$
- $2 \cdot 6 = 12$
- $12 ÷ 3 = 4$

3. Add:
$$
9 + 4 = 13
$$

✔ Answer: 13

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Bottom Left (Row 3, Col 1):

$$
[(3 + 9) ÷ 3 \cdot 2 + 2] \cdot (6 ÷ 3)
$$

1. Inside brackets:
- $3 + 9 = 12$
- $12 ÷ 3 = 4$
- $4 \cdot 2 = 8$
- $8 + 2 = 10$

2. Outside: $6 ÷ 3 = 2$

3. Multiply:
$$
10 \cdot 2 = 20
$$

✔ Answer: 20

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Bottom Right (Row 3, Col 2):

$$
[(3 + 9 ÷ 3) \cdot 2] + (2 \cdot 6 ÷ 3)
$$

1. Inside first bracket:
- $9 ÷ 3 = 3$
- $3 + 3 = 6$
- $6 \cdot 2 = 12$

2. Second part:
- $2 \cdot 6 = 12$
- $12 ÷ 3 = 4$

3. Add:
$$
12 + 4 = 16
$$

✔ Answer: 16

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Bottom Left (Row 4, Col 1):

$$
[3 + (9 ÷ 3) \cdot (2 + 2)] \cdot (6 ÷ 3)
$$

1. Inside:
- $9 ÷ 3 = 3$
- $2 + 2 = 4$
- $3 \cdot 4 = 12$
- $3 + 12 = 15$

2. $6 ÷ 3 = 2$

3. Multiply:
$$
15 \cdot 2 = 30
$$

✔ Answer: 30

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Bottom Right (Row 4, Col 2):

$$
(3 + 9) ÷ 3 \cdot 2 + [(2 \cdot 6) ÷ 3]
$$

1. $3 + 9 = 12$
- $12 ÷ 3 = 4$
- $4 \cdot 2 = 8$

2. $2 \cdot 6 = 12$
- $12 ÷ 3 = 4$

3. Add:
$$
8 + 4 = 12
$$

✔ Answer: 12

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Final Answers Grid:

| Expression | Answer |
|----------|--------|
| $3 + [(9 ÷ 3) \cdot 2] + [(2 \cdot 6) ÷ 3]$ | 13 |
| $[(3 + 9) ÷ (3 \cdot 2)] + [(2 \cdot 6) ÷ 3]$ | 6 |
| $(3 + 9) ÷ [(3 \cdot 2 + 2 \cdot 6) ÷ 3]$ | 2 |
| $(3 + 9 ÷ 3 \cdot 2) + (2 \cdot 6 ÷ 3)$ | 13 |
| $[(3 + 9) ÷ 3 \cdot 2 + 2] \cdot (6 ÷ 3)$ | 20 |
| $[(3 + 9 ÷ 3) \cdot 2] + (2 \cdot 6 ÷ 3)$ | 16 |
| $[3 + (9 ÷ 3) \cdot (2 + 2)] \cdot (6 ÷ 3)$ | 30 |
| $(3 + 9) ÷ 3 \cdot 2 + [(2 \cdot 6) ÷ 3]$ | 12 |

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✔ Summary of Answers:

1. 13
2. 6
3. 2
4. 13
5. 20
6. 16
7. 30
8. 12

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