Math worksheet for practicing the order of operations with multiple expressions.

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).

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Problem 1:

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

Step-by-step:

- First, simplify inside the brackets:
- $9 \div 3 = 3$
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$
- $12 \div 3 = 4$

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

✔ Answer: 13

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Problem 2:

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

Step-by-step:

- Simplify inside parentheses:
- $3 + 9 = 12$
- $3 \cdot 2 = 6$
- So, $12 \div 6 = 2$
- $2 \cdot 6 = 12$, then $12 \div 3 = 4$

Now add:
$$
2 + 4 = 6
$$

✔ Answer: 6

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Problem 3:

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

Step-by-step:

- Numerator: $3 + 9 = 12$
- Denominator: Inside the brackets:
- $3 \cdot 2 = 6$
- $2 \cdot 6 = 12$
- $6 + 12 = 18$
- $18 \div 3 = 6$

Now divide:
$$
12 \div 6 = 2
$$

✔ Answer: 2

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Problem 4:

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

Step-by-step:

We must follow order of operations inside each set of parentheses.

First part: $3 + 9 \div 3 \cdot 2$

- Division and multiplication from left to right:
- $9 \div 3 = 3$
- $3 \cdot 2 = 6$
- Then $3 + 6 = 9$

Second part: $2 \cdot 6 \div 3$

- $2 \cdot 6 = 12$
- $12 \div 3 = 4$

Now add:
$$
9 + 4 = 13
$$

✔ Answer: 13

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Problem 5:

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

Step-by-step:

First, simplify inside the first big bracket:

- $3 + 9 = 12$
- $12 \div 3 = 4$
- $4 \cdot 2 = 8$
- $8 + 2 = 10$

Now second part: $6 \div 3 = 2$

Now multiply:
$$
10 \cdot 2 = 20
$$

✔ Answer: 20

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Problem 6:

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

Step-by-step:

First bracket: $(3 + 9 \div 3) \cdot 2$

- $9 \div 3 = 3$
- $3 + 3 = 6$
- $6 \cdot 2 = 12$

Second part: $2 \cdot 6 \div 3$

- $2 \cdot 6 = 12$
- $12 \div 3 = 4$

Now add:
$$
12 + 4 = 16
$$

✔ Answer: 16

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✔ 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 particular step!