Order of Operations Practice Worksheet | Math = Love - Free Printable

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 row by row.

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Row 1

#### 1. $ 3 + [(9 \div 3) \cdot 2] + [(2 \cdot 6) \div 3] $

Break it down:
- $ 9 \div 3 = 3 $
- $ 3 \cdot 2 = 6 $
- $ 2 \cdot 6 = 12 $
- $ 12 \div 3 = 4 $

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

✔ Answer: 13

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

- $ 3 + 9 = 12 $
- $ 3 \cdot 2 = 6 $
- $ 12 \div 6 = 2 $
- $ 2 \cdot 6 = 12 $
- $ 12 \div 3 = 4 $

Now:
$$
2 + 4 = 6
$$

✔ Answer: 6

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Row 2

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

- $ 3 + 9 = 12 $
- Inside brackets: $ 3 \cdot 2 = 6 $, $ 2 \cdot 6 = 12 $ → $ 6 + 12 = 18 $
- $ 18 \div 3 = 6 $
- Now: $ 12 \div 6 = 2 $

✔ Answer: 2

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#### 4. $ (3 + 9 \div 3 \cdot 2) + (2 \cdot 6 \div 3) $

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

- $ 9 \div 3 = 3 $
- $ 3 \cdot 2 = 6 $
- So $ 3 + 6 = 9 $
- $ 2 \cdot 6 = 12 $
- $ 12 \div 3 = 4 $
- Now: $ 9 + 4 = 13 $

✔ Answer: 13

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Row 3

#### 5. $ [(3 + 9) \div 3 \cdot 2 + 2] \cdot (6 \div 3) $

Step-by-step:
- $ 3 + 9 = 12 $
- $ 12 \div 3 = 4 $
- $ 4 \cdot 2 = 8 $
- $ 8 + 2 = 10 $
- $ 6 \div 3 = 2 $
- $ 10 \cdot 2 = 20 $

✔ Answer: 20

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

- $ 9 \div 3 = 3 $
- $ 3 + 3 = 6 $
- $ 6 \cdot 2 = 12 $
- $ 2 \cdot 6 = 12 $
- $ 12 \div 3 = 4 $
- $ 12 + 4 = 16 $

✔ Answer: 16

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Row 4

#### 7. $ [(3 + 9 \div (3 \cdot 2) + 2] \cdot 6 \div 3 $

Parentheses first:
- $ 3 \cdot 2 = 6 $
- $ 9 \div 6 = 1.5 $
- $ 3 + 1.5 = 4.5 $
- $ 4.5 + 2 = 6.5 $
- $ 6.5 \cdot 6 = 39 $
- $ 39 \div 3 = 13 $

✔ Answer: 13

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#### 8. $ 3 + (9 \div 3) \cdot (2 + 2 \cdot 6 \div 3) $

Start with inner expressions:
- $ 9 \div 3 = 3 $
- Inside second parentheses: $ 2 \cdot 6 = 12 $, $ 12 \div 3 = 4 $, then $ 2 + 4 = 6 $
- Now: $ 3 \cdot 6 = 18 $
- Then: $ 3 + 18 = 21 $

✔ Answer: 21

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Row 5

#### 9. $ 3 + \{[(9 \div 3) \cdot (2 + 2)] \cdot (6 \div 3)\} $

- $ 9 \div 3 = 3 $
- $ 2 + 2 = 4 $
- $ 3 \cdot 4 = 12 $
- $ 6 \div 3 = 2 $
- $ 12 \cdot 2 = 24 $
- $ 3 + 24 = 27 $

✔ Answer: 27

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#### 10. $ (3 + 9) \div 3 \cdot 2 + [(2 \cdot 6) \div 3] $

- $ 3 + 9 = 12 $
- $ 12 \div 3 = 4 $
- $ 4 \cdot 2 = 8 $
- $ 2 \cdot 6 = 12 $
- $ 12 \div 3 = 4 $
- $ 8 + 4 = 12 $

✔ Answer: 12

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✔ Final Answers (Grid Format):

| Expression | Answer |
|----------|--------|
| 1. $ 3 + [(9 \div 3) \cdot 2] + [(2 \cdot 6) \div 3] $ | 13 |
| 2. $ [(3 + 9) \div (3 \cdot 2)] + [(2 \cdot 6) \div 3] $ | 6 |
| 3. $ (3 + 9) \div [(3 \cdot 2 + 2 \cdot 6) \div 3] $ | 2 |
| 4. $ (3 + 9 \div 3 \cdot 2) + (2 \cdot 6 \div 3) $ | 13 |
| 5. $ [(3 + 9) \div 3 \cdot 2 + 2] \cdot (6 \div 3) $ | 20 |
| 6. $ [(3 + 9 \div 3) \cdot 2] + (2 \cdot 6 \div 3) $ | 16 |
| 7. $ [(3 + 9 \div (3 \cdot 2) + 2] \cdot 6 \div 3 $ | 13 |
| 8. $ 3 + (9 \div 3) \cdot (2 + 2 \cdot 6 \div 3) $ | 21 |
| 9. $ 3 + \{[(9 \div 3) \cdot (2 + 2)] \cdot (6 \div 3)\} $ | 27 |
| 10. $ (3 + 9) \div 3 \cdot 2 + [(2 \cdot 6) \div 3] $ | 12 |

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🔍 Key Tips:

- Always follow PEMDAS.
- For multiplication/division and addition/subtraction, go left to right.
- Brackets `{}`, `[]`, `()` all have the same priority — work from the innermost out.
- Be careful with implied operations like $ 9 \div 3 \cdot 2 $ — this is $ (9 \div 3) \cdot 2 = 6 $, not $ 9 \div (3 \cdot 2) $.

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