Order of Operations Worksheet 6 Worksheets - Free Printable

Let's solve each problem step by step using the order of operations, often remembered by the acronym PEMDAS:

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

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1. 4 + (1 × 5 + 7²) ÷ 8

- First, evaluate inside parentheses:
- $ 1 × 5 = 5 $
- $ 7² = 49 $
- So: $ 5 + 49 = 54 $
- Now: $ 4 + 54 ÷ 8 $
- Division next: $ 54 ÷ 8 = 6.75 $
- Then addition: $ 4 + 6.75 = 10.75 $

✔ Answer: 10.75

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2. 6² + (2 − 6) ÷ 1 − 8

- $ 6² = 36 $
- $ (2 − 6) = -4 $
- $ -4 ÷ 1 = -4 $
- Now: $ 36 + (-4) − 8 = 36 − 4 − 8 = 24 $

✔ Answer: 24

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3. (6² × 7) ÷ 2

- $ 6² = 36 $
- $ 36 × 7 = 252 $
- $ 252 ÷ 2 = 126 $

✔ Answer: 126

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4. 9 − (5² + 7) ÷ 2

- $ 5² = 25 $
- $ 25 + 7 = 32 $
- $ 32 ÷ 2 = 16 $
- $ 9 − 16 = -7 $

✔ Answer: -7

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5. (6 ÷ 8 − 2)

- $ 6 ÷ 8 = 0.75 $
- $ 0.75 − 2 = -1.25 $

✔ Answer: -1.25

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6. (1 − 4²) × 2

- $ 4² = 16 $
- $ 1 − 16 = -15 $
- $ -15 × 2 = -30 $

✔ Answer: -30

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7. 5 + (4² + 1) ÷ 5

- $ 4² = 16 $
- $ 16 + 1 = 17 $
- $ 17 ÷ 5 = 3.4 $
- $ 5 + 3.4 = 8.4 $

✔ Answer: 8.4

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8. (4 + 6) ÷ 1

- $ 4 + 6 = 10 $
- $ 10 ÷ 1 = 10 $

✔ Answer: 10

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9. (2² ÷ 9 + 1)

- $ 2² = 4 $
- $ 4 ÷ 9 ≈ 0.444... $
- $ 0.444... + 1 ≈ 1.444... $

✔ Answer: 1.444... or $ \frac{13}{9} $

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10. (3 ÷ 6 − 1)

- $ 3 ÷ 6 = 0.5 $
- $ 0.5 − 1 = -0.5 $

✔ Answer: -0.5

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11. 3² + 9² − (8 + 7) ÷ 5

- $ 3² = 9 $
- $ 9² = 81 $
- $ 8 + 7 = 15 $
- $ 15 ÷ 5 = 3 $
- $ 9 + 81 − 3 = 87 $

✔ Answer: 87

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12. 2 + 3 × (5 − 5² + 1)

- $ 5² = 25 $
- $ 5 − 25 + 1 = -19 $
- $ 3 × (-19) = -57 $
- $ 2 + (-57) = -55 $

✔ Answer: -55

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13. (3² + 3 × 4 + 2) − 1

- $ 3² = 9 $
- $ 3 × 4 = 12 $
- $ 9 + 12 + 2 = 23 $
- $ 23 − 1 = 22 $

✔ Answer: 22

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14. (4² × 3² − 4)

- $ 4² = 16 $
- $ 3² = 9 $
- $ 16 × 9 = 144 $
- $ 144 − 4 = 140 $

✔ Answer: 140

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15. (9 × 9² + 4)

- $ 9² = 81 $
- $ 9 × 81 = 729 $
- $ 729 + 4 = 733 $

✔ Answer: 733

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16. 5 − 9 + (7 × 2² − 5)

- $ 2² = 4 $
- $ 7 × 4 = 28 $
- $ 28 − 5 = 23 $
- $ 5 − 9 = -4 $
- $ -4 + 23 = 19 $

✔ Answer: 19

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17. (8 − 3²) − 8

- $ 3² = 9 $
- $ 8 − 9 = -1 $
- $ -1 − 8 = -9 $

✔ Answer: -9

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18. (5³ + 3 − 2² + 6 − 8)

- $ 5³ = 125 $
- $ 2² = 4 $
- $ 125 + 3 − 4 + 6 − 8 $
- Step-by-step:
- $ 125 + 3 = 128 $
- $ 128 − 4 = 124 $
- $ 124 + 6 = 130 $
- $ 130 − 8 = 122 $

✔ Answer: 122

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19. (2 × 5 + 5)

- $ 2 × 5 = 10 $
- $ 10 + 5 = 15 $

✔ Answer: 15

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20. (1² + 7) × (5² − 6) × 1

- $ 1² = 1 $
- $ 1 + 7 = 8 $
- $ 5² = 25 $
- $ 25 − 6 = 19 $
- $ 8 × 19 = 152 $
- $ 152 × 1 = 152 $

✔ Answer: 152

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 10.75 |
| 2 | 24 |
| 3 | 126 |
| 4 | -7 |
| 5 | -1.25 |
| 6 | -30 |
| 7 | 8.4 |
| 8 | 10 |
| 9 | $ \frac{13}{9} $ or ~1.444 |
| 10 | -0.5 |
| 11 | 87 |
| 12 | -55 |
| 13 | 22 |
| 14 | 140 |
| 15 | 733 |
| 16 | 19 |
| 17 | -9 |
| 18 | 122 |
| 19 | 15 |
| 20 | 152 |

Let me know if you'd like these formatted as a printable answer sheet!