Math Worksheets: Order of Operations or PEMDAS - 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. $ 3 - (2^3 \div 1) + 5 $

- Exponent: $ 2^3 = 8 $
- Division: $ 8 \div 1 = 8 $
- Now: $ 3 - 8 + 5 $
- Left to right: $ 3 - 8 = -5 $, then $ -5 + 5 = 0 $

✔ Answer: 0

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2. $ (6^3 - 9 - 1) $

- Exponent: $ 6^3 = 216 $
- Now: $ 216 - 9 - 1 $
- Left to right: $ 216 - 9 = 207 $, $ 207 - 1 = 206 $

✔ Answer: 206

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3. $ (5 + 7^3) \div 7 \times 7 $

- Exponent: $ 7^3 = 343 $
- Inside parentheses: $ 5 + 343 = 348 $
- Now: $ 348 \div 7 \times 7 $
- Left to right:
- $ 348 \div 7 \approx 49.714 $ (but keep exact: $ \frac{348}{7} $)
- Then $ \frac{348}{7} \times 7 = 348 $

✔ Answer: 348

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4. $ (2 - 7) - 8 - 3 $

- Parentheses: $ 2 - 7 = -5 $
- Then: $ -5 - 8 = -13 $, $ -13 - 3 = -16 $

✔ Answer: -16

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5. $ (6 + 7^2) + 1 $

- Exponent: $ 7^2 = 49 $
- Add: $ 6 + 49 = 55 $
- Then: $ 55 + 1 = 56 $

✔ Answer: 56

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6. $ 4^3 - (2 + 2^3) \times 5 $

- Exponent: $ 4^3 = 64 $, $ 2^3 = 8 $
- Inside parentheses: $ 2 + 8 = 10 $
- Multiply: $ 10 \times 5 = 50 $
- Subtract: $ 64 - 50 = 14 $

✔ Answer: 14

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7. $ (6 - 1 + 7) $

- Left to right inside parentheses: $ 6 - 1 = 5 $, $ 5 + 7 = 12 $

✔ Answer: 12

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8. $ (3^2 - 3^2) + 5 $

- Exponents: $ 3^2 = 9 $, so $ 9 - 9 = 0 $
- Then: $ 0 + 5 = 5 $

✔ Answer: 5

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9. $ (7 + 8 - 4^2) \times 2 + 1 $

- Exponent: $ 4^2 = 16 $
- Inside parentheses: $ 7 + 8 = 15 $, $ 15 - 16 = -1 $
- Multiply: $ -1 \times 2 = -2 $
- Add: $ -2 + 1 = -1 $

✔ Answer: -1

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10. $ 6 - (8 + 3^3) - 4 $

- Exponent: $ 3^3 = 27 $
- Inside parentheses: $ 8 + 27 = 35 $
- Now: $ 6 - 35 = -29 $, $ -29 - 4 = -33 $

✔ Answer: -33

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11. $ (3 + 3 \times 6 + 3^2 - 3) $

- Exponent: $ 3^2 = 9 $
- Multiplication: $ 3 \times 6 = 18 $
- Now: $ 3 + 18 + 9 - 3 $
- Left to right: $ 3 + 18 = 21 $, $ 21 + 9 = 30 $, $ 30 - 3 = 27 $

✔ Answer: 27

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12. $ (7 + 2^3) \times 9 $

- Exponent: $ 2^3 = 8 $
- Inside: $ 7 + 8 = 15 $
- Multiply: $ 15 \times 9 = 135 $

✔ Answer: 135

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13. $ (3 \times 6) - 5 $

- Multiplication: $ 3 \times 6 = 18 $
- Subtract: $ 18 - 5 = 13 $

✔ Answer: 13

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14. $ 6 \times (2 \div 1) \div 1 $

- Inside parentheses: $ 2 \div 1 = 2 $
- Now: $ 6 \times 2 = 12 $
- Then: $ 12 \div 1 = 12 $

✔ Answer: 12

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15. $ (2^3 - 9 - 8) \div 3 \times 3 $

- Exponent: $ 2^3 = 8 $
- Inside parentheses: $ 8 - 9 = -1 $, $ -1 - 8 = -9 $
- Now: $ -9 \div 3 = -3 $
- Then: $ -3 \times 3 = -9 $

✔ Answer: -9

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16. $ 2^3 \div (7 \div 7 \div 8) $

- Exponent: $ 2^3 = 8 $
- Inside parentheses: $ 7 \div 7 = 1 $, $ 1 \div 8 = 0.125 $
- Now: $ 8 \div 0.125 = 64 $

✔ Answer: 64

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17. $ (6 + 6^2) \times 3 $

- Exponent: $ 6^2 = 36 $
- Inside: $ 6 + 36 = 42 $
- Multiply: $ 42 \times 3 = 126 $

✔ Answer: 126

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18. $ (3 + 1) \times 8 \times 4 $

- Parentheses: $ 3 + 1 = 4 $
- Multiply left to right: $ 4 \times 8 = 32 $, $ 32 \times 4 = 128 $

✔ Answer: 128

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19. $ (7^3 \times 4) + 7 $

- Exponent: $ 7^3 = 343 $
- Multiply: $ 343 \times 4 = 1372 $
- Add: $ 1372 + 7 = 1379 $

✔ Answer: 1379

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20. $ 6^2 - 3 \times (3^2 \times 2) + 5 $

- Exponent: $ 6^2 = 36 $, $ 3^2 = 9 $
- Inside parentheses: $ 9 \times 2 = 18 $
- Multiply: $ 3 \times 18 = 54 $
- Now: $ 36 - 54 = -18 $
- Add: $ -18 + 5 = -13 $

✔ Answer: -13

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 0 |
| 2 | 206 |
| 3 | 348 |
| 4 | -16 |
| 5 | 56 |
| 6 | 14 |
| 7 | 12 |
| 8 | 5 |
| 9 | -1 |
| 10 | -33 |
| 11 | 27 |
| 12 | 135 |
| 13 | 13 |
| 14 | 12 |
| 15 | -9 |
| 16 | 64 |
| 17 | 126 |
| 18 | 128 |
| 19 | 1379 |
| 20 | -13 |

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