Order of Operations Worksheets - Free Printable

The image you've uploaded is a math worksheet titled *"Using Order of Operations"*, which includes 10 problems that require evaluating expressions using the correct order of operations (PEMDAS):
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Let’s go through each problem step by step and verify the answers provided in the "Answer Key" column.

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Problem 1:

(9 × 9) + 7 + 54 ÷ 9

Step-by-step:
- First, multiplication: 9 × 9 = 81
- Then division: 54 ÷ 9 = 6
- Now add: 81 + 7 + 6 = 88 + 6 = 94

✔ Answer: 94 — Correct

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Problem 2:

10(15 ÷ 5 + 6) + 9

Step-by-step:
- Inside parentheses: 15 ÷ 5 = 3 → 3 + 6 = 9
- Multiply: 10 × 9 = 90
- Add: 90 + 9 = 99

✔ Answer: 99 — Correct

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Problem 3:

(8 + 20 ÷ 10) + 36 ÷ 4 + 3

Step-by-step:
- Division inside parentheses: 20 ÷ 10 = 2 → 8 + 2 = 10
- Now: 10 + 36 ÷ 4 + 3
- Division: 36 ÷ 4 = 9
- Now: 10 + 9 + 3 = 22

✔ Answer: 22 — Correct

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Problem 4:

6 × 3(10 + 8)

Note: This expression can be interpreted as:
- 6 × 3 × (10 + 8)
- First: 10 + 8 = 18
- Then: 6 × 3 = 18
- 18 × 18 = 324

Alternatively, if it's meant to be 6 × [3×(10+8)], same result:
- 3 × 18 = 54 → 6 × 54 = 324

✔ Answer: 324 — Correct

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Problem 5:

9 + 15 - 8(5 + 13 - 9)

Step-by-step:
- Inside parentheses: 5 + 13 - 9 = 18 - 9 = 9
- So: 9 + 15 - 8 × 9
- Multiplication: 8 × 9 = 72
- Now: 9 + 15 = 24 → 24 - 72 = -48

✔ Answer: -48 — Correct

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Problem 6:

6(28 ÷ 7 + 14 ÷ 7) + 8

Step-by-step:
- Inside parentheses:
- 28 ÷ 7 = 4
- 14 ÷ 7 = 2
- 4 + 2 = 6
- Now: 6 × 6 = 36
- 36 + 8 = 44

✔ Answer: 44 — Correct

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Problem 7:

7(5 × 2) + 8

Step-by-step:
- Inside parentheses: 5 × 2 = 10
- 7 × 10 = 70
- 70 + 8 = 78

✔ Answer: 78 — Correct

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Problem 8:

4(6 - 5 + 4) × 9

Step-by-step:
- Inside parentheses: 6 - 5 = 1 → 1 + 4 = 5
- Now: 4 × 5 = 20
- 20 × 9 = 180

✔ Answer: 180 — Correct

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Problem 9:

5 + 10(8 + 21 ÷ 3)

Step-by-step:
- Inside parentheses: 21 ÷ 3 = 7 → 8 + 7 = 15
- Now: 10 × 15 = 150
- 5 + 150 = 155

✔ Answer: 155 — Correct

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Problem 10:

(6 + 8) + 9 × 7

Step-by-step:
- Parentheses: 6 + 8 = 14
- Multiplication: 9 × 7 = 63
- Addition: 14 + 63 = 77

✔ Answer: 77 — Correct

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✔ Final Verification:

All answers in the Answer Key are correct. The solutions follow the order of operations (PEMDAS) properly.

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Summary:

| Problem | Expression | Answer |
|--------|------------|--------|
| 1 | (9×9)+7+54÷9 | 94 |
| 2 | 10(15÷5+6)+9 | 99 |
| 3 | (8+20÷10)+36÷4+3 | 22 |
| 4 | 6×3(10+8) | 324 |
| 5 | 9+15-8(5+13-9) | -48 |
| 6 | 6(28÷7+14÷7)+8 | 44 |
| 7 | 7(5×2)+8 | 78 |
| 8 | 4(6-5+4)×9 | 180 |
| 9 | 5+10(8+21÷3) | 155 |
| 10 | (6+8)+9×7 | 77 |

✔ All solutions are accurate and match the answer key.

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