Order of Operations worksheet with ten PEMDAS problems for practice.

Let's solve each of these Order of Operations (PEMDAS) problems step by step.
PEMDAS stands for:

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

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1) ((14 + 3) + (20 + 2)²) ÷ 5²

Step-by-step:
- First, simplify inside parentheses:
- (14 + 3) = 17
- (20 + 2) = 22 → then square it: 22² = 484
- Now: (17 + 484) = 501
- Denominator: 5² = 25
- Divide: 501 ÷ 25 = 20.04

✔ Answer: 20.04

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2) (12 - 3)² + ((10 - 4) × 6²)

Step-by-step:
- (12 - 3) = 9 → 9² = 81
- (10 - 4) = 6
- 6² = 36
- (6 × 36) = 216
- Add: 81 + 216 = 297

✔ Answer: 297

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3) (6² + (18 ÷ 9 + 5²)) - 3²

Step-by-step:
- 6² = 36
- 18 ÷ 9 = 2
- 5² = 25
- Inside inner parentheses: 2 + 25 = 27
- Now: 36 + 27 = 63
- 3² = 9
- Subtract: 63 - 9 = 54

✔ Answer: 54

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4) (6² + (8 ÷ 4 + 3²)) - 4²

Step-by-step:
- 6² = 36
- 8 ÷ 4 = 2
- 3² = 9
- Inside: 2 + 9 = 11
- 36 + 11 = 47
- 4² = 16
- 47 - 16 = 31

✔ Answer: 31

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5) ((18 - 3) - (20 + 2)²) × 7²

Step-by-step:
- (18 - 3) = 15
- (20 + 2) = 22 → 22² = 484
- 15 - 484 = -469
- 7² = 49
- Multiply: -469 × 49

Let’s compute:
- 469 × 49 = 469 × (50 - 1) = (469×50) - 469 = 23,450 - 469 = 22,981
- So: -22,981

✔ Answer: -22,981

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6) ((9 - 4)² + 4) + 13 + 5²

Step-by-step:
- (9 - 4) = 5 → 5² = 25
- 25 + 4 = 29
- 5² = 25
- Now: 29 + 13 + 25 = 67

✔ Answer: 67

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7) ((10 - 3)² + 7) - 4 + 6²

Step-by-step:
- (10 - 3) = 7 → 7² = 49
- 49 + 7 = 56
- 6² = 36
- Now: 56 - 4 + 36
- Left to right: 56 - 4 = 52; 52 + 36 = 88

✔ Answer: 88

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8) 10 + (10 + (10 - 5)²) ÷ 6

Step-by-step:
- (10 - 5) = 5 → 5² = 25
- 10 + 25 = 35
- 35 ÷ 6 ≈ 5.833...
- Now: 10 + 5.833... = 15.833... or 15⅚

But let's keep it as a fraction:
- 35/6 = 5⅚
- 10 + 5⅚ = 15⅚

Or as decimal: 15.833...

✔ Answer: 15⅚ or 15.833...

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9) 7 + (5 + (9 - 6)²) - 9

Step-by-step:
- (9 - 6) = 3 → 3² = 9
- 5 + 9 = 14
- 7 + 14 = 21
- 21 - 9 = 12

✔ Answer: 12

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10) (20 + 4)² + ((16 - 3) × 5²)

Step-by-step:
- (20 + 4) = 24 → 24² = 576
- (16 - 3) = 13
- 5² = 25
- 13 × 25 = 325
- Now: 576 + 325 = 901

✔ Answer: 901

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✔ Final Answers:

1) 20.04
2) 297
3) 54
4) 31
5) -22,981
6) 67
7) 88
8) 15⅚ or 15.833...
9) 12
10) 901

Let me know if you'd like these written in fractions or decimals!