Order of Operations Worksheets - Math Monks - Free Printable

Let's solve each problem step by step using PEMDAS, which stands for:

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

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1) (12 ÷ 2) × 5² - 8

- Parentheses: 12 ÷ 2 = 6
→ (6) × 5² - 8
- Exponents: 5² = 25
→ 6 × 25 - 8
- Multiplication: 6 × 25 = 150
→ 150 - 8
- Subtraction: 150 - 8 = 142

✔ Answer: 142

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2) (4³ ÷ 2) × 6 - 3

- Parentheses: First compute inside the parentheses.
- Exponent: 4³ = 64
- Division: 64 ÷ 2 = 32
→ (32) × 6 - 3
- Multiplication: 32 × 6 = 192
- Subtraction: 192 - 3 = 189

✔ Answer: 189

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3) 9 × [(-3) + 4 - (-2)²]

- Parentheses/Brackets: Work inside the brackets first.
- Exponent: (-2)² = 4 (negative squared is positive)
- Now: (-3) + 4 - 4
- (-3) + 4 = 1
- 1 - 4 = -3
→ 9 × (-3)
- Multiplication: 9 × (-3) = -27

✔ Answer: -27

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4) (14² × 15) - (2² + 20)

- Parentheses: Handle both sets separately.
- Left: 14² = 196 → 196 × 15 = 2940
- Right: 2² = 4 → 4 + 20 = 24
- Subtraction: 2940 - 24 = 2916

✔ Answer: 2916

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5) 4² + (8 - 2)² ÷ 4

- Exponents & Parentheses:
- 4² = 16
- (8 - 2) = 6 → 6² = 36
→ 16 + 36 ÷ 4
- Division: 36 ÷ 4 = 9
- Addition: 16 + 9 = 25

✔ Answer: 25

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6) (15² - 9) × 2 - 15

- Parentheses:
- 15² = 225
- 225 - 9 = 216
→ 216 × 2 - 15
- Multiplication: 216 × 2 = 432
- Subtraction: 432 - 15 = 417

✔ Answer: 417

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7) (6² + 4) ÷ (18 - 14)

- Parentheses:
- 6² = 36 → 36 + 4 = 40
- 18 - 14 = 4
→ 40 ÷ 4
- Division: 40 ÷ 4 = 10

✔ Answer: 10

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8) (6² + 18 - 8) ÷ 2

- Parentheses:
- 6² = 36
- 36 + 18 = 54
- 54 - 8 = 46
→ 46 ÷ 2
- Division: 46 ÷ 2 = 23

✔ Answer: 23

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✔ Final Answers:

1) 142
2) 189
3) -27
4) 2916
5) 25
6) 417
7) 10
8) 23

Let me know if you'd like this formatted as a printable answer key!