Order of Operations Worksheets - Math Monks - Free Printable

Sure! Let's solve each expression step by step using the Order of Operations (PEMDAS/BODMAS):

> Parentheses / Brackets
> Exponents / Orders
> Multiplication and Division (left to right)
> Addition and Subtraction (left to right)

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Problem 1:

2⁴ + {14 - [16 + (39 ÷ 3)]}

Step 1: Innermost parentheses → 39 ÷ 3 = 13
→ 2⁴ + {14 - [16 + 13]}

Step 2: Brackets → 16 + 13 = 29
→ 2⁴ + {14 - 29}

Step 3: Braces → 14 - 29 = -15
→ 2⁴ + (-15)

Step 4: Exponent → 2⁴ = 16
→ 16 - 15 = 1

✔ Answer: 1

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Problem 2:

5³ + {2² + [27 ÷ (3 × 3)]}

Step 1: Parentheses → 3 × 3 = 9
→ 5³ + {2² + [27 ÷ 9]}

Step 2: Brackets → 27 ÷ 9 = 3
→ 5³ + {2² + 3}

Step 3: Braces → 2² = 4 → 4 + 3 = 7
→ 5³ + 7

Step 4: Exponent → 5³ = 125
→ 125 + 7 = 132

✔ Answer: 132

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Problem 3:

2 × {3 + [7 × (69 ÷ 23) - 10]}

Step 1: Parentheses → 69 ÷ 23 = 3
→ 2 × {3 + [7 × 3 - 10]}

Step 2: Brackets → 7 × 3 = 21 → 21 - 10 = 11
→ 2 × {3 + 11}

Step 3: Braces → 3 + 11 = 14
→ 2 × 14 = 28

✔ Answer: 28

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Problem 4:

(21 × 3) - [(56 ÷ 8) - 2]

Step 1: Parentheses → 21 × 3 = 63
→ 63 - [(56 ÷ 8) - 2]

Step 2: Brackets → 56 ÷ 8 = 7 → 7 - 2 = 5
→ 63 - 5 = 58

✔ Answer: 58

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Problem 5:

3 + [6(11 + 1 - 4)] ÷ 8 × 2

Step 1: Parentheses → 11 + 1 = 12 → 12 - 4 = 8
→ 3 + [6 × 8] ÷ 8 × 2

Step 2: Brackets → 6 × 8 = 48
→ 3 + 48 ÷ 8 × 2

Step 3: Division and Multiplication left to right:
48 ÷ 8 = 6 → 6 × 2 = 12
→ 3 + 12 = 15

✔ Answer: 15

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Problem 6:

2{8² - 7[32 - 4(3² + 1)]}(-1)

This one is complex — let’s go slowly.

Step 1: Innermost parentheses → 3² = 9 → 9 + 1 = 10
→ 2{8² - 7[32 - 4×10]}(-1)

Step 2: Inside brackets → 4 × 10 = 40 → 32 - 40 = -8
→ 2{8² - 7×(-8)}(-1)

Step 3: Inside braces → 7 × (-8) = -56
→ 2{64 - (-56)}(-1) → 64 + 56 = 120
→ 2 × 120 × (-1)

Step 4: Multiply left to right:
2 × 120 = 240 → 240 × (-1) = -240

✔ Answer: -240

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Problem 7:

2{1 + [4(2 + 1) + 3]}

Step 1: Parentheses → 2 + 1 = 3
→ 2{1 + [4×3 + 3]}

Step 2: Brackets → 4×3 = 12 → 12 + 3 = 15
→ 2{1 + 15}

Step 3: Braces → 1 + 15 = 16
→ 2 × 16 = 32

✔ Answer: 32

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Problem 8:

[15 - {3(2 + 1) + 1}] × 4

Step 1: Parentheses → 2 + 1 = 3
→ [15 - {3×3 + 1}] × 4

Step 2: Braces → 3×3 = 9 → 9 + 1 = 10
→ [15 - 10] × 4

Step 3: Brackets → 15 - 10 = 5
→ 5 × 4 = 20

✔ Answer: 20

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## ✔ Final Answers:

1. 1
2. 132
3. 28
4. 58
5. 15
6. -240
7. 32
8. 20

Let me know if you’d like a printable version or explanation for any specific problem!