Order of Operations Worksheets - Math Monks - 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. $ 18 - (21 - 5) \div (22 - 18) $

Step 1: Simplify inside parentheses:
- $ 21 - 5 = 16 $
- $ 22 - 18 = 4 $

Now:
$ 18 - 16 \div 4 $

Step 2: Division:
- $ 16 \div 4 = 4 $

Step 3: Subtraction:
- $ 18 - 4 = 14 $

✔ Answer: 14

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2. $ 24 \div 6 + 4 \times (3 + 6) $

Step 1: Parentheses:
- $ 3 + 6 = 9 $

Now:
$ 24 \div 6 + 4 \times 9 $

Step 2: Multiplication and division (left to right):
- $ 24 \div 6 = 4 $
- $ 4 \times 9 = 36 $

Step 3: Addition:
- $ 4 + 36 = 40 $

✔ Answer: 40

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3. $ 5 + 10 \times (3 - 2)^2 $

Step 1: Parentheses:
- $ 3 - 2 = 1 $

Now:
$ 5 + 10 \times (1)^2 $

Step 2: Exponent:
- $ 1^2 = 1 $

Now:
$ 5 + 10 \times 1 $

Step 3: Multiplication:
- $ 10 \times 1 = 10 $

Step 4: Addition:
- $ 5 + 10 = 15 $

✔ Answer: 15

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4. $ (-7) + 2^3 \times 3 - 8 $

Step 1: Exponent:
- $ 2^3 = 8 $

Now:
$ -7 + 8 \times 3 - 8 $

Step 2: Multiplication:
- $ 8 \times 3 = 24 $

Now:
$ -7 + 24 - 8 $

Step 3: Left to right:
- $ -7 + 24 = 17 $
- $ 17 - 8 = 9 $

✔ Answer: 9

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5. $ 8 \div [(-8) - (-2) + 5]^3 $

Step 1: Simplify inside brackets:
- $ -8 - (-2) = -8 + 2 = -6 $
- $ -6 + 5 = -1 $

Now:
$ 8 \div (-1)^3 $

Step 2: Exponent:
- $ (-1)^3 = -1 $

Now:
$ 8 \div (-1) = -8 $

✔ Answer: -8

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6. $ 36 \div 3 \times [(7 - 2 - 4) \times 2] $

Step 1: Inside parentheses:
- $ 7 - 2 - 4 = 1 $

Now:
$ 36 \div 3 \times [1 \times 2] $

Step 2: Brackets:
- $ 1 \times 2 = 2 $

Now:
$ 36 \div 3 \times 2 $

Step 3: Division and multiplication (left to right):
- $ 36 \div 3 = 12 $
- $ 12 \times 2 = 24 $

✔ Answer: 24

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

Step 1: Exponent:
- $ 4^2 = 16 $

Now:
$ 7 \times (16 + 2 - 8) $

Step 2: Inside parentheses:
- $ 16 + 2 = 18 $
- $ 18 - 8 = 10 $

Now:
$ 7 \times 10 = 70 $

✔ Answer: 70

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8. $ [8 - (-4) + (-8)]^2 \times 4 $

Step 1: Simplify inside brackets:
- $ 8 - (-4) = 8 + 4 = 12 $
- $ 12 + (-8) = 12 - 8 = 4 $

Now:
$ (4)^2 \times 4 $

Step 2: Exponent:
- $ 4^2 = 16 $

Now:
$ 16 \times 4 = 64 $

✔ Answer: 64

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9. $ (81 \div 9) + 25 - 17 \times 2 $

Step 1: Division and multiplication (left to right):
- $ 81 \div 9 = 9 $
- $ 17 \times 2 = 34 $

Now:
$ 9 + 25 - 34 $

Step 2: Addition and subtraction (left to right):
- $ 9 + 25 = 34 $
- $ 34 - 34 = 0 $

✔ Answer: 0

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10. $ (-2)^2 \div 4 - 9 \times 8 $

Step 1: Exponent:
- $ (-2)^2 = 4 $

Now:
$ 4 \div 4 - 9 \times 8 $

Step 2: Division and multiplication:
- $ 4 \div 4 = 1 $
- $ 9 \times 8 = 72 $

Now:
$ 1 - 72 = -71 $

✔ Answer: -71

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✔ Final Answers:

1. 14
2. 40
3. 15
4. 9
5. -8
6. 24
7. 70
8. 64
9. 0
10. -71

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