Math worksheet for practicing order of operations with ten problems involving various arithmetic operations and parentheses.

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 $

So:
$ 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 $

So:
$ 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 $

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

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

So:
$ 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 $

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

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

So:
$ -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 $

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

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

So:
$ 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 $

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

Step 2: Simplify bracket:
- $ 1 \times 2 = 2 $

So:
$ 36 \div 3 \times 2 $

Step 3: 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 $

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

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

So:
$ 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) = 4 $

So:
$ [4]^2 \times 4 $

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

So:
$ 16 \times 4 = 64 $

✔ Answer: 64

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

Step 1: Parentheses and exponents:
- $ 81 \div 9 = 9 $

So:
$ 9 + 25 - 17 \times 2 $

Step 2: Multiplication:
- $ 17 \times 2 = 34 $

So:
$ 9 + 25 - 34 $

Step 3: 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 $

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

Step 2: Multiplication and division (left to right):
- $ 4 \div 4 = 1 $
- $ 9 \times 8 = 72 $

So:
$ 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 these explained in a different format!