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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Problem 1: $ 10^2 \div 5 - 3 \times 5 $

1. Exponents: $ 10^2 = 100 $
$$
100 \div 5 - 3 \times 5
$$
2. Division and Multiplication (left to right):
- $ 100 \div 5 = 20 $
- $ 3 \times 5 = 15 $
$$
20 - 15 = 5
$$

✔ Answer: 5

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Problem 2: $ 5^3 \div (2 \times 8 - 11) $

1. Exponents: $ 5^3 = 125 $
2. Parentheses: $ 2 \times 8 = 16 $, then $ 16 - 11 = 5 $
$$
125 \div 5 = 25
$$

✔ Answer: 25

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Problem 3: $ (11 + 7) \div 9 \times 4^3 $

1. Parentheses: $ 11 + 7 = 18 $
2. Exponents: $ 4^3 = 64 $
$$
18 \div 9 \times 64
$$
3. Division and Multiplication (left to right):
- $ 18 \div 9 = 2 $
- $ 2 \times 64 = 128 $

✔ Answer: 128

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Problem 4: $ 8^2 \div (3 + 11 - 12) $

1. Exponents: $ 8^2 = 64 $
2. Parentheses: $ 3 + 11 = 14 $, $ 14 - 12 = 2 $
$$
64 \div 2 = 32
$$

✔ Answer: 32

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Problem 5: $ (11^2 - 8 + 12) \times 3 $

1. Exponents: $ 11^2 = 121 $
$$
(121 - 8 + 12) \times 3
$$
2. Inside parentheses (left to right):
- $ 121 - 8 = 113 $
- $ 113 + 12 = 125 $
3. Multiplication: $ 125 \times 3 = 375 $

✔ Answer: 375

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Problem 6: $ 5 \times (4 + 17 + 10) - 11^2 $

1. Parentheses: $ 4 + 17 + 10 = 31 $
2. Exponents: $ 11^2 = 121 $
$$
5 \times 31 - 121
$$
3. Multiplication: $ 5 \times 31 = 155 $
4. Subtraction: $ 155 - 121 = 34 $

✔ Answer: 34

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Problem 7: $ 6 - 7 \times 3^2 + 2 $

1. Exponents: $ 3^2 = 9 $
$$
6 - 7 \times 9 + 2
$$
2. Multiplication: $ 7 \times 9 = 63 $
$$
6 - 63 + 2
$$
3. Addition and Subtraction (left to right):
- $ 6 - 63 = -57 $
- $ -57 + 2 = -55 $

✔ Answer: -55

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Problem 8: $ (-3) \times 9 - 3^2 + 4 $

1. Exponents: $ 3^2 = 9 $
$$
(-3) \times 9 - 9 + 4
$$
2. Multiplication: $ (-3) \times 9 = -27 $
$$
-27 - 9 + 4
$$
3. Left to right:
- $ -27 - 9 = -36 $
- $ -36 + 4 = -32 $

✔ Answer: -32

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Problem 9: $ 2 \times 5^2 - 10 \div 5 $

1. Exponents: $ 5^2 = 25 $
$$
2 \times 25 - 10 \div 5
$$
2. Multiplication and Division (left to right):
- $ 2 \times 25 = 50 $
- $ 10 \div 5 = 2 $
$$
50 - 2 = 48
$$

✔ Answer: 48

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Problem 10: $ 4 \times 6 + 2^2 - 10 $

1. Exponents: $ 2^2 = 4 $
$$
4 \times 6 + 4 - 10
$$
2. Multiplication: $ 4 \times 6 = 24 $
$$
24 + 4 - 10
$$
3. Addition and Subtraction (left to right):
- $ 24 + 4 = 28 $
- $ 28 - 10 = 18 $

✔ Answer: 18

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 5 |
| 2 | 25 |
| 3 | 128 |
| 4 | 32 |
| 5 | 375 |
| 6 | 34 |
| 7 | -55 |
| 8 | -32 |
| 9 | 48 |
| 10 | 18 |

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