6th Grade Order of Operations Worksheets - Free Printable

Let's solve each expression 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) $ 4 + 7 \times 3 - 6 $

- Multiply first: $ 7 \times 3 = 21 $
- Then: $ 4 + 21 - 6 = 25 - 6 = 19 $
✔ Answer: 19

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2) $ (7 + 11) \div 3 - 5 $

- Parentheses: $ 7 + 11 = 18 $
- Divide: $ 18 \div 3 = 6 $
- Subtract: $ 6 - 5 = 1 $
✔ Answer: 1

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3) $ 9 \times (8 - 5) + 6 $

- Parentheses: $ 8 - 5 = 3 $
- Multiply: $ 9 \times 3 = 27 $
- Add: $ 27 + 6 = 33 $
✔ Answer: 33

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4) $ 6 - 2 \times 5 + 8 $

- Multiply: $ 2 \times 5 = 10 $
- Now: $ 6 - 10 + 8 $
- Left to right: $ 6 - 10 = -4 $, then $ -4 + 8 = 4 $
✔ Answer: 4

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5) $ 8 \times 5 \div 4 - 9 $

- Multiply and divide left to right:
- $ 8 \times 5 = 40 $
- $ 40 \div 4 = 10 $
- Then: $ 10 - 9 = 1 $
✔ Answer: 1

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6) $ 4 - 7 \times (5 - 3) + 6 $

- Parentheses: $ 5 - 3 = 2 $
- Multiply: $ 7 \times 2 = 14 $
- Now: $ 4 - 14 + 6 $
- Left to right: $ 4 - 14 = -10 $, then $ -10 + 6 = -4 $
✔ Answer: -4

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7) $ 30 - (10 - 8) \times (4 + 3) $

- Parentheses: $ 10 - 8 = 2 $, $ 4 + 3 = 7 $
- Multiply: $ 2 \times 7 = 14 $
- Subtract: $ 30 - 14 = 16 $
✔ Answer: 16

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8) $ 4 \times 8 - 7 \times 6 $

- Multiplications: $ 4 \times 8 = 32 $, $ 7 \times 6 = 42 $
- Subtract: $ 32 - 42 = -10 $
✔ Answer: -10

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9) $ \frac{1}{2} \times (12 + 6) - 4 $

- Parentheses: $ 12 + 6 = 18 $
- Multiply: $ \frac{1}{2} \times 18 = 9 $
- Subtract: $ 9 - 4 = 5 $
✔ Answer: 5

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10) $ 8 \times \left( \frac{3}{4} + \frac{1}{4} \right) - 5 $

- Parentheses: $ \frac{3}{4} + \frac{1}{4} = 1 $
- Multiply: $ 8 \times 1 = 8 $
- Subtract: $ 8 - 5 = 3 $
✔ Answer: 3

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11) $ (5 + 4)^2 $

- Parentheses: $ 5 + 4 = 9 $
- Exponent: $ 9^2 = 81 $
✔ Answer: 81

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12) $ 5^2 - (3 + 2)^2 $

- Exponents and parentheses:
- $ 5^2 = 25 $
- $ 3 + 2 = 5 $, so $ 5^2 = 25 $
- Subtract: $ 25 - 25 = 0 $
✔ Answer: 0

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13) $ \frac{1}{2} \times (23 - 9) + \frac{1}{4} \times (15 - 7) $

- Parentheses:
- $ 23 - 9 = 14 $
- $ 15 - 7 = 8 $
- Multiply:
- $ \frac{1}{2} \times 14 = 7 $
- $ \frac{1}{4} \times 8 = 2 $
- Add: $ 7 + 2 = 9 $
✔ Answer: 9

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14) $ 18 \div (2^2 + 5) $

- Exponent: $ 2^2 = 4 $
- Parentheses: $ 4 + 5 = 9 $
- Divide: $ 18 \div 9 = 2 $
✔ Answer: 2

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15) $ (6^2 + 12) \div (3^2 - 1) $

- Exponents:
- $ 6^2 = 36 $
- $ 3^2 = 9 $
- Parentheses:
- $ 36 + 12 = 48 $
- $ 9 - 1 = 8 $
- Divide: $ 48 \div 8 = 6 $
✔ Answer: 6

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16) $ \frac{3}{4} \times (5 + 12 \div 4) $

- Inside parentheses:
- $ 12 \div 4 = 3 $
- $ 5 + 3 = 8 $
- Multiply: $ \frac{3}{4} \times 8 = 6 $
✔ Answer: 6

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17) $ (3^2 - 7) \times (2^2 + 8) $

- Exponents:
- $ 3^2 = 9 $
- $ 2^2 = 4 $
- Parentheses:
- $ 9 - 7 = 2 $
- $ 4 + 8 = 12 $
- Multiply: $ 2 \times 12 = 24 $
✔ Answer: 24

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18) $ 7 \times 5 - 4 \times 6 + 3 \times 9 $

- Multiplications:
- $ 7 \times 5 = 35 $
- $ 4 \times 6 = 24 $
- $ 3 \times 9 = 27 $
- Now: $ 35 - 24 + 27 $
- Left to right: $ 35 - 24 = 11 $, $ 11 + 27 = 38 $
✔ Answer: 38

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19) $ 7 \times 4 \div 2 + 5 \times 3 $

- Multiplications and divisions left to right:
- $ 7 \times 4 = 28 $
- $ 28 \div 2 = 14 $
- $ 5 \times 3 = 15 $
- Add: $ 14 + 15 = 29 $
✔ Answer: 29

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20) $ (5^2 - 7) \div (4^2 + 2) $

- Exponents:
- $ 5^2 = 25 $
- $ 4^2 = 16 $
- Parentheses:
- $ 25 - 7 = 18 $
- $ 16 + 2 = 18 $
- Divide: $ 18 \div 18 = 1 $
✔ Answer: 1

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✔ Final Answers:

1) 19
2) 1
3) 33
4) 4
5) 1
6) -4
7) 16
8) -10
9) 5
10) 3
11) 81
12) 0
13) 9
14) 2
15) 6
16) 6
17) 24
18) 38
19) 29
20) 1

Let me know if you'd like this in a printable format or need explanations for any specific problem!