Order of Operations Worksheets - Math Monks - Free Printable

To solve the given expressions using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), let's evaluate each expression step by step.

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Expression 1: \( 9 - (36 \div 1 \times 6 + 3) - 1 - 8 \)

1. Parentheses: Evaluate inside the parentheses first.
\[
36 \div 1 \times 6 + 3
\]
- Perform division and multiplication from left to right:
\[
36 \div 1 = 36
\]
\[
36 \times 6 = 216
\]
- Add 3:
\[
216 + 3 = 219
\]
So, the expression becomes:
\[
9 - 219 - 1 - 8
\]

2. Subtraction: Perform subtraction from left to right:
\[
9 - 219 = -210
\]
\[
-210 - 1 = -211
\]
\[
-211 - 8 = -219
\]

Answer for Expression 1: \(\boxed{-219}\)

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Expression 2: \( (4 \times 10) \times 9 + 16 \div 4 \)

1. Parentheses: Evaluate inside the parentheses first.
\[
4 \times 10 = 40
\]
So, the expression becomes:
\[
40 \times 9 + 16 \div 4
\]

2. Multiplication and Division: Perform multiplication and division from left to right.
- Multiply \(40 \times 9\):
\[
40 \times 9 = 360
\]
- Divide \(16 \div 4\):
\[
16 \div 4 = 4
\]
So, the expression becomes:
\[
360 + 4
\]

3. Addition: Perform addition:
\[
360 + 4 = 364
\]

Answer for Expression 2: \(\boxed{364}\)

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Expression 3: \( 4 \times 5 + (14 + 8) - 36 \div 9 \)

1. Parentheses: Evaluate inside the parentheses first.
\[
14 + 8 = 22
\]
So, the expression becomes:
\[
4 \times 5 + 22 - 36 \div 9
\]

2. Multiplication and Division: Perform multiplication and division from left to right.
- Multiply \(4 \times 5\):
\[
4 \times 5 = 20
\]
- Divide \(36 \div 9\):
\[
36 \div 9 = 4
\]
So, the expression becomes:
\[
20 + 22 - 4
\]

3. Addition and Subtraction: Perform addition and subtraction from left to right.
- Add \(20 + 22\):
\[
20 + 22 = 42
\]
- Subtract \(42 - 4\):
\[
42 - 4 = 38
\]

Answer for Expression 3: \(\boxed{38}\)

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Expression 4: \( (6 + 2) \div [7 - 3 \times (10 - 8)] \)

1. Parentheses: Evaluate inside the innermost parentheses first.
- Innermost parentheses: \(10 - 8\):
\[
10 - 8 = 2
\]
- Next, evaluate \(3 \times 2\):
\[
3 \times 2 = 6
\]
- Finally, evaluate \(7 - 6\):
\[
7 - 6 = 1
\]
So, the expression becomes:
\[
(6 + 2) \div 1
\]

2. Parentheses: Evaluate \(6 + 2\):
\[
6 + 2 = 8
\]
So, the expression becomes:
\[
8 \div 1
\]

3. Division: Perform the division:
\[
8 \div 1 = 8
\]

Answer for Expression 4: \(\boxed{8}\)

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Expression 5: \( (5 \times 3 - 10) \div (6 + 4 - 9) \)

1. Parentheses: Evaluate inside both sets of parentheses.
- Left parentheses: \(5 \times 3 - 10\):
\[
5 \times 3 = 15
\]
\[
15 - 10 = 5
\]
- Right parentheses: \(6 + 4 - 9\):
\[
6 + 4 = 10
\]
\[
10 - 9 = 1
\]
So, the expression becomes:
\[
5 \div 1
\]

2. Division: Perform the division:
\[
5 \div 1 = 5
\]

Answer for Expression 5: \(\boxed{5}\)

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Expression 6: \( 6 \times (8 + 2 - 4) \div (7 - 3) \)

1. Parentheses: Evaluate inside both sets of parentheses.
- Left parentheses: \(8 + 2 - 4\):
\[
8 + 2 = 10
\]
\[
10 - 4 = 6
\]
- Right parentheses: \(7 - 3\):
\[
7 - 3 = 4
\]
So, the expression becomes:
\[
6 \times 6 \div 4
\]

2. Multiplication and Division: Perform multiplication and division from left to right.
- Multiply \(6 \times 6\):
\[
6 \times 6 = 36
\]
- Divide \(36 \div 4\):
\[
36 \div 4 = 9
\]

Answer for Expression 6: \(\boxed{9}\)

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Expression 7: \( 18 \div 6 \times (4 - 3) + 6 \)

1. Parentheses: Evaluate inside the parentheses first.
\[
4 - 3 = 1
\]
So, the expression becomes:
\[
18 \div 6 \times 1 + 6
\]

2. Division and Multiplication: Perform division and multiplication from left to right.
- Divide \(18 \div 6\):
\[
18 \div 6 = 3
\]
- Multiply \(3 \times 1\):
\[
3 \times 1 = 3
\]
So, the expression becomes:
\[
3 + 6
\]

3. Addition: Perform addition:
\[
3 + 6 = 9
\]

Answer for Expression 7: \(\boxed{9}\)

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Expression 8: \( (6 + 3 - 4 \times 2) \div (10 - 9) \)

1. Parentheses: Evaluate inside both sets of parentheses.
- Left parentheses: \(6 + 3 - 4 \times 2\):
- Perform multiplication first:
\[
4 \times 2 = 8
\]
- Then perform addition and subtraction from left to right:
\[
6 + 3 = 9
\]
\[
9 - 8 = 1
\]
- Right parentheses: \(10 - 9\):
\[
10 - 9 = 1
\]
So, the expression becomes:
\[
1 \div 1
\]

2. Division: Perform the division:
\[
1 \div 1 = 1
\]

Answer for Expression 8: \(\boxed{1}\)

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Final Answers

1. \(\boxed{-219}\)
2. \(\boxed{364}\)
3. \(\boxed{38}\)
4. \(\boxed{8}\)
5. \(\boxed{5}\)
6. \(\boxed{9}\)
7. \(\boxed{9}\)
8. \(\boxed{1}\)