Order of Operations Worksheets - Math Monks - Free Printable

To solve the given problems, we need to follow the order of operations, often remembered by the acronym PEMDAS:

1. Parentheses (or brackets)
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Let's solve each problem step by step.

---

Problem 1: \( 18 - (21 - 5) \div (22 - 18) \)

1. Solve the expressions inside the parentheses:
\[
21 - 5 = 16 \quad \text{and} \quad 22 - 18 = 4
\]
So the expression becomes:
\[
18 - 16 \div 4
\]

2. Perform the division:
\[
16 \div 4 = 4
\]
So the expression becomes:
\[
18 - 4
\]

3. Perform the subtraction:
\[
18 - 4 = 14
\]

Answer: \( 14 \)

---

Problem 2: \( 24 \div 6 + 4 \times (3 + 6) \)

1. Solve the expression inside the parentheses:
\[
3 + 6 = 9
\]
So the expression becomes:
\[
24 \div 6 + 4 \times 9
\]

2. Perform the division and multiplication (from left to right):
\[
24 \div 6 = 4 \quad \text{and} \quad 4 \times 9 = 36
\]
So the expression becomes:
\[
4 + 36
\]

3. Perform the addition:
\[
4 + 36 = 40
\]

Answer: \( 40 \)

---

Problem 3: \( 5 + 10 \times (3 - 2)^2 \)

1. Solve the expression inside the parentheses:
\[
3 - 2 = 1
\]
So the expression becomes:
\[
5 + 10 \times 1^2
\]

2. Solve the exponent:
\[
1^2 = 1
\]
So the expression becomes:
\[
5 + 10 \times 1
\]

3. Perform the multiplication:
\[
10 \times 1 = 10
\]
So the expression becomes:
\[
5 + 10
\]

4. Perform the addition:
\[
5 + 10 = 15
\]

Answer: \( 15 \)

---

Problem 4: \( (-7) + 2^3 \times 3 - 8 \)

1. Solve the exponent:
\[
2^3 = 8
\]
So the expression becomes:
\[
(-7) + 8 \times 3 - 8
\]

2. Perform the multiplication:
\[
8 \times 3 = 24
\]
So the expression becomes:
\[
(-7) + 24 - 8
\]

3. Perform the addition and subtraction from left to right:
\[
(-7) + 24 = 17 \quad \text{and} \quad 17 - 8 = 9
\]

Answer: \( 9 \)

---

Problem 5: \( 8 \div [(-8) - (-2) + 5]^3 \)

1. Solve the expression inside the brackets:
\[
(-8) - (-2) = -8 + 2 = -6
\]
So the expression inside the brackets becomes:
\[
-6 + 5 = -1
\]
So the expression becomes:
\[
8 \div (-1)^3
\]

2. Solve the exponent:
\[
(-1)^3 = -1
\]
So the expression becomes:
\[
8 \div (-1)
\]

3. Perform the division:
\[
8 \div (-1) = -8
\]

Answer: \( -8 \)

---

Problem 6: \( 36 \div 3 \times [(7 - 2 - 4) \times 2] \)

1. Solve the expression inside the innermost parentheses:
\[
7 - 2 - 4 = 5 - 4 = 1
\]
So the expression becomes:
\[
36 \div 3 \times [1 \times 2]
\]

2. Solve the expression inside the brackets:
\[
1 \times 2 = 2
\]
So the expression becomes:
\[
36 \div 3 \times 2
\]

3. Perform the division and multiplication (from left to right):
\[
36 \div 3 = 12 \quad \text{and} \quad 12 \times 2 = 24
\]

Answer: \( 24 \)

---

Problem 7: \( 7 \times (4^2 + 2 - 8) \)

1. Solve the exponent:
\[
4^2 = 16
\]
So the expression becomes:
\[
7 \times (16 + 2 - 8)
\]

2. Solve the expression inside the parentheses:
\[
16 + 2 - 8 = 18 - 8 = 10
\]
So the expression becomes:
\[
7 \times 10
\]

3. Perform the multiplication:
\[
7 \times 10 = 70
\]

Answer: \( 70 \)

---

Problem 8: \( [8 - (-4) + (-8)]^2 \times 4 \)

1. Solve the expression inside the brackets:
\[
8 - (-4) = 8 + 4 = 12
\]
So the expression inside the brackets becomes:
\[
12 + (-8) = 12 - 8 = 4
\]
So the expression becomes:
\[
4^2 \times 4
\]

2. Solve the exponent:
\[
4^2 = 16
\]
So the expression becomes:
\[
16 \times 4
\]

3. Perform the multiplication:
\[
16 \times 4 = 64
\]

Answer: \( 64 \)

---

Problem 9: \( (81 \div 9) + 25 - 17 \times 2 \)

1. Perform the division:
\[
81 \div 9 = 9
\]
So the expression becomes:
\[
9 + 25 - 17 \times 2
\]

2. Perform the multiplication:
\[
17 \times 2 = 34
\]
So the expression becomes:
\[
9 + 25 - 34
\]

3. Perform the addition and subtraction from left to right:
\[
9 + 25 = 34 \quad \text{and} \quad 34 - 34 = 0
\]

Answer: \( 0 \)

---

Problem 10: \( (-2)^2 \div 4 - 9 \times 8 \)

1. Solve the exponent:
\[
(-2)^2 = 4
\]
So the expression becomes:
\[
4 \div 4 - 9 \times 8
\]

2. Perform the division and multiplication (from left to right):
\[
4 \div 4 = 1 \quad \text{and} \quad 9 \times 8 = 72
\]
So the expression becomes:
\[
1 - 72
\]

3. Perform the subtraction:
\[
1 - 72 = -71
\]

Answer: \( -71 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 14 \\
2. & 40 \\
3. & 15 \\
4. & 9 \\
5. & -8 \\
6. & 24 \\
7. & 70 \\
8. & 64 \\
9. & 0 \\
10. & -71 \\
\end{array}
}
\]