Order of Operations Worksheets -Worksheets Library - Free Printable

To solve the problems in the image, we will use 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)

Let's solve each problem step by step.

---

Problem 1:

\[
(5 \times 4) \times 8 - 5
\]

1. Parentheses: \( 5 \times 4 = 20 \)
\[
20 \times 8 - 5
\]

2. Multiplication: \( 20 \times 8 = 160 \)
\[
160 - 5
\]

3. Subtraction: \( 160 - 5 = 155 \)

Answer: \(\boxed{155}\)

---

Problem 2:

\[
(2 \times 3) \times 6^2 - 3
\]

1. Parentheses: \( 2 \times 3 = 6 \)
\[
6 \times 6^2 - 3
\]

2. Exponents: \( 6^2 = 36 \)
\[
6 \times 36 - 3
\]

3. Multiplication: \( 6 \times 36 = 216 \)
\[
216 - 3
\]

4. Subtraction: \( 216 - 3 = 213 \)

Answer: \(\boxed{213}\)

---

Problem 3:

\[
(9 - 3^2) + 3 \div 7
\]

1. Parentheses: First, calculate the exponent inside the parentheses: \( 3^2 = 9 \)
\[
9 - 9 = 0
\]
So, the expression becomes:
\[
0 + 3 \div 7
\]

2. Division: \( 3 \div 7 = \frac{3}{7} \)
\[
0 + \frac{3}{7}
\]

3. Addition: \( 0 + \frac{3}{7} = \frac{3}{7} \)

Answer: \(\boxed{\frac{3}{7}}\)

---

Problem 4:

\[
(9^2 \times 1 \times 8)
\]

1. Exponents: \( 9^2 = 81 \)
\[
81 \times 1 \times 8
\]

2. Multiplication: Perform the multiplications from left to right:
\[
81 \times 1 = 81
\]
\[
81 \times 8 = 648
\]

Answer: \(\boxed{648}\)

---

Problem 5:

\[
(1 \times 7 \times 5) - 7
\]

1. Parentheses: Perform the multiplication inside the parentheses:
\[
1 \times 7 = 7
\]
\[
7 \times 5 = 35
\]
So, the expression becomes:
\[
35 - 7
\]

2. Subtraction: \( 35 - 7 = 28 \)

Answer: \(\boxed{28}\)

---

Problem 6:

\[
(7^2 \times 6 - 8) + 2
\]

1. Parentheses: First, calculate the exponent inside the parentheses: \( 7^2 = 49 \)
\[
49 \times 6 - 8
\]

2. Multiplication: \( 49 \times 6 = 294 \)
\[
294 - 8
\]

3. Subtraction: \( 294 - 8 = 286 \)

4. Addition: Add the result to 2:
\[
286 + 2 = 288
\]

Answer: \(\boxed{288}\)

---

Problem 7:

\[
(3 \times 5 + 3) \div 3
\]

1. Parentheses: Perform the multiplication and addition inside the parentheses:
\[
3 \times 5 = 15
\]
\[
15 + 3 = 18
\]
So, the expression becomes:
\[
18 \div 3
\]

2. Division: \( 18 \div 3 = 6 \)

Answer: \(\boxed{6}\)

---

Problem 8:

\[
(3^2 \times 5^2) \div 9
\]

1. Exponents: Calculate the exponents:
\[
3^2 = 9
\]
\[
5^2 = 25
\]
So, the expression becomes:
\[
(9 \times 25) \div 9
\]

2. Multiplication: \( 9 \times 25 = 225 \)
\[
225 \div 9
\]

3. Division: \( 225 \div 9 = 25 \)

Answer: \(\boxed{25}\)

---

Problem 9:

\[
(7^2 - 4 \times 7)
\]

1. Parentheses: First, calculate the exponent and the multiplication:
\[
7^2 = 49
\]
\[
4 \times 7 = 28
\]
So, the expression becomes:
\[
49 - 28
\]

2. Subtraction: \( 49 - 28 = 21 \)

Answer: \(\boxed{21}\)

---

Problem 10:

\[
5^2 \div (5 + 5 - 4)
\]

1. Parentheses: Perform the operations inside the parentheses:
\[
5 + 5 = 10
\]
\[
10 - 4 = 6
\]
So, the expression becomes:
\[
5^2 \div 6
\]

2. Exponents: \( 5^2 = 25 \)
\[
25 \div 6
\]

3. Division: \( 25 \div 6 = \frac{25}{6} \)

Answer: \(\boxed{\frac{25}{6}}\)

---

Problem 11:

\[
(8^2 \times 5) - 9
\]

1. Parentheses: First, calculate the exponent:
\[
8^2 = 64
\]
So, the expression becomes:
\[
64 \times 5 - 9
\]

2. Multiplication: \( 64 \times 5 = 320 \)
\[
320 - 9
\]

3. Subtraction: \( 320 - 9 = 311 \)

Answer: \(\boxed{311}\)

---

Problem 12:

\[
(6^2 + 6^2) \times 4
\]

1. Parentheses: First, calculate the exponents:
\[
6^2 = 36
\]
So, the expression becomes:
\[
(36 + 36) \times 4
\]

2. Addition: \( 36 + 36 = 72 \)
\[
72 \times 4
\]

3. Multiplication: \( 72 \times 4 = 288 \)

Answer: \(\boxed{288}\)

---

Final Answers:

\[
\boxed{155, 213, \frac{3}{7}, 648, 28, 288, 6, 25, 21, \frac{25}{6}, 311, 288}
\]