Grade 5 Order of Operations Worksheets | Free Worksheets | Printables - Free Printable

To solve the problems, we need to follow the Order of Operations, often remembered by the acronym PEMDAS:

- P: Parentheses
- E: Exponents
- M/D: Multiplication and Division (from left to right)
- A/S: Addition and Subtraction (from left to right)

Let's solve each problem step by step.

---

Problem 1: \( 14 + 3^2 \times 3^2 + 26 \)

1. Exponents: Calculate \( 3^2 \).
\[
3^2 = 9
\]
So, the expression becomes:
\[
14 + 9 \times 9 + 26
\]

2. Multiplication: Perform \( 9 \times 9 \).
\[
9 \times 9 = 81
\]
So, the expression becomes:
\[
14 + 81 + 26
\]

3. Addition: Add the numbers from left to right.
\[
14 + 81 = 95
\]
\[
95 + 26 = 121
\]

Answer: \( 121 \)

---

Problem 2: \( 5(42 \div 7) + 30 \)

1. Parentheses: Solve \( 42 \div 7 \).
\[
42 \div 7 = 6
\]
So, the expression becomes:
\[
5 \times 6 + 30
\]

2. Multiplication: Perform \( 5 \times 6 \).
\[
5 \times 6 = 30
\]
So, the expression becomes:
\[
30 + 30
\]

3. Addition: Add the numbers.
\[
30 + 30 = 60
\]

Answer: \( 60 \)

---

Problem 3: \( 8 \times 9 + 6 \times 6 \)

1. Multiplication: Perform \( 8 \times 9 \) and \( 6 \times 6 \).
\[
8 \times 9 = 72
\]
\[
6 \times 6 = 36
\]
So, the expression becomes:
\[
72 + 36
\]

2. Addition: Add the numbers.
\[
72 + 36 = 108
\]

Answer: \( 108 \)

---

Problem 4: \( 5^2 + 8 \times 4 + 3^2 \)

1. Exponents: Calculate \( 5^2 \) and \( 3^2 \).
\[
5^2 = 25
\]
\[
3^2 = 9
\]
So, the expression becomes:
\[
25 + 8 \times 4 + 9
\]

2. Multiplication: Perform \( 8 \times 4 \).
\[
8 \times 4 = 32
\]
So, the expression becomes:
\[
25 + 32 + 9
\]

3. Addition: Add the numbers from left to right.
\[
25 + 32 = 57
\]
\[
57 + 9 = 66
\]

Answer: \( 66 \)

---

Problem 5: \( 108 \div 12 \times 9 \)

1. Division: Perform \( 108 \div 12 \).
\[
108 \div 12 = 9
\]
So, the expression becomes:
\[
9 \times 9
\]

2. Multiplication: Perform \( 9 \times 9 \).
\[
9 \times 9 = 81
\]

Answer: \( 81 \)

---

Problem 6: \( 8(5 + 5) \times 2 \)

1. Parentheses: Solve \( 5 + 5 \).
\[
5 + 5 = 10
\]
So, the expression becomes:
\[
8 \times 10 \times 2
\]

2. Multiplication: Perform the multiplications from left to right.
\[
8 \times 10 = 80
\]
\[
80 \times 2 = 160
\]

Answer: \( 160 \)

---

Problem 7: \( 4 \times 8 + 3(3 \times 3) \)

1. Parentheses: Solve \( 3 \times 3 \).
\[
3 \times 3 = 9
\]
So, the expression becomes:
\[
4 \times 8 + 3 \times 9
\]

2. Multiplication: Perform \( 4 \times 8 \) and \( 3 \times 9 \).
\[
4 \times 8 = 32
\]
\[
3 \times 9 = 27
\]
So, the expression becomes:
\[
32 + 27
\]

3. Addition: Add the numbers.
\[
32 + 27 = 59
\]

Answer: \( 59 \)

---

Problem 8: \( 75 \div 5 \times 2 \)

1. Division: Perform \( 75 \div 5 \).
\[
75 \div 5 = 15
\]
So, the expression becomes:
\[
15 \times 2
\]

2. Multiplication: Perform \( 15 \times 2 \).
\[
15 \times 2 = 30
\]

Answer: \( 30 \)

---

Problem 9: \( 8 \times 5 + 9 \times 5 \)

1. Multiplication: Perform \( 8 \times 5 \) and \( 9 \times 5 \).
\[
8 \times 5 = 40
\]
\[
9 \times 5 = 45
\]
So, the expression becomes:
\[
40 + 45
\]

2. Addition: Add the numbers.
\[
40 + 45 = 85
\]

Answer: \( 85 \)

---

Problem 10: \( 144 \div 12 \times 2(5 \times 2) \)

1. Parentheses: Solve \( 5 \times 2 \).
\[
5 \times 2 = 10
\]
So, the expression becomes:
\[
144 \div 12 \times 2 \times 10
\]

2. Division: Perform \( 144 \div 12 \).
\[
144 \div 12 = 12
\]
So, the expression becomes:
\[
12 \times 2 \times 10
\]

3. Multiplication: Perform the multiplications from left to right.
\[
12 \times 2 = 24
\]
\[
24 \times 10 = 240
\]

Answer: \( 240 \)

---

Final Answers

\[
\boxed{
\begin{aligned}
1. & \ 121 \\
2. & \ 60 \\
3. & \ 108 \\
4. & \ 66 \\
5. & \ 81 \\
6. & \ 160 \\
7. & \ 59 \\
8. & \ 30 \\
9. & \ 85 \\
10. & \ 240
\end{aligned}
}
\]