Order of Operations Worksheet: 19 Resources For Your Class - Free Printable

To solve the problems in "Arcturus' Order of Operations Quest," we need to follow the order of operations, often remembered by the acronym PEMDAS:

1. Parentheses (simplify inside parentheses first)
2. Exponents (solve any exponents next)
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: \( 5 \times 4 + 13 \)

- Step 1: Perform multiplication first.
\[
5 \times 4 = 20
\]
- Step 2: Add the result to 13.
\[
20 + 13 = 33
\]
- Answer: \( \boxed{33} \)

---

Problem 2: \( 110 - 100 \div 5 \)

- Step 1: Perform division first.
\[
100 \div 5 = 20
\]
- Step 2: Subtract the result from 110.
\[
110 - 20 = 90
\]
- Answer: \( \boxed{90} \)

---

Problem 3: \( 11 + 18 \div 6 \)

- Step 1: Perform division first.
\[
18 \div 6 = 3
\]
- Step 2: Add the result to 11.
\[
11 + 3 = 14
\]
- Answer: \( \boxed{14} \)

---

Problem 4: \( 8 \times 8 - 14 \)

- Step 1: Perform multiplication first.
\[
8 \times 8 = 64
\]
- Step 2: Subtract 14 from the result.
\[
64 - 14 = 50
\]
- Answer: \( \boxed{50} \)

---

Problem 5: \( 3 \times 4 - 8 \)

- Step 1: Perform multiplication first.
\[
3 \times 4 = 12
\]
- Step 2: Subtract 8 from the result.
\[
12 - 8 = 4
\]
- Answer: \( \boxed{4} \)

---

Problem 6: \( 3 + 7 \times 5 \)

- Step 1: Perform multiplication first.
\[
7 \times 5 = 35
\]
- Step 2: Add the result to 3.
\[
3 + 35 = 38
\]
- Answer: \( \boxed{38} \)

---

Problem 7: \( 30 - 21 \div 3 \)

- Step 1: Perform division first.
\[
21 \div 3 = 7
\]
- Step 2: Subtract the result from 30.
\[
30 - 7 = 23
\]
- Answer: \( \boxed{23} \)

---

Problem 8: \( 60 \div 12 + 9 \)

- Step 1: Perform division first.
\[
60 \div 12 = 5
\]
- Step 2: Add the result to 9.
\[
5 + 9 = 14
\]
- Answer: \( \boxed{14} \)

---

Problem 9: \( 9 \times 9 - 22 \)

- Step 1: Perform multiplication first.
\[
9 \times 9 = 81
\]
- Step 2: Subtract 22 from the result.
\[
81 - 22 = 59
\]
- Answer: \( \boxed{59} \)

---

Problem 10: \( 72 - 63 \div 9 \)

- Step 1: Perform division first.
\[
63 \div 9 = 7
\]
- Step 2: Subtract the result from 72.
\[
72 - 7 = 65
\]
- Answer: \( \boxed{65} \)

---

Problem 11: \( 35 + 25 \div 5 \)

- Step 1: Perform division first.
\[
25 \div 5 = 5
\]
- Step 2: Add the result to 35.
\[
35 + 5 = 40
\]
- Answer: \( \boxed{40} \)

---

Problem 12: \( 9 \times 4 - 16 \)

- Step 1: Perform multiplication first.
\[
9 \times 4 = 36
\]
- Step 2: Subtract 16 from the result.
\[
36 - 16 = 20
\]
- Answer: \( \boxed{20} \)

---

Problem 13: \( 24 \div 3 - 5 \)

- Step 1: Perform division first.
\[
24 \div 3 = 8
\]
- Step 2: Subtract 5 from the result.
\[
8 - 5 = 3
\]
- Answer: \( \boxed{3} \)

---

Problem 14: \( 80 - 8 \times 9 \)

- Step 1: Perform multiplication first.
\[
8 \times 9 = 72
\]
- Step 2: Subtract the result from 80.
\[
80 - 72 = 8
\]
- Answer: \( \boxed{8} \)

---

Problem 15: \( 80 - 7 \times 6 \)

- Step 1: Perform multiplication first.
\[
7 \times 6 = 42
\]
- Step 2: Subtract the result from 80.
\[
80 - 42 = 38
\]
- Answer: \( \boxed{38} \)

---

Problem 16: \( 66 \div 6 - 6 \)

- Step 1: Perform division first.
\[
66 \div 6 = 11
\]
- Step 2: Subtract 6 from the result.
\[
11 - 6 = 5
\]
- Answer: \( \boxed{5} \)

---

Problem 17: \( 6 \div 3 + 14 \)

- Step 1: Perform division first.
\[
6 \div 3 = 2
\]
- Step 2: Add the result to 14.
\[
2 + 14 = 16
\]
- Answer: \( \boxed{16} \)

---

Problem 18: \( 12 + 132 \div 12 \)

- Step 1: Perform division first.
\[
132 \div 12 = 11
\]
- Step 2: Add the result to 12.
\[
12 + 11 = 23
\]
- Answer: \( \boxed{23} \)

---

Problem 19: \( 6 + 54 \div 9 \)

- Step 1: Perform division first.
\[
54 \div 9 = 6
\]
- Step 2: Add the result to 6.
\[
6 + 6 = 12
\]
- Answer: \( \boxed{12} \)

---

Problem 20: \( 7 + 9 \times 7 \)

- Step 1: Perform multiplication first.
\[
9 \times 7 = 63
\]
- Step 2: Add the result to 7.
\[
7 + 63 = 70
\]
- Answer: \( \boxed{70} \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 33 \\
2. & 90 \\
3. & 14 \\
4. & 50 \\
5. & 4 \\
6. & 38 \\
7. & 23 \\
8. & 14 \\
9. & 59 \\
10. & 65 \\
11. & 40 \\
12. & 20 \\
13. & 3 \\
14. & 8 \\
15. & 38 \\
16. & 5 \\
17. & 16 \\
18. & 23 \\
19. & 12 \\
20. & 70 \\
\end{array}
}
\]