Whole Numbers Order of Operations Worksheet with 24 problems requiring step-by-step solutions.

Problem: Solve the given problems using the order of operations (PEMDAS/BODMAS rules).

The order of operations is as follows:
1. Parentheses/Brackets (`()` or `[]`)
2. Exponents/Orders (`^` or `²`, `³`, etc.)
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: \( 5 \cdot 2 + 3 \)

- Step 1: Perform multiplication first.
\[
5 \cdot 2 = 10
\]
- Step 2: Add the result to 3.
\[
10 + 3 = 13
\]
- Answer: \( \boxed{13} \)

---

Problem 2: \( 8 + 2 - 3 \)

- Step 1: Perform addition and subtraction from left to right.
\[
8 + 2 = 10
\]
\[
10 - 3 = 7
\]
- Answer: \( \boxed{7} \)

---

Problem 3: \( 3^2 + 4 \)

- Step 1: Calculate the exponent.
\[
3^2 = 9
\]
- Step 2: Add the result to 4.
\[
9 + 4 = 13
\]
- Answer: \( \boxed{13} \)

---

Problem 4: \( 3(8 - 6) - 1^2 \)

- Step 1: Solve the expression inside the parentheses.
\[
8 - 6 = 2
\]
- Step 2: Multiply 3 by the result.
\[
3 \cdot 2 = 6
\]
- Step 3: Calculate the exponent.
\[
1^2 = 1
\]
- Step 4: Subtract the result of the exponent from 6.
\[
6 - 1 = 5
\]
- Answer: \( \boxed{5} \)

---

Problem 5: \( 16 - (10 + 5) \div 3 \)

- Step 1: Solve the expression inside the parentheses.
\[
10 + 5 = 15
\]
- Step 2: Perform the division.
\[
15 \div 3 = 5
\]
- Step 3: Subtract the result from 16.
\[
16 - 5 = 11
\]
- Answer: \( \boxed{11} \)

---

Problem 6: \( 2^3 + 8 - 6 \)

- Step 1: Calculate the exponent.
\[
2^3 = 8
\]
- Step 2: Add 8 to the result.
\[
8 + 8 = 16
\]
- Step 3: Subtract 6 from the result.
\[
16 - 6 = 10
\]
- Answer: \( \boxed{10} \)

---

Problem 7: \( 5 \cdot 2^2 + 3^2 \)

- Step 1: Calculate the exponents.
\[
2^2 = 4, \quad 3^2 = 9
\]
- Step 2: Multiply 5 by the result of \( 2^2 \).
\[
5 \cdot 4 = 20
\]
- Step 3: Add the results.
\[
20 + 9 = 29
\]
- Answer: \( \boxed{29} \)

---

Problem 8: \( 5 - (3 - 1) + 1 \)

- Step 1: Solve the expression inside the parentheses.
\[
3 - 1 = 2
\]
- Step 2: Subtract 2 from 5.
\[
5 - 2 = 3
\]
- Step 3: Add 1 to the result.
\[
3 + 1 = 4
\]
- Answer: \( \boxed{4} \)

---

Problem 9: \( 18 - 4^2 + 8 \)

- Step 1: Calculate the exponent.
\[
4^2 = 16
\]
- Step 2: Subtract 16 from 18.
\[
18 - 16 = 2
\]
- Step 3: Add 8 to the result.
\[
2 + 8 = 10
\]
- Answer: \( \boxed{10} \)

---

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

- Step 1: Solve the expression inside the parentheses.
\[
5 - 2 = 3
\]
- Step 2: Calculate the exponent for \( 3 \).
\[
3^2 = 9
\]
- Step 3: Multiply 3 by the result of \( 3^2 \).
\[
3 \cdot 9 = 27
\]
- Step 4: Calculate the exponent for \( 2 \).
\[
2^2 = 4
\]
- Step 5: Add the results.
\[
4 + 27 = 31
\]
- Answer: \( \boxed{31} \)

---

Problem 11: \( 3^2 - 2(3) \)

- Step 1: Calculate the exponent.
\[
3^2 = 9
\]
- Step 2: Multiply 2 by 3.
\[
2 \cdot 3 = 6
\]
- Step 3: Subtract the result from 9.
\[
9 - 6 = 3
\]
- Answer: \( \boxed{3} \)

---

Problem 12: \( 24 - 2(1 + 2)^2 \)

- Step 1: Solve the expression inside the parentheses.
\[
1 + 2 = 3
\]
- Step 2: Calculate the exponent.
\[
3^2 = 9
\]
- Step 3: Multiply 2 by the result of \( 3^2 \).
\[
2 \cdot 9 = 18
\]
- Step 4: Subtract the result from 24.
\[
24 - 18 = 6
\]
- Answer: \( \boxed{6} \)

---

Problem 13: \( 5(7 - 4) - 1 \)

- Step 1: Solve the expression inside the parentheses.
\[
7 - 4 = 3
\]
- Step 2: Multiply 5 by the result.
\[
5 \cdot 3 = 15
\]
- Step 3: Subtract 1 from the result.
\[
15 - 1 = 14
\]
- Answer: \( \boxed{14} \)

---

Problem 14: \( 20 - (2 + 4) \div 3 \)

- Step 1: Solve the expression inside the parentheses.
\[
2 + 4 = 6
\]
- Step 2: Perform the division.
\[
6 \div 3 = 2
\]
- Step 3: Subtract the result from 20.
\[
20 - 2 = 18
\]
- Answer: \( \boxed{18} \)

---

Problem 15: \( 23 + 1^4 - 4 \cdot 5 \div 4 - 1 \)

- Step 1: Calculate the exponent.
\[
1^4 = 1
\]
- Step 2: Perform the multiplication and division from left to right.
\[
4 \cdot 5 = 20
\]
\[
20 \div 4 = 5
\]
- Step 3: Add and subtract from left to right.
\[
23 + 1 = 24
\]
\[
24 - 5 = 19
\]
\[
19 - 1 = 18
\]
- Answer: \( \boxed{18} \)

---

Problem 16: \( 20 - 10 + 5 \)

- Step 1: Perform addition and subtraction from left to right.
\[
20 - 10 = 10
\]
\[
10 + 5 = 15
\]
- Answer: \( \boxed{15} \)

---

Problem 17: \( 14 - 2 \cdot 6 \)

- Step 1: Perform multiplication.
\[
2 \cdot 6 = 12
\]
- Step 2: Subtract the result from 14.
\[
14 - 12 = 2
\]
- Answer: \( \boxed{2} \)

---

Problem 18: \( 5^2 - 5 + 2 \)

- Step 1: Calculate the exponent.
\[
5^2 = 25
\]
- Step 2: Subtract 5 from 25.
\[
25 - 5 = 20
\]
- Step 3: Add 2 to the result.
\[
20 + 2 = 22
\]
- Answer: \( \boxed{22} \)

---

Problem 19: \( 15 - (9 + 3) \div 6 \)

- Step 1: Solve the expression inside the parentheses.
\[
9 + 3 = 12
\]
- Step 2: Perform the division.
\[
12 \div 6 = 2
\]
- Step 3: Subtract the result from 15.
\[
15 - 2 = 13
\]
- Answer: \( \boxed{13} \)

---

Problem 20: \( 4(13 + 2) + 5 \)

- Step 1: Solve the expression inside the parentheses.
\[
13 + 2 = 15
\]
- Step 2: Multiply 4 by the result.
\[
4 \cdot 15 = 60
\]
- Step 3: Add 5 to the result.
\[
60 + 5 = 65
\]
- Answer: \( \boxed{65} \)

---

Problem 21: \( 20 - 2^3 - 4 \)

- Step 1: Calculate the exponent.
\[
2^3 = 8
\]
- Step 2: Subtract 8 from 20.
\[
20 - 8 = 12
\]
- Step 3: Subtract 4 from the result.
\[
12 - 4 = 8
\]
- Answer: \( \boxed{8} \)

---

Problem 22: \( 12 - 8 + 2 \)

- Step 1: Perform addition and subtraction from left to right.
\[
12 - 8 = 4
\]
\[
4 + 2 = 6
\]
- Answer: \( \boxed{6} \)

---

Problem 23: \( 24 + 2 - 3 \cdot 4 \)

- Step 1: Perform multiplication.
\[
3 \cdot 4 = 12
\]
- Step 2: Add and subtract from left to right.
\[
24 + 2 = 26
\]
\[
26 - 12 = 14
\]
- Answer: \( \boxed{14} \)

---

Problem 24: \( 5^2 + 4(15 + 3) \)

- Step 1: Solve the expression inside the parentheses.
\[
15 + 3 = 18
\]
- Step 2: Multiply 4 by the result.
\[
4 \cdot 18 = 72
\]
- Step 3: Calculate the exponent.
\[
5^2 = 25
\]
- Step 4: Add the results.
\[
25 + 72 = 97
\]
- Answer: \( \boxed{97} \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 13 \\
2. & \ 7 \\
3. & \ 13 \\
4. & \ 5 \\
5. & \ 11 \\
6. & \ 10 \\
7. & \ 29 \\
8. & \ 4 \\
9. & \ 10 \\
10. & \ 31 \\
11. & \ 3 \\
12. & \ 6 \\
13. & \ 14 \\
14. & \ 18 \\
15. & \ 18 \\
16. & \ 15 \\
17. & \ 2 \\
18. & \ 22 \\
19. & \ 13 \\
20. & \ 65 \\
21. & \ 8 \\
22. & \ 6 \\
23. & \ 14 \\
24. & \ 97 \\
\end{aligned}
}
\]