Order of Operations Worksheet 7 Worksheets - Free Printable

Problem Description:

The image contains a worksheet titled "Modified #7" with 20 mathematical problems. Each problem involves arithmetic operations, including addition, subtraction, multiplication, division, and exponentiation. The goal is to solve each problem step by step using the order of operations (PEMDAS/BODMAS rules):
1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

---

Solution:

#### Problem 1: \( 3 - (2^3 + 1) + 5 = 0 \)
1. Solve the exponent: \( 2^3 = 8 \)
\[
3 - (8 + 1) + 5
\]
2. Solve inside the parentheses: \( 8 + 1 = 9 \)
\[
3 - 9 + 5
\]
3. Perform subtraction and addition from left to right:
\[
3 - 9 = -6
\]
\[
-6 + 5 = -1
\]
Answer: \(-1\)

---

#### Problem 2: \( (6 \cdot 9 - 9) \div 1 = 20b \)
1. Solve inside the parentheses:
\[
6 \cdot 9 = 54
\]
\[
54 - 9 = 45
\]
2. Divide by 1:
\[
45 \div 1 = 45
\]
Answer: \(45\)

---

#### Problem 3: \( (5 + 7^2) \div 7 = 346 \)
1. Solve the exponent: \( 7^2 = 49 \)
\[
(5 + 49) \div 7
\]
2. Solve inside the parentheses:
\[
5 + 49 = 54
\]
3. Divide:
\[
54 \div 7 = 7.714 \quad (\text{or } \frac{54}{7})
\]
Answer: \(7.714\) or \(\frac{54}{7}\)

---

#### Problem 4: \( (2 - 7) - 6 - 3 = -16 \)
1. Solve inside the parentheses:
\[
2 - 7 = -5
\]
2. Perform subtraction from left to right:
\[
-5 - 6 = -11
\]
\[
-11 - 3 = -14
\]
Answer: \(-14\)

---

#### Problem 5: \( (6 + 7^2) + 1 = 55 \)
1. Solve the exponent: \( 7^2 = 49 \)
\[
(6 + 49) + 1
\]
2. Solve inside the parentheses:
\[
6 + 49 = 55
\]
3. Add:
\[
55 + 1 = 56
\]
Answer: \(56\)

---

#### Problem 6: \( 4^2 - (2 + 2^3) \times 5 = 14 \)
1. Solve the exponents:
\[
4^2 = 16, \quad 2^3 = 8
\]
\[
16 - (2 + 8) \times 5
\]
2. Solve inside the parentheses:
\[
2 + 8 = 10
\]
3. Multiply:
\[
10 \times 5 = 50
\]
4. Subtract:
\[
16 - 50 = -34
\]
Answer: \(-34\)

---

#### Problem 7: \( (6 - 1 + 7) \times 2 = 12 \)
1. Solve inside the parentheses:
\[
6 - 1 = 5
\]
\[
5 + 7 = 12
\]
2. Multiply:
\[
12 \times 2 = 24
\]
Answer: \(24\)

---

#### Problem 8: \( (3^2 - 3^2) + 5 = 5 \)
1. Solve the exponents:
\[
3^2 = 9
\]
\[
9 - 9 = 0
\]
2. Add:
\[
0 + 5 = 5
\]
Answer: \(5\)

---

#### Problem 9: \( (7 + 8 - 4^2) \times 2 + 1 = -1 \)
1. Solve the exponent: \( 4^2 = 16 \)
\[
(7 + 8 - 16) \times 2 + 1
\]
2. Solve inside the parentheses:
\[
7 + 8 = 15
\]
\[
15 - 16 = -1
\]
3. Multiply:
\[
-1 \times 2 = -2
\]
4. Add:
\[
-2 + 1 = -1
\]
Answer: \(-1\)

---

#### Problem 10: \( 6 - (6 + 3) \times 4 - 4 = -33 \)
1. Solve inside the parentheses:
\[
6 + 3 = 9
\]
2. Multiply:
\[
9 \times 4 = 36
\]
3. Subtract:
\[
6 - 36 = -30
\]
\[
-30 - 4 = -34
\]
Answer: \(-34\)

---

#### Problem 11: \( (3 + 5 \times 6 + 3^2 - 3) = 27 \)
1. Solve the exponent: \( 3^2 = 9 \)
\[
(3 + 5 \times 6 + 9 - 3)
\]
2. Perform multiplication:
\[
5 \times 6 = 30
\]
3. Solve inside the parentheses:
\[
3 + 30 = 33
\]
\[
33 + 9 = 42
\]
\[
42 - 3 = 39
\]
Answer: \(39\)

---

#### Problem 12: \( (7 - 2^3) \times 9 = 135 \)
1. Solve the exponent: \( 2^3 = 8 \)
\[
(7 - 8) \times 9
\]
2. Solve inside the parentheses:
\[
7 - 8 = -1
\]
3. Multiply:
\[
-1 \times 9 = -9
\]
Answer: \(-9\)

---

#### Problem 13: \( (3 \times 6) - 5 = 13 \)
1. Solve the multiplication:
\[
3 \times 6 = 18
\]
2. Subtract:
\[
18 - 5 = 13
\]
Answer: \(13\)

---

#### Problem 14: \( 6 \times (2 + 1) + 1 = 12 \)
1. Solve inside the parentheses:
\[
2 + 1 = 3
\]
2. Multiply:
\[
6 \times 3 = 18
\]
3. Add:
\[
18 + 1 = 19
\]
Answer: \(19\)

---

#### Problem 15: \( (2^3 - 9 - 8) \div 3 + 3 = -9 \)
1. Solve the exponent: \( 2^3 = 8 \)
\[
(8 - 9 - 8) \div 3 + 3
\]
2. Solve inside the parentheses:
\[
8 - 9 = -1
\]
\[
-1 - 8 = -9
\]
3. Divide:
\[
-9 \div 3 = -3
\]
4. Add:
\[
-3 + 3 = 0
\]
Answer: \(0\)

---

#### Problem 16: \( 2^3 + (7 + 7 \div 8) = 64 \)
1. Solve the exponent: \( 2^3 = 8 \)
\[
8 + (7 + 7 \div 8)
\]
2. Solve the division inside the parentheses:
\[
7 \div 8 = 0.875
\]
3. Solve inside the parentheses:
\[
7 + 0.875 = 7.875
\]
4. Add:
\[
8 + 7.875 = 15.875
\]
Answer: \(15.875\)

---

#### Problem 17: \( (6 + 6^2) \times 3 = 126 \)
1. Solve the exponent: \( 6^2 = 36 \)
\[
(6 + 36) \times 3
\]
2. Solve inside the parentheses:
\[
6 + 36 = 42
\]
3. Multiply:
\[
42 \times 3 = 126
\]
Answer: \(126\)

---

#### Problem 18: \( [3 + 1] \times 8 \times 4 = 128 \)
1. Solve inside the brackets:
\[
3 + 1 = 4
\]
2. Multiply:
\[
4 \times 8 = 32
\]
\[
32 \times 4 = 128
\]
Answer: \(128\)

---

#### Problem 19: \( (7^2 \times 4) + 7 = 1579 \)
1. Solve the exponent: \( 7^2 = 49 \)
\[
(49 \times 4) + 7
\]
2. Multiply:
\[
49 \times 4 = 196
\]
3. Add:
\[
196 + 7 = 203
\]
Answer: \(203\)

---

#### Problem 20: \( 5^2 - 3 \times (3^2 \times 2) + 5 = -13 \)
1. Solve the exponents:
\[
5^2 = 25, \quad 3^2 = 9
\]
\[
25 - 3 \times (9 \times 2) + 5
\]
2. Solve inside the parentheses:
\[
9 \times 2 = 18
\]
3. Multiply:
\[
3 \times 18 = 54
\]
4. Subtract and add:
\[
25 - 54 = -29
\]
\[
-29 + 5 = -24
\]
Answer: \(-24\)

---

Final Answers:

\[
\boxed{
\begin{aligned}
&1. -1, \quad 2. 45, \quad 3. 7.714 \text{ or } \frac{54}{7}, \quad 4. -14, \quad 5. 56, \\
&6. -34, \quad 7. 24, \quad 8. 5, \quad 9. -1, \quad 10. -34, \\
&11. 39, \quad 12. -9, \quad 13. 13, \quad 14. 19, \quad 15. 0, \\
&16. 15.875, \quad 17. 126, \quad 18. 128, \quad 19. 203, \quad 20. -24
\end{aligned}
}
\]