Order of Operations Worksheet #2 featuring 20 math problems to solve using PEMDAS rules.

Here are the step-by-step solutions for each problem on the worksheet. Remember to follow the Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), and Addition/Subtraction (left to right).

1. $3 - (2^3 \div 1) + 5$
* Inside parentheses: Calculate exponent first ($2^3 = 8$). Then divide ($8 \div 1 = 8$).
* Equation becomes: $3 - 8 + 5$
* Subtract: $3 - 8 = -5$
* Add: $-5 + 5 = 0$
Answer: 0

2. $(6^3 - 9 - 1)$
* Inside parentheses: Calculate exponent first ($6^3 = 6 \times 6 \times 6 = 216$).
* Equation becomes: $216 - 9 - 1$
* Subtract: $216 - 9 = 207$
* Subtract: $207 - 1 = 206$
Answer: 206

3. $(5 + 7^3) \div 7 \times 7$
* Inside parentheses: Calculate exponent first ($7^3 = 343$). Then add ($5 + 343 = 348$).
* Equation becomes: $348 \div 7 \times 7$
* Divide: $348 \div 7 \approx 49.71$ (Note: In many school contexts, this might be a typo for $7^2$ or similar to make it clean, but strictly following math rules: $348/7 \times 7$ cancels out to 348). Let's look closer. Actually, division and multiplication are inverse operations here. $348 \div 7 \times 7 = 348$.
Answer: 348

4. $(2 - 7) - 8 - 3$
* Inside parentheses: $2 - 7 = -5$
* Equation becomes: $-5 - 8 - 3$
* Subtract: $-5 - 8 = -13$
* Subtract: $-13 - 3 = -16$
Answer: -16

5. $(6 + 7^2) + 1$
* Inside parentheses: Calculate exponent first ($7^2 = 49$). Then add ($6 + 49 = 55$).
* Equation becomes: $55 + 1$
* Add: $56$
Answer: 56

6. $4^3 - (2 + 2^3) \times 5$
* Exponent outside: $4^3 = 64$
* Inside parentheses: Exponent first ($2^3 = 8$). Then add ($2 + 8 = 10$).
* Equation becomes: $64 - 10 \times 5$
* Multiply: $10 \times 5 = 50$
* Subtract: $64 - 50 = 14$
Answer: 14

7. $(6 - 1 + 7)$
* Inside parentheses: Work left to right.
* Subtract: $6 - 1 = 5$
* Add: $5 + 7 = 12$
Answer: 12

8. $(3^2 - 3^2) + 5$
* Inside parentheses: Exponents first ($3^2 = 9$ and $3^2 = 9$).
* Subtract: $9 - 9 = 0$
* Equation becomes: $0 + 5$
* Add: $5$
Answer: 5

9. $(7 + 8 - 4^2) \times 2 + 1$
* Inside parentheses: Exponent first ($4^2 = 16$).
* Inside parentheses: Add/Subtract left to right ($7 + 8 = 15$; $15 - 16 = -1$).
* Equation becomes: $-1 \times 2 + 1$
* Multiply: $-1 \times 2 = -2$
* Add: $-2 + 1 = -1$
Answer: -1

10. $6 - (8 + 3^3) - 4$
* Inside parentheses: Exponent first ($3^3 = 27$). Then add ($8 + 27 = 35$).
* Equation becomes: $6 - 35 - 4$
* Subtract: $6 - 35 = -29$
* Subtract: $-29 - 4 = -33$
Answer: -33

11. $(3 + 3 \times 6 + 3^2 - 3)$
* Inside parentheses: Exponent first ($3^2 = 9$).
* Inside parentheses: Multiplication next ($3 \times 6 = 18$).
* Inside parentheses: Add/Subtract left to right ($3 + 18 = 21$; $21 + 9 = 30$; $30 - 3 = 27$).
Answer: 27

12. $(7 + 2^3) \times 9$
* Inside parentheses: Exponent first ($2^3 = 8$). Then add ($7 + 8 = 15$).
* Equation becomes: $15 \times 9$
* Multiply: $135$
Answer: 135

13. $(3 \times 6) - 5$
* Inside parentheses: $3 \times 6 = 18$
* Equation becomes: $18 - 5$
* Subtract: $13$
Answer: 13

14. $6 \times (2 \div 1) \div 1$
* Inside parentheses: $2 \div 1 = 2$
* Equation becomes: $6 \times 2 \div 1$
* Multiply: $6 \times 2 = 12$
* Divide: $12 \div 1 = 12$
Answer: 12

15. $(2^3 - 9 - 8) \div 3 \times 3$
* Inside parentheses: Exponent first ($2^3 = 8$).
* Inside parentheses: Subtract left to right ($8 - 9 = -1$; $-1 - 8 = -9$).
* Equation becomes: $-9 \div 3 \times 3$
* Divide: $-9 \div 3 = -3$
* Multiply: $-3 \times 3 = -9$
Answer: -9

16. $2^3 \div (7 \div 7 \div 8)$
* Exponent outside: $2^3 = 8$
* Inside parentheses: Divide left to right ($7 \div 7 = 1$; $1 \div 8 = 0.125$ or $1/8$).
* Equation becomes: $8 \div 0.125$ (or $8 \div \frac{1}{8}$)
* Divide: $8 \times 8 = 64$
Answer: 64

17. $(6 + 6^2) \times 3$
* Inside parentheses: Exponent first ($6^2 = 36$). Then add ($6 + 36 = 42$).
* Equation becomes: $42 \times 3$
* Multiply: $126$
Answer: 126

18. $(3 + 1) \times 8 \times 4$
* Inside parentheses: $3 + 1 = 4$
* Equation becomes: $4 \times 8 \times 4$
* Multiply: $4 \times 8 = 32$
* Multiply: $32 \times 4 = 128$
Answer: 128

19. $(7^3 \times 4) + 7$
* Inside parentheses: Exponent first ($7^3 = 343$). Then multiply ($343 \times 4 = 1372$).
* Equation becomes: $1372 + 7$
* Add: $1379$
Answer: 1379

20. $6^2 - 3 \times (3^2 \times 2) + 5$
* Exponent outside: $6^2 = 36$
* Inside parentheses: Exponent first ($3^2 = 9$). Then multiply ($9 \times 2 = 18$).
* Equation becomes: $36 - 3 \times 18 + 5$
* Multiply: $3 \times 18 = 54$
* Equation becomes: $36 - 54 + 5$
* Subtract: $36 - 54 = -18$
* Add: $-18 + 5 = -13$
Answer: -13

Final Answer:
1. 0
2. 206
3. 348
4. -16
5. 56
6. 14
7. 12
8. 5
9. -1
10. -33
11. 27
12. 135
13. 13
14. 12
15. -9
16. 64
17. 126
18. 128
19. 1379
20. -13