Let's solve each problem step by step using the
order of operations, often remembered by the acronym
PEMDAS:
-
Parentheses
-
Exponents
-
Multiplication and
Division (from left to right)
-
Addition and
Subtraction (from left to right)
---
1. $ 4^2 + (1 \times 5 + 7^2) + 8 $
- $ 4^2 = 16 $
- $ 7^2 = 49 $
- Inside parentheses: $ 1 \times 5 = 5 $, then $ 5 + 49 = 54 $
- Now: $ 16 + 54 + 8 = 78 $
✔ Answer: 78
---
2. $ 6^2 \div (2 - 8) + 1 - 8 $
- $ 6^2 = 36 $
- $ 2 - 8 = -6 $
- $ 36 \div (-6) = -6 $
- $ -6 + 1 = -5 $
- $ -5 - 8 = -13 $
✔ Answer: -13
---
3. $ (6^2 \times 7) \div 2 $
- $ 6^2 = 36 $
- $ 36 \times 7 = 252 $
- $ 252 \div 2 = 126 $
✔ Answer: 126
---
4. $ 9 - (5^2 + 7) \div 2 $
- $ 5^2 = 25 $
- $ 25 + 7 = 32 $
- $ 32 \div 2 = 16 $
- $ 9 - 16 = -7 $
✔ Answer: -7
---
5. $ (6 + 8 - 2) $
- $ 6 + 8 = 14 $
- $ 14 - 2 = 12 $
✔ Answer: 12
---
6. $ (1 - 4^2) \times 2 $
- $ 4^2 = 16 $
- $ 1 - 16 = -15 $
- $ -15 \times 2 = -30 $
✔ Answer: -30
---
7. $ 5 + (4^3 + 1) + 8 $
- $ 4^3 = 64 $
- $ 64 + 1 = 65 $
- $ 5 + 65 = 70 $
- $ 70 + 8 = 78 $
✔ Answer: 78
---
8. $ (4 + 8) + 1 $
- $ 4 + 8 = 12 $
- $ 12 + 1 = 13 $
✔ Answer: 13
---
9. $ (2^2 + 9 \div 1) $
- $ 2^2 = 4 $
- $ 9 \div 1 = 9 $
- $ 4 + 9 = 13 $
✔ Answer: 13
---
10. $ (3 + 8 - 1) $
- $ 3 + 8 = 11 $
- $ 11 - 1 = 10 $
✔ Answer: 10
---
11. $ 3^2 + 9^2 - (8 + 7) \div 5 $
- $ 3^2 = 9 $
- $ 9^2 = 81 $
- $ 8 + 7 = 15 $
- $ 15 \div 5 = 3 $
- $ 9 + 81 = 90 $
- $ 90 - 3 = 87 $
✔ Answer: 87
---
12. $ 2 + 3 \times (8 + 5^3 \div 1) $
- $ 5^3 = 125 $
- $ 125 \div 1 = 125 $
- $ 8 + 125 = 133 $
- $ 3 \times 133 = 399 $
- $ 2 + 399 = 401 $
✔ Answer: 401
---
13. $ (3^2 \times 3 + 4 + 2) - 1 $
- $ 3^2 = 9 $
- $ 9 \times 3 = 27 $
- $ 27 + 4 = 31 $
- $ 31 + 2 = 33 $
- $ 33 - 1 = 32 $
✔ Answer: 32
---
14. $ (4^3 \times 3^2 \div 4) $
- $ 4^3 = 64 $
- $ 3^2 = 9 $
- $ 64 \times 9 = 576 $
- $ 576 \div 4 = 144 $
✔ Answer: 144
---
15. $ (9 \times 9^3 + 4) $
- $ 9^3 = 729 $
- $ 9 \times 729 = 6561 $
- $ 6561 + 4 = 6565 $
✔ Answer: 6565
---
16. $ 5 - 9 + (7 \times 2^2 - 8) $
- $ 2^2 = 4 $
- $ 7 \times 4 = 28 $
- $ 28 - 8 = 20 $
- $ 5 - 9 = -4 $
- $ -4 + 20 = 16 $
✔ Answer: 16
---
17. $ (8 - 3^2) - 8 $
- $ 3^2 = 9 $
- $ 8 - 9 = -1 $
- $ -1 - 8 = -9 $
✔ Answer: -9
---
18. $ (5^3 + 3 - 2^3 + 6 - 8) $
- $ 5^3 = 125 $
- $ 2^3 = 8 $
- Now: $ 125 + 3 = 128 $
- $ 128 - 8 = 120 $
- $ 120 + 6 = 126 $
- $ 126 - 8 = 118 $
✔ Answer: 118
---
19. $ (2 \times 5 \div 5) $
- $ 2 \times 5 = 10 $
- $ 10 \div 5 = 2 $
✔ Answer: 2
---
20. $ (1^2 \times 7) \times (8^2 - 8) \times 1 $
- $ 1^2 = 1 $
- $ 1 \times 7 = 7 $
- $ 8^2 = 64 $
- $ 64 - 8 = 56 $
- $ 7 \times 56 = 392 $
- $ 392 \times 1 = 392 $
✔ Answer: 392
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 78 |
| 2 | -13 |
| 3 | 126 |
| 4 | -7 |
| 5 | 12 |
| 6 | -30 |
| 7 | 78 |
| 8 | 13 |
| 9 | 13 |
| 10 | 10 |
| 11 | 87 |
| 12 | 401 |
| 13 | 32 |
| 14 | 144 |
| 15 | 6565 |
| 16 | 16 |
| 17 | -9 |
| 18 | 118 |
| 19 | 2 |
| 20 | 392 |
>
Score: 20/20 – All problems solved correctly!
Let me know if you'd like this formatted as a printable worksheet or with more explanation on any specific problem!
Parent Tip: Review the logic above to help your child master the concept of order of operations worksheet pdf.
