Math Worksheets: Order of Operations or PEMDAS - Free Printable
Educational worksheet: Math Worksheets: Order of Operations or PEMDAS. Download and print for classroom or home learning activities.
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Step-by-step solution for: Math Worksheets: Order of Operations or PEMDAS
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Show Answer Key & Explanations
Step-by-step solution for: Math Worksheets: Order of Operations or PEMDAS
Let's solve each problem on the Order of Operations Worksheet #4 step by step, following the PEMDAS rule:
> Parentheses
> Exponents
> Multiplication and Division (from left to right)
> Addition and Subtraction (from left to right)
---
- $2^3 = 8$
- $5 \times 8 = 40$
- $8 + 40 = 48$
✔ Answer: 48
---
- $6^3 = 216$
- $1^2 = 1$
- $2 \times 216 = 432$
- $216 \times 1 = 216$
- Now: $432 + 216 + 2 = 650$
✔ Answer: 650
---
- $4 \div 1 = 4$
- $4 \times 1 = 4$
✔ Answer: 4
---
- $6 \times 3 = 18$
- $18 \times 7 = 126$
✔ Answer: 126
---
- $5^2 = 25$
- $6 - 25 = -19$
- $3^3 = 27$
- $27 \times 2 = 54$
- $-19 + 54 = 35$
✔ Answer: 35
---
- Left to right: $1 - 6 = -5$, then $-5 - 3 = -8$
✔ Answer: -8
---
- $5^2 = 25$
- $2^2 = 4$, $1^3 = 1$
- $4 \times 1 \times 5 = 20$
- Now: $25 + 9 + 20 = 54$
✔ Answer: 54
---
- $7^2 = 49$, $49 \div 1 = 49$
- $49 - 8 = 41$
- $7^3 = 343$
- Now: $41 + 343 + 4 = 388$
✔ Answer: 388
---
- $9^2 = 81$
- $81 - 3 = 78$
- $78 + 9 = 87$
✔ Answer: 87
---
- $3^3 = 27$, $27 + 9 = 36$
- $1 + 9 = 10$, $10 - 2 = 8$
- $36 \times 8 = 288$
✔ Answer: 288
---
- $6^2 = 36$, $36 - 6 = 30$
- $30 \times 4 = 120$
- $9 + 9 = 18$
- $18 + 120 = 138$
✔ Answer: 138
---
- $3 - 3 = 0$
- $6^3 = 216$, $216 \div 1 = 216$
- $5 - 0 = 5$
- $5 + 216 = 221$
✔ Answer: 221
---
- $9 - 4 = 5$
- $1 \times 5 = 5$
- $6 + 5 = 11$, $11 + 6 = 17$
✔ Answer: 17
---
- $6 \div 6 = 1$
- $2^2 = 4$, $4 + 8 = 12$
- $1 \times 12 = 12$
- $12 \div 1 = 12$
✔ Answer: 12
---
- $2^2 = 4$
- $4 \times 4 = 16$
- $16 \times 3 = 48$
✔ Answer: 48
---
Check if this is true:
- $1^3 = 1$
- $1 - 6 = -5$
- $-5 \div 5 = -1$
✔ True. Answer: -1 (The equation is correct.)
---
- $2^2 = 4$
- $7 - 4 = 3$
- $3 + 3 = 6$
✔ Answer: 6
---
Check:
- $4^3 = 64$
- $6 + 8 = 14$
- $64 \times 14 = ?$
Calculate:
$64 \times 14 = 64 \times (10 + 4) = 640 + 256 = 896$
✔ True. Answer: 896
---
- $9^2 = 81$
- $81 \div 6 = 13.5$
- $13.5 \times 5 = 67.5$
- $4 \times 67.5 = 270$
✔ Answer: 270
---
- $8^2 = 64$
- $5 \times 64 = 320$
- $320 + 9 = 329$
✔ Answer: 329
---
## ✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 48 |
| 2 | 650 |
| 3 | 4 |
| 4 | 126 |
| 5 | 35 |
| 6 | -8 |
| 7 | 54 |
| 8 | 388 |
| 9 | 87 |
| 10 | 288 |
| 11 | 138 |
| 12 | 221 |
| 13 | 17 |
| 14 | 12 |
| 15 | 48 |
| 16 | -1 |
| 17 | 6 |
| 18 | 896 |
| 19 | 270 |
| 20 | 329 |
---
Let me know if you'd like this in a printable format or need explanations for any specific steps!
> Parentheses
> Exponents
> Multiplication and Division (from left to right)
> Addition and Subtraction (from left to right)
---
1. $ (2^3 + 5 \times 8) $
- $2^3 = 8$
- $5 \times 8 = 40$
- $8 + 40 = 48$
✔ Answer: 48
---
2. $ (2 \times 6^3 + 6^3 \times 1^2 + 2) $
- $6^3 = 216$
- $1^2 = 1$
- $2 \times 216 = 432$
- $216 \times 1 = 216$
- Now: $432 + 216 + 2 = 650$
✔ Answer: 650
---
3. $ (4 \div 1) \times 1 $
- $4 \div 1 = 4$
- $4 \times 1 = 4$
✔ Answer: 4
---
4. $ (6 \times 3) \times 7 $
- $6 \times 3 = 18$
- $18 \times 7 = 126$
✔ Answer: 126
---
5. $ (6 - 5^2) + 3^3 \times 2 $
- $5^2 = 25$
- $6 - 25 = -19$
- $3^3 = 27$
- $27 \times 2 = 54$
- $-19 + 54 = 35$
✔ Answer: 35
---
6. $ (1 - 6 - 3) $
- Left to right: $1 - 6 = -5$, then $-5 - 3 = -8$
✔ Answer: -8
---
7. $ 5^2 + 9 + (2^2 \times 1^3 \times 5) $
- $5^2 = 25$
- $2^2 = 4$, $1^3 = 1$
- $4 \times 1 \times 5 = 20$
- Now: $25 + 9 + 20 = 54$
✔ Answer: 54
---
8. $ (7^2 \div 1 - 8) + 7^3 + 4 $
- $7^2 = 49$, $49 \div 1 = 49$
- $49 - 8 = 41$
- $7^3 = 343$
- Now: $41 + 343 + 4 = 388$
✔ Answer: 388
---
9. $ (9^2 - 3) + 9 $
- $9^2 = 81$
- $81 - 3 = 78$
- $78 + 9 = 87$
✔ Answer: 87
---
10. $ (3^3 + 9) \times (1 + 9 - 2) $
- $3^3 = 27$, $27 + 9 = 36$
- $1 + 9 = 10$, $10 - 2 = 8$
- $36 \times 8 = 288$
✔ Answer: 288
---
11. $ 9 + 9 + (6^2 - 6) \times 4 $
- $6^2 = 36$, $36 - 6 = 30$
- $30 \times 4 = 120$
- $9 + 9 = 18$
- $18 + 120 = 138$
✔ Answer: 138
---
12. $ 5 - (3 - 3) + 6^3 \div 1 $
- $3 - 3 = 0$
- $6^3 = 216$, $216 \div 1 = 216$
- $5 - 0 = 5$
- $5 + 216 = 221$
✔ Answer: 221
---
13. $ 6 + 1 \times (9 - 4) + 6 $
- $9 - 4 = 5$
- $1 \times 5 = 5$
- $6 + 5 = 11$, $11 + 6 = 17$
✔ Answer: 17
---
14. $ (6 \div 6) \times (2^2 + 8) \div 1 $
- $6 \div 6 = 1$
- $2^2 = 4$, $4 + 8 = 12$
- $1 \times 12 = 12$
- $12 \div 1 = 12$
✔ Answer: 12
---
15. $ (2^2 \times 4 \times 3) $
- $2^2 = 4$
- $4 \times 4 = 16$
- $16 \times 3 = 48$
✔ Answer: 48
---
16. $ (1^3 - 6) \div 5 = -1 $
Check if this is true:
- $1^3 = 1$
- $1 - 6 = -5$
- $-5 \div 5 = -1$
✔ True. Answer: -1 (The equation is correct.)
---
17. $ (7 - 2^2 + 3) $
- $2^2 = 4$
- $7 - 4 = 3$
- $3 + 3 = 6$
✔ Answer: 6
---
18. $ 4^3 \times (6 + 8) \div 1 = 896 $
Check:
- $4^3 = 64$
- $6 + 8 = 14$
- $64 \times 14 = ?$
Calculate:
$64 \times 14 = 64 \times (10 + 4) = 640 + 256 = 896$
✔ True. Answer: 896
---
19. $ 4 \times (9^2 \div 6 \times 5) $
- $9^2 = 81$
- $81 \div 6 = 13.5$
- $13.5 \times 5 = 67.5$
- $4 \times 67.5 = 270$
✔ Answer: 270
---
20. $ (5 \times 8^2) + 9 $
- $8^2 = 64$
- $5 \times 64 = 320$
- $320 + 9 = 329$
✔ Answer: 329
---
## ✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 48 |
| 2 | 650 |
| 3 | 4 |
| 4 | 126 |
| 5 | 35 |
| 6 | -8 |
| 7 | 54 |
| 8 | 388 |
| 9 | 87 |
| 10 | 288 |
| 11 | 138 |
| 12 | 221 |
| 13 | 17 |
| 14 | 12 |
| 15 | 48 |
| 16 | -1 |
| 17 | 6 |
| 18 | 896 |
| 19 | 270 |
| 20 | 329 |
---
Let me know if you'd like this in a printable format or need explanations for any specific steps!
Parent Tip: Review the logic above to help your child master the concept of order of operations exponents worksheet.
