Let's solve each problem step by step using the
order of operations, often remembered by the acronym
PEMDAS:
-
Parentheses
-
Exponents (and roots)
-
Multiplication and
Division (from left to right)
-
Addition and
Subtraction (from left to right)
---
1. $ 8 + (12 - 3) = $
- First, solve inside parentheses: $ 12 - 3 = 9 $
- Then add: $ 8 + 9 = 17 $
✔ Answer: 17
---
2. $ (12 ÷ 3) × 8 + 2 = $
- Parentheses first: $ 12 ÷ 3 = 4 $
- Then multiplication: $ 4 × 8 = 32 $
- Then addition: $ 32 + 2 = 34 $
✔ Answer: 34
---
3. $ (15 - 9) × 3 - 2 = $
- Parentheses: $ 15 - 9 = 6 $
- Multiplication: $ 6 × 3 = 18 $
- Subtraction: $ 18 - 2 = 16 $
✔ Answer: 16
---
4. $ 11 × 3 - 4^2 = $
- Exponent first: $ 4^2 = 16 $
- Multiplication: $ 11 × 3 = 33 $
- Subtraction: $ 33 - 16 = 17 $
✔ Answer: 17
---
5. $ 5^2 ÷ (12 - 7) = $
- Exponent: $ 5^2 = 25 $
- Parentheses: $ 12 - 7 = 5 $
- Division: $ 25 ÷ 5 = 5 $
✔ Answer: 5
---
6. $ 2^3 - (4 + 2) = $
- Exponent: $ 2^3 = 8 $
- Parentheses: $ 4 + 2 = 6 $
- Subtraction: $ 8 - 6 = 2 $
✔ Answer: 2
---
7. $ (6 × 3) - 4^2 = $
- Parentheses: $ 6 × 3 = 18 $
- Exponent: $ 4^2 = 16 $
- Subtraction: $ 18 - 16 = 2 $
✔ Answer: 2
---
8. $ 7 × 3 ÷ 3 = $
- Left to right: $ 7 × 3 = 21 $
- Then divide: $ 21 ÷ 3 = 7 $
✔ Answer: 7
---
9. $ (2 × 5^2) - (19 - 7) = $
- Exponent: $ 5^2 = 25 $
- Multiplication: $ 2 × 25 = 50 $
- Parentheses: $ 19 - 7 = 12 $
- Subtraction: $ 50 - 12 = 38 $
✔ Answer: 38
---
10. $ 10^2 - \sqrt{81} = $
- Exponent: $ 10^2 = 100 $
- Square root: $ \sqrt{81} = 9 $
- Subtraction: $ 100 - 9 = 91 $
✔ Answer: 91
---
11. $ 12 ÷ \sqrt{16} + 11 = $
- Square root: $ \sqrt{16} = 4 $
- Division: $ 12 ÷ 4 = 3 $
- Addition: $ 3 + 11 = 14 $
✔ Answer: 14
---
12. $ (10 + \sqrt{64}) - 3 = $
- Square root: $ \sqrt{64} = 8 $
- Parentheses: $ 10 + 8 = 18 $
- Subtraction: $ 18 - 3 = 15 $
✔ Answer: 15
---
✔ Final Answers:
1. 17
2. 34
3. 16
4. 17
5. 5
6. 2
7. 2
8. 7
9. 38
10. 91
11. 14
12. 15
Let me know if you'd like this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of whole number worksheet.
