Absolutely! Let’s solve each problem step by step using the
Order of Operations — often remembered by the acronym
PEMDAS:
>
Parentheses
>
Exponents
>
Multiplication and
Division (left to right)
>
Addition and
Subtraction (left to right)
---
🔢 Problem 1: `(14 + 7 + 9) × 12`
-
Parentheses first: `14 + 7 + 9 = 30`
- Then multiply: `30 × 12 = 360`
✔ Answer: 360
---
🔢 Problem 2: `(7² × 7) × 7`
-
Exponent first: `7² = 49`
- Multiply inside parentheses: `49 × 7 = 343`
- Then multiply by 7: `343 × 7 = 2401`
✔ Answer: 2401
*(Note: You could also think of this as 7³ × 7 = 7⁴ = 2401)*
---
🔢 Problem 3: `15 + 18 × (7 + 3²)`
-
Exponent: `3² = 9`
-
Parentheses: `7 + 9 = 16`
-
Multiplication: `18 × 16 = 288`
-
Addition: `15 + 288 = 303`
✔ Answer: 303
---
🔢 Problem 4: `(7 × 9) ÷ 7 + 8`
-
Parentheses: `7 × 9 = 63`
-
Division: `63 ÷ 7 = 9`
-
Addition: `9 + 8 = 17`
✔ Answer: 17
---
🔢 Problem 5: `45 ÷ 9 + (15 × 2²)`
-
Exponent: `2² = 4`
-
Parentheses: `15 × 4 = 60`
-
Division: `45 ÷ 9 = 5`
-
Addition: `5 + 60 = 65`
✔ Answer: 65
---
🔢 Problem 6: `68 ÷ (4² + 1)`
-
Exponent: `4² = 16`
-
Parentheses: `16 + 1 = 17`
-
Division: `68 ÷ 17 = 4`
✔ Answer: 4
---
🔢 Problem 7: `(30 × 5 + 3) ÷ 3`
-
Multiplication inside parentheses: `30 × 5 = 150`
-
Addition: `150 + 3 = 153`
-
Division: `153 ÷ 3 = 51`
✔ Answer: 51
---
🔢 Problem 8: `60 ÷ 10 × (17 + 24)`
-
Parentheses: `17 + 24 = 41`
-
Left to right: `60 ÷ 10 = 6`, then `6 × 41 = 246`
✔ Answer: 246
---
🔢 Problem 9: `3³ + (3 + 8)`
-
Exponent: `3³ = 27`
-
Parentheses: `3 + 8 = 11`
-
Addition: `27 + 11 = 38`
✔ Answer: 38
---
🔢 Problem 10: `(4 + 3 + 3)`
- Just add: `4 + 3 + 3 = 10`
✔ Answer: 10
---
🔢 Problem 11: `6 + (6 + 6²) × 2`
-
Exponent: `6² = 36`
-
Parentheses: `6 + 36 = 42`
-
Multiplication: `42 × 2 = 84`
-
Addition: `6 + 84 = 90`
✔ Answer: 90
---
🔢 Problem 12: `(6 + 3 × 5) + 4²`
-
Multiplication inside parentheses: `3 × 5 = 15`
-
Parentheses: `6 + 15 = 21`
-
Exponent: `4² = 16`
-
Addition: `21 + 16 = 37`
✔ Answer: 37
---
##
✔ Final Answers (Left to Right, Top to Bottom):
1.
360
2.
2401
3.
303
4.
17
5.
65
6.
4
7.
51
8.
246
9.
38
10.
10
11.
90
12.
37
Let me know if you’d like a printable version or to check your work! 😊
Parent Tip: Review the logic above to help your child master the concept of pemdas worksheet pdf.
