Let’s solve each problem step by step using PEMDAS:
Parentheses →
Exponents →
Multiplication &
Division (left to right) →
Addition &
Subtraction (left to right)
---
1) (12 ÷ 2) × 5² - 8
- Parentheses first: 12 ÷ 2 = 6
- Exponent: 5² = 25
- Multiply: 6 × 25 = 150
- Subtract: 150 - 8 =
142
✔ Final Answer for #1:
142
---
2) (4³ ÷ 2) × 6 - 3
- Exponent inside parentheses: 4³ = 64
- Division inside parentheses: 64 ÷ 2 = 32
- Multiply: 32 × 6 = 192
- Subtract: 192 - 3 =
189
✔ Final Answer for #2:
189
---
3) 9 × [(-3) + 4 - (-2)²]
- First, handle exponent inside brackets: (-2)² = 4
- Now inside brackets: (-3) + 4 - 4
- (-3) + 4 = 1
- 1 - 4 = -3
- Multiply: 9 × (-3) =
-27
✔ Final Answer for #3:
-27
---
4) (14² × 15) - (2² + 20)
- Left side: 14² = 196; 196 × 15 = let's compute:
- 200 × 15 = 3000, minus 4×15=60 → 3000 - 60 = 2940
- Right side: 2² = 4; 4 + 20 = 24
- Subtract: 2940 - 24 =
2916
✔ Final Answer for #4:
2916
---
5) 4² + (8 - 2)² ÷ 4
- Exponents and parentheses first:
- 4² = 16
- (8 - 2) = 6 → 6² = 36
- Division: 36 ÷ 4 = 9
- Addition: 16 + 9 =
25
✔ Final Answer for #5:
25
---
6) (15² - 9) × 2 - 15
- Exponent: 15² = 225
- Inside parentheses: 225 - 9 = 216
- Multiply: 216 × 2 = 432
- Subtract: 432 - 15 =
417
✔ Final Answer for #6:
417
---
7) (6² + 4) ÷ (18 - 14)
- Left parentheses: 6² = 36; 36 + 4 = 40
- Right parentheses: 18 - 14 = 4
- Divide: 40 ÷ 4 =
10
✔ Final Answer for #7:
10
---
8) (6² + 18 - 8) ÷ 2
- Exponent: 6² = 36
- Inside parentheses: 36 + 18 = 54; 54 - 8 = 46
- Divide: 46 ÷ 2 =
23
✔ Final Answer for #8:
23
---
Final Answer:
1) 142
2) 189
3) -27
4) 2916
5) 25
6) 417
7) 10
8) 23
Parent Tip: Review the logic above to help your child master the concept of order of operations worksheet 6th grade.
