I'll solve each of these order of operations problems step by step, following PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Problem 1: 5 × (6 + 4) - 4²
- First: Parentheses → (6 + 4) = 10
- Second: Exponents → 4² = 16
- Third: Multiplication → 5 × 10 = 50
- Fourth: Subtraction → 50 - 16 = 34
Problem 2: (7 - 2)² + (16 ÷ 8)
- First: Parentheses → (7 - 2) = 5 and (16 ÷ 8) = 2
- Second: Exponents → 5² = 25
- Third: Addition → 25 + 2 = 27
Problem 3: (12 - 9)² + (8 ÷ 4)
- First: Parentheses → (12 - 9) = 3 and (8 ÷ 4) = 2
- Second: Exponents → 3² = 9
- Third: Addition → 9 + 2 = 11
Problem 4: (20 - 4²) ÷ (10 - 6)
- First: Inside first parentheses, do exponent first → 4² = 16, then 20 - 16 = 4
- Second: Second parentheses → (10 - 6) = 4
- Third: Division → 4 ÷ 4 = 1
Problem 5: (64 - 2²) ÷ (17 + 3)
- First: Inside first parentheses, do exponent first → 2² = 4, then 64 - 4 = 60
- Second: Second parentheses → (17 + 3) = 20
- Third: Division → 60 ÷ 20 = 3
Problem 6: (32 - 2) ÷ 5 - 2²
- First: Parentheses → (32 - 2) = 30
- Second: Exponents → 2² = 4
- Third: Division → 30 ÷ 5 = 6
- Fourth: Subtraction → 6 - 4 = 2
Final Answer:
1. 34
2. 27
3. 11
4. 1
5. 3
6. 2
Parent Tip: Review the logic above to help your child master the concept of order of operations with exponents worksheet.
