We are given a worksheet titled “Order of Operations (C)” with six expressions to simplify using the correct order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right).
Let’s solve each one step by step.
---
Problem 1:
(4² − 7 + (−9))³ ÷ (2 × 8)
Step 1: Evaluate inside parentheses.
- 4² = 16
- So inside first parentheses: 16 − 7 + (−9) = 9 − 9 = 0
- Now we have: (0)³ ÷ (2 × 8)
Step 2: Exponent and multiplication:
- 0³ = 0
- 2 × 8 = 16
Step 3: Division:
- 0 ÷ 16 =
0
✔ Answer: 0
---
Problem 2:
((−2) − 2²) × ((−3) + (−5)) ÷ ((−9) + 6)
Step 1: Evaluate exponents and innermost parentheses.
- 2² = 4 → so (−2) − 4 = −6
- (−3) + (−5) = −8
- (−9) + 6 = −3
Now expression is:
(−6) × (−8) ÷ (−3)
Step 2: Multiply and divide left to right.
- (−6) × (−8) = 48
- 48 ÷ (−3) =
−16
✔ Answer: −16
---
Problem 3:
(10 ÷ ((−7) − (−8))) × (−10) + 8² + (−5)
Step 1: Innermost parentheses:
- (−7) − (−8) = −7 + 8 = 1
→ So: 10 ÷ 1 = 10
Expression becomes:
10 × (−10) + 8² + (−5)
Step 2: Exponent:
- 8² = 64
Expression:
10 × (−10) + 64 + (−5)
Step 3: Multiplication:
- 10 × (−10) = −100
Expression:
−100 + 64 + (−5)
Step 4: Left to right addition/subtraction:
- −100 + 64 = −36
- −36 + (−5) =
−41
✔ Answer: −41
---
Problem 4:
(((−9) + 9) × 3) ÷ (8 − 5)³ ÷ 4
Step 1: Innermost parentheses:
- (−9) + 9 = 0 → so 0 × 3 = 0
- (8 − 5) = 3 → 3³ = 27
Expression becomes:
0 ÷ 27 ÷ 4
Step 2: Division left to right:
- 0 ÷ 27 = 0
- 0 ÷ 4 =
0
✔ Answer: 0
---
Problem 5:
(6 + (−5)) ÷ (8 − 7) × (−3) + (−9)²
Step 1: Parentheses:
- 6 + (−5) = 1
- 8 − 7 = 1
- (−9)² = 81
Expression becomes:
1 ÷ 1 × (−3) + 81
Step 2: Division and multiplication left to right:
- 1 ÷ 1 = 1
- 1 × (−3) = −3
Expression:
−3 + 81 = 78
✔ Answer: 78
---
Problem 6:
((−6) × (10 − 2 + (−8)))³ ÷ 8²
Step 1: Inside innermost parentheses:
- 10 − 2 + (−8) = 8 + (−8) = 0
Expression becomes:
((−6) × 0)³ ÷ 8²
Step 2: Multiply:
- (−6) × 0 = 0 → 0³ = 0
Step 3: Denominator:
- 8² = 64
Final:
0 ÷ 64 = 0
✔ Answer: 0
---
##
✔ Final Answers:
1.
0
2.
−16
3.
−41
4.
0
5.
78
6.
0
These were solved using PEMDAS/BODMAS rules carefully, handling negative numbers and exponents correctly.
Parent Tip: Review the logic above to help your child master the concept of operations on integers worksheet.
