order of operations with integers worksheet

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23-11-2024

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Meta Description: Conquer integer operations! This guide provides a comprehensive worksheet on the order of operations (PEMDAS/BODMAS) with integers, complete with examples, practice problems, and solutions. Master simplifying expressions and avoid common pitfalls. Perfect for students and anyone needing a refresher!

Understanding the Order of Operations (PEMDAS/BODMAS)

The order of operations, often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), dictates the sequence in which we solve mathematical expressions. This is crucial, especially when working with integers (positive and negative whole numbers). Ignoring the order of operations will almost always lead to incorrect answers.

PEMDAS/BODMAS Explained

• Parentheses/Brackets: Always solve the expressions within parentheses or brackets first. Work from the innermost set outwards.
• Exponents/Orders: Next, calculate any exponents (powers) or roots.
• Multiplication and Division: Perform multiplication and division from left to right. They have equal precedence.
• Addition and Subtraction: Finally, perform addition and subtraction from left to right. They also have equal precedence.

Working with Integers: Key Reminders

When dealing with integers within the order of operations, remember these key points:

• Sign Rules: Pay close attention to the rules for adding, subtracting, multiplying, and dividing integers. Remember that:

  • A negative times a negative equals a positive.
  • A negative times a positive equals a negative.
  • Subtracting a negative is the same as adding a positive.

• Careful Calculation: Take your time and be meticulous with each step. Errors in one step will cascade through the entire calculation.

• Use of Parentheses: Parentheses can clarify the order of operations and help avoid mistakes.

Practice Worksheet: Order of Operations with Integers

Here are some practice problems to help you solidify your understanding. Remember to follow PEMDAS/BODMAS carefully!

Level 1: Basic Problems

1. -5 + 2 × 3
2. (10 - 4) ÷ 2 + (-3)
3. -8 × (-2) + 6 ÷ 3
4. 15 ÷ (-5) - 4 + (-2) × 6
5. (-3)³ + 12 - 4 × (-2)

Level 2: Intermediate Problems

1. -2 × [(5 + (-3)) ÷ (-1) + 4]
2. (-4)² - 3 × (-5) + (-10) ÷ 5
3. [(-2) + 6] ÷ 2 × (-4) - 7
4. 12 - [5 + (-2) × 4] ÷ 6
5. (-3) × (4 - 7)² + 5

Level 3: Advanced Problems

1. -5 + 2 × [(-3)³ + 4] ÷ (-2)
2. [(10 ÷ (-5) + 2) × (-3)]² + (-6)
3. (-2)³ + 5 × (4 - 8) ÷ (-2) + (-1)²
4. [(-6 + 9) ÷ 3 × (-2)] - (-8 ÷ 4 + 2)
5. -4 × [2² + (-3) × (-2 + 5)] + (-10) ÷ 5

Solutions to the Practice Worksheet

Level 1 Solutions:

1. 1
2. 1
3. 16
4. -17
5. -17

Level 2 Solutions:

1. -10
2. 21
3. -19
4. 9
5. 32

Level 3 Solutions:

1. 21
2. 6
3. -4
4. -2
5. -38

Tips for Success

• Break it Down: If an equation seems overwhelming, break it down into smaller, manageable steps.
• Check Your Work: After completing a problem, review your calculations to catch potential errors.
• Practice Regularly: Consistent practice will build your skills and confidence.

By consistently following the order of operations (PEMDAS/BODMAS) and understanding the rules of integer arithmetic, you'll successfully navigate any expression involving integers! Remember to practice, practice, practice! Mastering these concepts is key to success in algebra and beyond.