Understanding the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction), is crucial for accurate mathematical calculations. This worksheet focuses on applying these rules specifically with integers, which include both positive and negative whole numbers. Mastering this skill is essential for algebra and beyond.
What are Integers?
Integers are whole numbers, including zero, and their negative counterparts. Examples include -3, -2, -1, 0, 1, 2, 3, and so on. Understanding how to work with negative numbers is key to correctly solving equations involving the order of operations. Remember that a negative number multiplied by a negative number results in a positive number, while a negative number multiplied by a positive number results in a negative number. The same rules apply to division.
The PEMDAS/BODMAS Order of Operations
Let's recap the order of operations:
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Parentheses/Brackets: Always solve expressions within parentheses or brackets first. Work from the innermost set outwards.
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Exponents/Orders: Calculate any exponents (powers) or roots next.
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Multiplication and Division: Perform multiplication and division from left to right. These operations have equal precedence.
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Addition and Subtraction: Finally, perform addition and subtraction from left to right. These operations also have equal precedence.
Practice Problems: Order of Operations with Integers
Let's put this into practice with some example problems: Remember to show your work step-by-step!
Problem 1: -5 + 2 * (-3)
Solution:
- Multiplication first: 2 * (-3) = -6
- Addition: -5 + (-6) = -11
Answer: -11
Problem 2: (4 - 8) / 2 + (-6) * 3
Solution:
- Parentheses first: (4 - 8) = -4
- Division: -4 / 2 = -2
- Multiplication: (-6) * 3 = -18
- Addition: -2 + (-18) = -20
Answer: -20
Problem 3: -2² + 5 * (-1) - 10 ÷ (-5)
Solution:
- Exponents: -2² = -4 (Note: This is -1 * 2² = -4. (-2)² = 4)
- Multiplication: 5 * (-1) = -5
- Division: -10 ÷ (-5) = 2
- Addition and Subtraction (left to right): -4 + (-5) = -9; -9 + 2 = -7
Answer: -7
Problem 4: 12 ÷ (-3) * 2 + 7 - (-4)
Solution:
- Division: 12 ÷ (-3) = -4
- Multiplication: -4 * 2 = -8
- Addition: -8 + 7 = -1
- Subtraction: -1 - (-4) = 3
Answer: 3
Frequently Asked Questions (FAQs)
What happens if there are multiple sets of parentheses?
Work from the innermost parentheses outwards. Solve the expressions inside the innermost parentheses first, then move to the next level of parentheses, and so on.
Does it matter if I do multiplication before division or addition before subtraction?
No, multiplication and division have equal precedence, so you perform them from left to right. The same applies to addition and subtraction.
How do I handle negative numbers with exponents?
Be careful! The exponent only applies to the base number immediately preceding it. For example, -2² is -(2²) = -4, while (-2)² = 4.
What if I forget the order of operations?
Forgetting the order can lead to incorrect answers. It's crucial to memorize and consistently apply PEMDAS/BODMAS to ensure accuracy in your calculations. Regular practice is key!
This worksheet provides a solid foundation for understanding and applying the order of operations with integers. Consistent practice is key to mastering this essential mathematical skill. Remember to always show your work step-by-step to avoid errors.