This worksheet focuses on solidifying your understanding of the order of operations, often remembered by the acronym PEMDAS/BODMAS, when working with integers. We'll cover the basics and then delve into more complex examples to ensure you're comfortable tackling any problem. Remember, mastering this is crucial for success in algebra and beyond!
What is the Order of Operations?
The order of operations dictates the sequence in which you perform calculations within a mathematical expression. It ensures everyone arrives at the same answer, regardless of their approach. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) helps us remember the order:
- Parentheses/Brackets: Solve any expressions inside parentheses or brackets first.
- Exponents/Orders: Calculate any exponents (powers) or roots.
- Multiplication and Division: Perform multiplication and division from left to right. They have equal precedence.
- Addition and Subtraction: Perform addition and subtraction from left to right. They also have equal precedence.
Let's illustrate with some examples:
Example Problems and Solutions
Example 1: -5 + 3 * 2 - (4 + 1)
- Parentheses: 4 + 1 = 5. The expression becomes: -5 + 3 * 2 - 5
- Multiplication: 3 * 2 = 6. The expression becomes: -5 + 6 - 5
- Addition and Subtraction (left to right): -5 + 6 = 1; 1 - 5 = -4
Therefore, the answer is -4.
Example 2: 10 ÷ 2 + 3² - (-2) * 4
- Exponents: 3² = 9. The expression becomes: 10 ÷ 2 + 9 - (-2) * 4
- Division and Multiplication (left to right): 10 ÷ 2 = 5; (-2) * 4 = -8. The expression becomes: 5 + 9 - (-8)
- Addition and Subtraction (left to right): 5 + 9 = 14; 14 - (-8) = 14 + 8 = 22
Therefore, the answer is 22.
Frequently Asked Questions (FAQs)
What if I have multiple sets of parentheses?
Work from the innermost parentheses outwards. Solve the expressions within the innermost parentheses first, then the next set, and so on.
Does it matter if I do multiplication before division or addition before subtraction?
No, multiplication and division have the same precedence, as do addition and subtraction. Perform these operations from left to right within the expression.
How do negative signs affect the order of operations?
Negative signs are treated as part of the number. For example, in -2 * 4, the negative sign is part of the -2. Apply the order of operations as usual.
What if I have a mix of positive and negative integers?
Follow the rules for integers during each step of the order of operations. Remember the rules for adding, subtracting, multiplying, and dividing integers.
Can you provide more practice problems?
Practice Problems:
- -8 + 4 * (-2) - 6 ÷ 2
- (5 - 9)³ + 12 ÷ (-3) * 2
- -10 + 20 ÷ (-5) + 7 * (-2) - 4
- (-3)² + 5 * (-2) - (1 - 4)
- 15 ÷ 3 + 6 * (-2) + (-1)
Solutions (Check your answers!):
- -16
- -32
- -31
- -3
- -5
By working through these examples and practice problems, you'll build confidence and mastery of the order of operations with integers. Remember to take your time, break down each problem step-by-step, and double-check your work. Good luck!
