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Questions and Answers
What is the correct order of operations in evaluating an expression?
If you have the expression $3 + -5 - 2$, what is the first step according to the order of operations?
In the expression $2 - 3 + 4$, what operation is performed first?
How would you evaluate $-5 - -8$ using addition?
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When adding $7 + -2$, what is the resultant sign of the answer?
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If you misapply the order of operations and evaluate $2 + 3 imes 4$ incorrectly as $(2 + 3) imes 4$, what result do you get?
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What is the sum of the integers $-6 + -2$?
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What common mistake occurs with the operation $7 - 5 + 4$?
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When simplifying the expression $4 imes (2 + 3)$, what is the first step?
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Study Notes
Adding and Subtracting Integers: Order of Operations
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Order of Operations: The rules that dictate the correct sequence to evaluate a mathematical expression. It is often remembered by the acronym PEMDAS:
- P: Parentheses
- E: Exponents (powers and square roots, etc.)
- MD: Multiplication and Division (from left to right)
- AS: Addition and Subtraction (from left to right)
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Steps for Adding and Subtracting Integers:
- Identify Operations: Look for parentheses and evaluate those first.
- Evaluate Exponents: Resolve any exponents next.
- Multiplication and Division: Process from left to right.
- Addition and Subtraction: Finally, perform addition and subtraction from left to right.
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Working with Integers:
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Adding Two Positive Integers: Sum is positive (e.g., 3 + 4 = 7).
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Adding Two Negative Integers: Sum is negative (e.g., -3 + -4 = -7).
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Adding a Positive and a Negative Integer:
- If the positive integer has a greater absolute value, the result is positive (e.g., 5 + -3 = 2).
- If the negative integer has a greater absolute value, the result is negative (e.g., -7 + 4 = -3).
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Subtracting Integers: Convert subtraction into addition by adding the opposite.
- Example: 5 - 3 → 5 + (-3) = 2
- Example: -4 - -3 → -4 + 3 = -1
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Practical Tips:
- Keep track of signs when adding and subtracting.
- Double-check calculations, especially when dealing with negative integers.
- Use a number line for visualization if needed.
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Common Mistakes:
- Neglecting to change the signs when converting subtraction to addition.
- Misapplying order of operations by not evaluating parentheses first.
Understanding and applying the order of operations is crucial for solving expressions involving integers accurately.
Order of Operations (PEMDAS)
- Parentheses are evaluated first.
- Exponents are evaluated next.
- Multiplication and Division are done from left to right.
- Addition and Subtraction are done from left to right.
Adding Integers
- Adding two positive integers always results in a positive sum.
- Adding two negative integers always results in a negative sum.
- Adding a positive and a negative integer:
- If the positive integer has a larger absolute value, the sum is positive.
- If the negative integer has a larger absolute value, the sum is negative.
Subtracting Integers
- Subtraction can be converted into addition by adding the opposite of the subtrahend.
- Example: 5 - 3 is the same as 5 + (-3)
- Example: -4 - (-3) is the same as -4 + 3
Common Mistakes
- Forgetting to change the sign when converting subtraction to addition.
- Not evaluating expressions within parentheses first.
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Description
This quiz focuses on the rules for adding and subtracting integers, emphasizing the order of operations known by the acronym PEMDAS. Test your understanding of how to properly evaluate mathematical expressions using integers and the steps involved. Ensure you grasp the processes for different integer combinations.
