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Questions and Answers
What is the correct order of operations in evaluating an expression?
What is the correct order of operations in evaluating an expression?
- Parentheses, Exponents, Addition, Subtraction, Multiplication and Division
- Exponents, Parentheses, Addition, Multiplication, Division
- Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (correct)
- Multiplication, Addition, Division, Exponents, Parentheses
If you have the expression $3 + -5 - 2$, what is the first step according to the order of operations?
If you have the expression $3 + -5 - 2$, what is the first step according to the order of operations?
- Calculate $-5 - 2$
- Perform no operation as it is only addition and subtraction
- Calculate $3 + -5$ (correct)
- Convert $-5$ to $+5$ before calculation
In the expression $2 - 3 + 4$, what operation is performed first?
In the expression $2 - 3 + 4$, what operation is performed first?
- Addition, then Subtraction
- Both operations at the same time
- Evaluate Parentheses first (if any)
- Subtraction, then Addition (correct)
How would you evaluate $-5 - -8$ using addition?
How would you evaluate $-5 - -8$ using addition?
When adding $7 + -2$, what is the resultant sign of the answer?
When adding $7 + -2$, what is the resultant sign of the answer?
If you misapply the order of operations and evaluate $2 + 3 imes 4$ incorrectly as $(2 + 3) imes 4$, what result do you get?
If you misapply the order of operations and evaluate $2 + 3 imes 4$ incorrectly as $(2 + 3) imes 4$, what result do you get?
What is the sum of the integers $-6 + -2$?
What is the sum of the integers $-6 + -2$?
What common mistake occurs with the operation $7 - 5 + 4$?
What common mistake occurs with the operation $7 - 5 + 4$?
When simplifying the expression $4 imes (2 + 3)$, what is the first step?
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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