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Questions and Answers
What is the result of the operation $3 + 7$?
What is the result of the operation $3 + 7$?
- $11$
- $10$ (correct)
- $12$
- $9$
Which property states that the order of addition does not affect the sum?
Which property states that the order of addition does not affect the sum?
- Commutative Property (correct)
- Identity Property
- Associative Property
- Distributive Property
Which statement about subtraction is true?
Which statement about subtraction is true?
- Subtraction is associative.
- The result of subtraction depends on the order of operations. (correct)
- Subtraction can yield a larger result than its terms.
- Subtraction is commutative.
What is the identity property of subtraction?
What is the identity property of subtraction?
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If $10 - (2 - 3)$ is calculated, what is the result?
If $10 - (2 - 3)$ is calculated, what is the result?
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Which of the following describes how the result of addition compares to its operands?
Which of the following describes how the result of addition compares to its operands?
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Study Notes
Addition
- Definition: Combining two or more numbers to get a total.
- Notation: Represented by the symbol
+. - Properties:
- Commutative Property: a + b = b + a (order does not matter).
- Associative Property: (a + b) + c = a + (b + c) (grouping does not matter).
- Identity Property: a + 0 = a (adding zero does not change the number).
- Example:
- 3 + 5 = 8
- 2 + (4 + 6) = 2 + 10 = 12
Subtraction
- Definition: Taking one number away from another.
- Notation: Represented by the symbol
-. - Properties:
- Not Commutative: a - b ≠b - a (order matters).
- Not Associative: (a - b) - c ≠a - (b - c) (grouping matters).
- Identity Property: a - 0 = a (subtracting zero does not change the number).
- Example:
- 8 - 3 = 5
- 10 - (4 - 2) = 10 - 2 = 8
Key Differences
- Operation:
- Addition combines values.
- Subtraction removes values.
- Result:
- Addition results in a larger or equal number.
- Subtraction results in a smaller or equal number.
Addition
- Definition: The process of combining two or more numbers to yield a total.
- Symbol: Represented by the
+sign. - Commutative Property: The order of numbers does not affect the sum; e.g., a + b = b + a.
- Associative Property: The way numbers are grouped does not change the sum; e.g., (a + b) + c = a + (b + c).
- Identity Property: Adding zero to a number leaves it unchanged; e.g., a + 0 = a.
- Examples:
- Simple addition: 3 + 5 = 8.
- Grouping example: 2 + (4 + 6) simplifies to 2 + 10 = 12.
Subtraction
- Definition: The process of taking one number away from another.
- Symbol: Represented by the
-sign. - Non-Commutative: The order of numbers matters; a - b ≠b - a.
- Non-Associative: The way numbers are grouped affects the result; (a - b) - c ≠a - (b - c).
- Identity Property: Subtracting zero from a number does not change it; e.g., a - 0 = a.
- Examples:
- Simple subtraction: 8 - 3 = 5.
- Grouping example: 10 - (4 - 2) simplifies to 10 - 2 = 8.
Key Differences
- Operation Nature:
- Addition is a process of combining values.
- Subtraction is a process of removing values.
- Result Implications:
- Addition generally yields a larger or equal result.
- Subtraction results in a smaller or equal outcome.
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