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Questions and Answers
What is the definition of Additive Identity?
What is the definition of Additive Identity?
What is the concept of Additive Inverse?
What is the concept of Additive Inverse?
a + (-a) = 0
Which property states that a * 1 = a?
Which property states that a * 1 = a?
Define the Multiplicative Inverse.
Define the Multiplicative Inverse.
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What does the Multiplicative Property of Zero state?
What does the Multiplicative Property of Zero state?
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The Reflexive Property states that a quantity can be greater than itself.
The Reflexive Property states that a quantity can be greater than itself.
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Describe the Symmetric Property.
Describe the Symmetric Property.
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What is the Transitive Property?
What is the Transitive Property?
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Explain the Substitution Property.
Explain the Substitution Property.
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Which property shows that a + b = b + a?
Which property shows that a + b = b + a?
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What is the Commutative Property of Multiplication?
What is the Commutative Property of Multiplication?
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What does the Associative Property of Addition express?
What does the Associative Property of Addition express?
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Explain the Associative Property of Multiplication.
Explain the Associative Property of Multiplication.
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What is the Distributive Property?
What is the Distributive Property?
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Study Notes
Additive Properties
- Additive Identity: Adding zero to any number does not change the value (a + 0 = a).
- Additive Inverse: The sum of a number and its negative is zero (a + (-a) = 0).
Multiplicative Properties
- Multiplicative Identity: Multiplying any number by one leaves the number unchanged (a × 1 = a).
- Multiplicative Inverse: The product of a number and its reciprocal equals one (a/b × b/a = 1), given b ≠ 0.
- Multiplicative Property of Zero: Any number multiplied by zero equals zero (a × 0 = 0).
Properties of Equality
- Reflexive Property: Any number is equal to itself (a = a).
- Symmetric Property: If one number equals another, then the second number equals the first (if a = b, then b = a).
- Transitive Property: If one number equals a second, and that second equals a third, then the first equals the third (if a = b and b = c, then a = c).
- Substitution Property: If two quantities are equal, one can be replaced with the other in any expression (if a = b, a can be replaced by b).
Commutative Properties
- Commutative Property of Addition: The order of addition does not affect the sum (a + b = b + a).
- Commutative Property of Multiplication: The order of multiplication does not affect the product (a × b = b × a).
Associative Properties
- Associative Property of Addition: Rearranging the grouping of numbers in addition does not affect the sum ((a + b) + c = a + (b + c)).
- Associative Property of Multiplication: Rearranging the grouping of numbers in multiplication does not affect the product ((a × b) × c = a × (b × c)).
Distributive Property
- Distributive Property: Multiplication distributes over addition and subtraction (a × (b + c) = a × b + a × c and a × (b - c) = a × b - a × c).
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Description
Test your understanding of key algebraic properties with these flashcards. Learn the definitions of additive and multiplicative identities and inverses that are fundamental to Algebra. Perfect for students looking to reinforce their knowledge in Algebra 1.
