Warm Up: Algebraic Properties

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What is the Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

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What is the Commutative Property of Addition?

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The Commutative Property of Addition states that changing the order of the addends does not change the sum, i.e., a + b = b + a.

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What is the Commutative Property of Multiplication?

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The Commutative Property of Multiplication states that changing the order of the factors does not change the product, i.e., a × b = b × a.

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What is the Associative Property of Addition?

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The Associative Property of Addition states that the way in which numbers are grouped does not change their sum, i.e., (a + b) + c = a + (b + c).

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What is the Associative Property of Multiplication?

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The Associative Property of Multiplication states that the way in which numbers are grouped does not change their product, i.e., (a × b) × c = a × (b × c).

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How does the Distributive Property apply to subtraction?

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The Distributive Property can also apply to subtraction, such that a(b - c) = ab - ac.

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Can you give an example of the Distributive Property in action?

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For example, 3(4 + 5) = 3×4 + 3×5, which simplifies to 12 + 15 = 27.

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What is the identity property of addition?

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The identity property of addition states that adding zero to any number does not change the number, i.e., a + 0 = a.

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What is the identity property of multiplication?

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The identity property of multiplication states that multiplying any number by one does not change the number, i.e., a × 1 = a.

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What is the inverse property of addition?

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The inverse property of addition states that for every number a, there exists a number -a such that a + (-a) = 0.