Algebraic Properties

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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. For example, 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. For example, 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 the sum. For example, (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 the product. For example, (a × b) × c = a × (b × c).

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What is the Addition Property of Zero?

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The Addition Property of Zero states that adding zero to any number does not change the value of that number. For example, a + 0 = a.

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What is the Multiplication Property of One?

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The Multiplication Property of One states that multiplying any number by one does not change the value of that number. For example, a × 1 = a.

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What is the Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac, meaning that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products.

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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.

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What is the Inverse Property of Multiplication?

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The Inverse Property of Multiplication states that for every non-zero number a, there exists a number 1/a such that a × (1/a) = 1.

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What is the Identity Property of Addition?

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The Identity Property of Addition states that the sum of any number and zero is that number. For example, a + 0 = a.