Algebra 1 Properties

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What is the Associative Property?

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The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. For example, (a + b) + c = a + (b + c).

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What is the Commutative Property?

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The Commutative Property states that the order in which two numbers are added or multiplied does not change their sum or product. For example, a + b = b + a.

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What is the Distributive Property?

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The Distributive Property states that a number multiplied by a sum is equal to the sum of the individual products. For example, a(b + c) = ab + ac.

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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 value of that number. For example, 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 value of that number. For example, a × 1 = a.

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What is the Addition Property of Equality?

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The Addition Property of Equality states that if you add the same number to both sides of an equation, the two sides remain equal. For example, if a = b, then a + c = b + c.

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What is the Multiplication Property of Equality?

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The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the two sides remain equal. For example, if a = b, then ac = bc.

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What is an example of the Associative Property of Addition?

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An example is 8 + (5 + 2) = (8 + 5) + 2.

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What is an example of the Commutative Property of Multiplication?

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An example is 6 × 7 = 7 × 6.

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What does it mean for two expressions to be equivalent?

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Two expressions are equivalent if they have the same value for all values of their variables.