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 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. 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 their product. For example, (a • b) • c = a • (b • c).

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What is the Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

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 identity element for addition?

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The identity element for addition is 0, because adding 0 to any number does not change the number. For example, a + 0 = a.

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What is the identity element for multiplication?

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The identity element for multiplication is 1, because multiplying any number by 1 does not change the number. For example, 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.

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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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How does the Distributive Property apply to subtraction?

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