Properties of Addition and Multiplication

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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 in an addition problem does not change the sum. For example, 12 + (3 + 4) = (12 + 3) + 4.

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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 numbers in an addition problem does not change the sum. For example, 4 + -3 = -3 + 4.

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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 products. For example, 2(5 + 4) = (2 x 5) + (2 x 4).

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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 in a multiplication problem does not change the product. For example, (2 x 3) x 4 = 2 x (3 x 4).

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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 numbers in a multiplication problem does not change the product. For example, 3 x 4 = 4 x 3.

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What is the Additive Identity?

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The Additive Identity is the number 0, because adding 0 to any number does not change the value of that number. For example, 5 + 0 = 5.

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What is the Additive Inverse?

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The Additive Inverse of a number is the value that, when added to the original number, results in zero. For example, the additive inverse of 3 is -3, because 3 + (-3) = 0.

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What is the Multiplicative Identity?

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The Multiplicative Identity is the number 1, because multiplying any number by 1 does not change the value of that number. For example, 7 x 1 = 7.

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What is the Multiplicative Inverse?

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The Multiplicative Inverse of a number is the value that, when multiplied by the original number, results in one. For example, the multiplicative inverse of 4 is 1/4, because 4 x (1/4) = 1.

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What does the Commutative Property of Multiplication state?

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The Commutative Property of Multiplication states that the order of the numbers in a multiplication equation does not change the product. For example, 2 x 3 = 3 x 2.