Properties of Real Numbers

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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 number by a sum by distributing the multiplication to each addend.

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What is the Identity Property of Multiplication?

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The Identity Property of Multiplication states that any number multiplied by 1 remains unchanged. For example, 1 × x = x.

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What is the Additive Inverse of a number?

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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 -7 is 7.

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What is the Multiplicative Inverse of a number?

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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 5 is 1/5.

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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 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 an example of the Distributive Property?

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An example of the Distributive Property is 3(4 + 5) = 3×4 + 3×5, which simplifies to 12 + 15 = 27.

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If a number is multiplied by its Multiplicative Inverse, what is the result?

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The result is 1. For example, 5 × (1/5) = 1.