Properties of Real Numbers

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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 Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a number across a sum.

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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, a + 0 = a.

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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, a × 1 = a.

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What is the Additive Inverse?

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The Additive Inverse of a number is what you add to that number to get 0. For example, the additive inverse of 2 is -2.

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What is the Multiplicative Inverse?

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The Multiplicative Inverse of a number is what you multiply by that number to get 1. For example, the multiplicative inverse of 2 is 1/2.

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What does it mean to say that a number is rational?

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A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.