Properties of Algebra

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What is the Commutative Property?

Back

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

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What is the Associative Property?

Back

The Associative Property states that the way in which numbers are grouped when adding or multiplying does not change the sum or product. For example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).

Front

What is the Distributive Property?

Back

The Distributive Property states that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products. For example, a(b + c) = ab + ac.

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What is the Multiplicative Inverse Property?

Back

The Multiplicative Inverse Property states that any number multiplied by its reciprocal equals 1. For example, 5 × (1/5) = 1.

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What is the Additive Identity Property?

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The Additive Identity Property states that any number plus zero equals the number itself. For example, a + 0 = a.

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What is the Multiplicative Identity Property?

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The Multiplicative Identity Property states that any number multiplied by one equals the number itself. For example, a × 1 = a.

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What is the Additive Inverse Property?

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The Additive Inverse Property states that a number plus its opposite equals zero. For example, a + (-a) = 0.

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What is the Transitive Property?

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The Transitive Property states that if a = b and b = c, then a = c.

Front

What is an example of the Commutative Property in addition?

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An example is: 3 + 4 = 4 + 3.

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What is an example of the Associative Property in multiplication?

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An example is: (2 × 3) × 4 = 2 × (3 × 4).