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Algebra Properties Definition Numeric Example Algebraic Example

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Commutative Property of Addition We can change the order when adding without affecting the sum.

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Commutative Property of Multiplication We can change the order when multiplying without affecting the product.

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Associative Property of Addition Numbers can be grouped in any order for addition.

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Associative Property of Multiplication Numbers can be grouped in any order for multiplication.

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Identity Property of Addition Adding 0 to any number gives that number.

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Identity Property of Multiplication Multiplying a number by 1 gives that number.

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Additive Inverse Property Two rational numbers whose sum is 0.

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Multiplicative Inverse Property Two rational numbers whose product is 1.

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Distributive Property Multiplying a number over addition or subtraction.

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The Inverse of a Sum Property The additive inverse of a sum is the sum of the additive inverses.

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Multiplicative Property of Zero The product of 0 and any rational number is 0.

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Multiplicative Property of -1 Negative one times a is the additive inverse of a.

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The Addition Property of Equality Adding the same number to both sides of an equation results in an equivalent equation.

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The Subtraction Property of Equality Subtracting the same number to both sides of an equation results in an equivalent equation.

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The Multiplication Property of Equality Multiplying the same number to both sides of an equation results in an equivalent equation.

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The Division Property of Equality Dividing the same number to both sides of an equation results in an equivalent equation.

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Symmetric Property Two equal quantities can be written in any order.

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Transitive Property

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