Math Properties

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What is the Commutative Property?

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

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What is the Associative Property?

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

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What is the Identity Property?

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The Identity Property states that when you add zero to a number, the result is the number itself (a + 0 = a), and when you multiply a number by one, the result is the number itself (a × 1 = a).

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What is the Inverse Property?

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The Inverse Property states that for every number, there is an additive inverse (a + (-a) = 0) and a multiplicative inverse (a × (1/a) = 1) that will yield the identity element.

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What is the Property of Zero?

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The Property of Zero states that when you multiply any number by zero, the result is zero (a × 0 = 0).

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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 Reflexive Property?

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The Reflexive Property states that any quantity is equal to itself, expressed as a = a.

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What is the Symmetric Property?

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The Symmetric Property states that if one quantity equals another, then the second quantity equals the first, expressed as if a = b, then b = a.

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What is the Transitive Property?

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The Transitive Property states that if one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third, expressed as if a = b and b = c, then a = c.

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Example of Commutative Property: 3 + 5 = ?

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3 + 5 = 5 + 3 = 8.