Mathematical Properties

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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 in addition or multiplication does not change their sum or product. For example, (a + b) + c = a + (b + c) or (a · b) · c = a · (b · c).

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What is the Identity Property of Addition?

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The Identity Property of Addition states that when you add zero to any number, the result is that number. For example, b + 0 = b.

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What is the Identity Property of Multiplication?

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The Identity Property of Multiplication states that when you multiply any number by one, the result is that number. For example, b · 1 = b.

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What is the Inverse Property of Addition?

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The Inverse Property of Addition states that for every number, there is another number that, when added together, results in zero. For example, b + (-b) = 0.

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What is the Inverse Property of Multiplication?

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The Inverse Property of Multiplication states that for every non-zero number, there is another number (its reciprocal) that, when multiplied together, results in one. For example, b · (1/b) = 1.

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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 their sum or product. For example, a + b = b + a or a · b = b · a.

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What is the Distributive Property?

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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 Zero Property of Multiplication?

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The Zero Property of Multiplication states that when you multiply any number by zero, the result is zero. For example, b · 0 = 0.

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Example of Associative Property: (5 + 10) + 15 = ?

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5 + (10 + 15) = 30.

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Example of Identity Property of Addition: 7 + ? = 7

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7 + 0 = 7.