Math 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) and (a × b) × c = a × (b × c).

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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 and a × b = b × a.

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What is the Distributive Property?

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The Distributive Property states that a number multiplied by a sum is equal to the sum of the individual products. For example, a(b + c) = ab + ac.

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What is the Identity Property of Addition?

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The Identity Property of Addition states that the sum of any number and zero is that number. For example, a + 0 = a.

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What is the Identity Property of Multiplication?

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The Identity Property of Multiplication states that the product of any number and one is that number. For example, a × 1 = a.

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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 exists an additive inverse such that their sum is zero. For example, a + (-a) = 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 exists a multiplicative inverse such that their product is one. For example, a × (1/a) = 1.

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Provide an example of the Associative Property in addition.

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Example: (2 + 3) + 4 = 2 + (3 + 4) = 9.

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Provide an example of the Commutative Property in multiplication.

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Example: 4 × 5 = 5 × 4 = 20.

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What is the difference between the Associative and Commutative Properties?

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The Associative Property involves grouping of numbers, while the Commutative Property involves the order of numbers.