Associative and Commutative & Distributive Property

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What is the Associative Property of Addition?

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The Associative Property of Addition states that the way in which numbers are grouped in addition does not change their sum. For example, 5 + (8 + 14) = (5 + 8) + 14.

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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 affect the result. For example, 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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How do you apply the Distributive Property to 2(c - 8)?

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Using the Distributive Property, 2(c - 8) becomes 2c - 16.

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How do you apply the Distributive Property to 4(p - 6)?

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Using the Distributive Property, 4(p - 6) becomes 4p - 24.

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What is the Associative Property of Multiplication?

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The Associative Property of Multiplication states that the way in which numbers are grouped in multiplication does not change their product. For example, 9 x (3 x 2) = (9 x 3) x 2.

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Can you give an example of the Commutative Property in multiplication?

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Yes, an example of the Commutative Property in multiplication is 4 x 5 = 5 x 4.

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What is the difference between the Associative and Commutative Properties?

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

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How can you identify the Associative Property in an equation?

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You can identify the Associative Property in an equation by looking for a grouping of numbers that can be rearranged without changing the result, such as (a + b) + c = a + (b + c).

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What is an example of the Distributive Property in action?

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An example of the Distributive Property is 3(2 + 4) = 3*2 + 3*4, which simplifies to 6 + 12 = 18.