Algebraic Properties

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What is the Commutative Property of Addition?

Back

The Commutative Property of Addition states that changing the order of the addends does not change the sum. For example, a + b = b + a.

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What is the Commutative Property of Multiplication?

Back

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. For example, a × b = b × a.

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What is the Associative Property of Addition?

Back

The Associative Property of Addition states that the way in which numbers are grouped does not change the sum. For example, (a + b) + c = a + (b + c).

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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 does not change the product. For example, (a × b) × c = a × (b × c).

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What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

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How does the Commutative Property apply to subtraction?

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The Commutative Property does not apply to subtraction. For example, a - b is not equal to b - a.

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How does the Commutative Property apply to division?

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The Commutative Property does not apply to division. For example, a ÷ b is not equal to b ÷ a.

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What is an example of the Associative Property of Multiplication?

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An example is (2 × 3) × 4 = 2 × (3 × 4), both equal 24.

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What is an example of the Distributive Property?

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An example is 3(4 + 5) = 3 × 4 + 3 × 5, which simplifies to 12 + 15 = 27.

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What is the identity element for addition?

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The identity element for addition is 0, because adding 0 to any number does not change its value (a + 0 = a).