Properties of Algebra

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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 (ab)c = a(bc).

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What is the Distributive Property?

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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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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 sum or product. For example, a + b = b + a and ab = ba.

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What is the Multiplicative Identity Property?

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The Multiplicative Identity Property states that any number multiplied by one equals itself. For example, 7 × 1 = 7.

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What is the Additive Inverse Property?

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The Additive Inverse Property states that for every number a, there exists a number -a such that a + (-a) = 0.

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What is the Multiplicative Inverse Property?

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The Multiplicative Inverse Property states that for every number a (except zero), there exists a number 1/a such that a × (1/a) = 1.

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What is the Zero Property of Multiplication?

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The Zero Property of Multiplication states that any number multiplied by zero equals zero. For example, 5 × 0 = 0.

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What is the Transitive Property?

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The Transitive Property states that if a = b and b = c, then a = c. It is often used in equations.

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What is an example of the Associative Property in addition?

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An example is (2 + 3) + 4 = 2 + (3 + 4). Both equal 9.

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What is an example of the Commutative Property in multiplication?

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An example is 4 × 5 = 5 × 4. Both equal 20.