Algebraic properties

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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 an addition problem does not change the sum. For example, (a + b) + c = a + (b + c).

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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 of Addition?

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The Commutative Property of Addition states that the order in which two numbers are added does not change the sum. For example, a + b = b + a.

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What is the Commutative Property of Multiplication?

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The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not change the product. For example, a × b = b × a.

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How does the Associative Property differ from the Commutative Property?

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The Associative Property deals with grouping of numbers, while the Commutative Property deals with the order of numbers. Associative: (a + b) + c = a + (b + c); Commutative: a + b = b + a.

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Can you give an example of the Distributive Property in action?

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Yes! For example, if you have 3(4 + 5), using the Distributive Property, you can calculate it as 3 × 4 + 3 × 5 = 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 the value of that number. For example, a + 0 = a.

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What is the identity element for multiplication?

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The identity element for multiplication is 1, because multiplying any number by 1 does not change the value of 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 a, there exists a number -a such that 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 number a (except 0), there exists a number 1/a such that a × (1/a) = 1.