2.1 Algebraic Proofs

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

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What does the Multiplication Property of Equality state?

Back

The Multiplication Property of Equality states that if two quantities are equal, multiplying both sides by the same number will keep them equal.

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What is the Symmetric Property of Equality?

Back

The Symmetric Property of Equality states that if a = b, then b = a.

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What is typically the first statement in the reason column of a proof?

Back

The first statement in the reason column of a proof is usually 'Given'.

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How do you simplify the expression 6(x + 3) using the Distributive Property?

Back

You apply the Distributive Property: 6(x + 3) = 6x + 18.

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What is the Associative Property of Addition?

Back

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

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What is the Commutative Property of Addition?

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The Commutative Property of Addition states that a + b = b + a, meaning the order of addition does not affect the sum.

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What is the definition of an algebraic proof?

Back

An algebraic proof is a sequence of algebraic statements that demonstrate the truth of a mathematical statement.

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What is the purpose of a proof in mathematics?

Back

The purpose of a proof is to provide a logical argument that establishes the truth of a mathematical statement.

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What is the definition of a variable in algebra?

Back

A variable is a symbol, often a letter, that represents one or more numbers.